does temperature affect the rate of diffusion experiment

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Simple Experiments for the Relationship Between Diffusion & Temperature

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Diffusion happens when substances move from an area of high concentration to an area of low concentration. When the temperature is higher, it affects the diffusion process because molecules have more energy and move faster. Read on to learn more about diffusion versus temperature with simple experiments.

Experiment 1: Diffusion in a Liquid

For the first simple experiment, you will need a clear container filled with water, food coloring, a darker color such as red is best, and you will need a watch. To start, add a single drop of coloring to the water’s edge in the container and start timing the moment the drop hits the water. Stop timing as soon as the color first reaches the opposite edge of the container. Repeat the procedure after cooling the water in the freezer or heating it up in the microwave or on the stove and compare the results.

Considerations

Make sure that the water stays calm throughout the experiment. For additional variability, you could also use clear liquids other than water, such as vinegar. Use caution when testing other liquids as they may be hazardous, especially when heated or cooled.

Expected Results

At higher temperatures, the water molecules in the container are moving more rapidly, which should cause the food coloring molecules to move more rapidly from one end of the container to the other. The opposite is true when the water is cold.

Experiment 2: Diffusion in a Gas

For the second experiment, you will need a strong-smelling substance and a room connected to an air conditioning system, along with a watch and a second person. Have the other person stand on the opposite side of the room from you and expose the scent to the air. For example, light a candle or spray some air freshener. At the same moment, start timing. When you first detect the scent, stop timing. Next, cool the room down or heat it up using the AC system and repeat the experiment, then compare the results.

Try to remove all sources of air flow from the room. Close all windows and turn off all fans, including the AC fan. Exact times will differ between individuals because each person’s nervous system reacts to smells at different concentrations. Therefore, exact results will not be the same when performed by a second person.

For the purposes of this experiment, the only real difference between a gas and a liquid is how far apart the molecules are, so the results for the second experiment should be similar to the first. At a higher room temperature, the smell should travel faster than at lower room temperatures.

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• What is diffusion?

About the Author

Robert Mullis is is a graduate of Liberty University with a bachelor's degree in biochemistry and a second degree in accounting. As a writer, he specialized in math, biology, chemistry, literature, and business.

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Science project, rate of diffusion.

Ever notice that when you pour a darker liquid into clear water the overall color changes into a shade between both? Diffusion is the passive process of particles spreading from areas of high concentration to areas of low concentration until they become evenly distributed throughout a space. We call diffusion passive because it requires no input of energy to occur: it’s caused by Brownian motion , the seemingly random movement of particles within liquid or gas.

So what explains Brownian motion? Even though you can’t see it happening, all atoms vibrate ( and the hotter they are, the faster and harder they do so). Because vibrating atoms in fluid (a liquid or gas) are in close contact with each other, they bump each other around as they collide. Over time, it’s easy to see how two gasses or liquids can get all mixed up when put in the same container. The rate of diffusion refers to how quickly or slowly this process happens.

In this experiment, we will first be looking at how diffusion occurs in hot and cold homogenous mixtures . A homogenous mixture is one that is made up of materials that are evenly distributed throughout the mixture. Using food coloring as our solute , or material to be dissolved, we will watch and observe the rate of diffusion occurring in both hot and cold water solvent. Then, we can explore how the shape of a container affects the movement of particles.

How is diffusion affected by hot and cold temperature, and why does the shape of the container make a difference?

• Food coloring (red & blue)
• 2 clear glass cups of the exact same size and shape
• 2 differently shaped clear containers (narrow and wide), preferably about the same size

Procedure: Temperature Difference

• Fill one glass cup with hot water. Fill the second glass cup with cold water.
• Drop 1-2 drops of red food coloring in the hot cup, and 1-2 drops of blue food coloring in the cold in the cold one.
• Watch and wait for color to disperse entirely.

Observations & Results

You should have noticed that the red food coloring in the hot water dispersed much more quickly than the blue food coloring in the cold water did. This is because particles vibrate faster and harder when they’re warmer—the hot water molecules struck the food coloring molecules harder and more frequently, scattering them until the cup ended up containing a homogeneous solution.

Procedure: Differently Shaped Containers

• Fill both containers with the same temperature of water.
• Drop one drop of food coloring in each of container and compare their rate of diffusion.

The narrowest container will likely have demonstrated the slower rate of diffusion because fewer molecules are in contact with each other, meaning fewer collisions of the solvent with the solute.

Conclusions

Temperature and the shape of the containers affected the rate of diffusion in both experiments. Particles move faster in warmer water, so the red coloring spread more quickly through the cup. The narrow shape of the containers used in the second experiment slowed down diffusion because of the container’s effect on Brownian motion (the mechanism behind diffusion).

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What is Diffusion

Diffusion is defined as the movement of atoms, ions, and molecules from a region of high concentration to a region of low concentration, or ‘down their concentration gradient ’. The word ‘diffusion’ is derived from the Latin word, ‘diffundere’, meaning ‘to spread out’.

What Causes Diffusion and What Happens During the Process

The random movement of ‘molecules existing in any state of solid, liquid, or gas’ increases the kinetic energy of the system. Since diffusion equalizes the concentration of the substance on both sides of the region, it helps the solution to attain the state of equilibrium or minimum randomness through this process.

If Fick’s laws can describe a diffusion process, it is called a normal or Fickian diffusion, otherwise, it is named as anomalous or non-Fickian diffusion.

Examples of Diffusion

• The spreading of the odor of a scent or a perfume from the region applied to a nearby region
• Dissolving ice, sugar, salt crystals in water to form a uniform solution

Basic Characteristics of Diffusion

• It is a fast and spontaneous process
• When occurring across a biological membrane, it is a type of passive transport
• Requires no energy expenditure
• It depends upon the interaction between the diffusing material and the medium in which the diffusion occurs
• It continues until the concentration of the molecules becomes even throughout the region, or equilibrium is reached 
• Takes place only when the diffusing material on both sides of the concentration gradient is fully or partially miscible
• Diffusion of any one material is independent of the diffusion of any other substance

What is the Importance of Diffusion in Cellular Processes

a) Gas exchange – Oxygen passes through the capillary membrane and enters cells to make the concentration even on both the regions

b) Respiration – The balance between oxygen and carbon dioxide within the cell is maintained by removing the excess carbon dioxide from the blood 

c) Excretion –  Waste products are eliminated from the body 

d) Cellular Transport – Essential ions, small molecules, food, water, and minerals are taken up inside the cell

What Factors Affect Diffusion

The different factors that affect diffusion either individually or collectively are:

1) Temperature : Warmer the temperature, higher is the rate of diffusion.

2) Area of Interaction :  More the surface area of interacting molecules, higher is the rate of diffusion.

3) The Extent of the Concentration Gradient :  Greater the difference in concentration between the regions, higher is the rate of diffusion.

4) Diffusion Distance : Smaller the distance covered by the diffusing molecules, faster is the rate of diffusion.

5) Types of Diffusing Materials :  At a particular temperature, materials with lighter atoms diffuse faster than heavier ones.

6) Particle Size : At any given temperature, the diffusion of a smaller particle will be more rapid than the larger ones.

What are the Different Types of Diffusion

Since the distribution of molecules occurs in a variety of conditions, diffusion can be classified into two major types:

1) Simple Diffusion

It is the process in which substances move across a biologically active semi-permeable membrane along the concentration gradient without the involvement of any other molecules.

Example: Breathing in oxygen and releasing carbon dioxide out of the body during respiration

2) Facilitated Diffusion

It is the process in which the diffusing material requires the presence of another molecule or a facilitator to perform diffusion.

Example: Glucose, sodium ions, and potassium ions are transported in and out of the cell with the help of specific carrier proteins and protein channels

• Diffusion – Biologydictionary.net
• Diffusion – Freeexamacademy.com
• What is diffusion? – Bbc.co.uk
• Diffusion – Biologyonline.com

Article was last reviewed on Tuesday, November 21, 2023

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Agar Cell Diffusion

All biological cells require the transport of materials across the plasma membrane into and out of the cell. By infusing cubes of agar with a pH indicator, and then soaking the treated cubes in vinegar, you can model how diffusion occurs in cells. Then, by observing cubes of different sizes, you can discover why larger cells might need extra help to transport materials.

• Agar-agar powder
• Digital scale
• Graduated cylinder
• Whisk or fork
• Microwaveable bowl or container at least 500ml in volume
• Microwave (not shown)
• Hot pad or oven mitt
• Heat-safe surface
• pH indicator, such as bromothymol blue or phenolphthalein
• Small glass baking pan or cube-shaped silicone ice-cube molds
• Clear plastic metric ruler
• Sharp knife
• Clear container for immersing agar cubes
• Pencil and notepaper
• White paper or plate

• Measure out 1.6 g of agar-agar and 200 ml water. Mix them together with a whisk or fork in a large microwave-safe bowl.
• Heat the solution in the microwave on high for 30 seconds. Remove to a heat-safe surface using a hot pad or oven mitts, stir, and return to the microwave for 30 seconds. Repeat this process until the mixture boils. (Keep your eye on it as it can boil over very easily!) When done, remove the container, and set it on a trivet or other heat-safe surface.

• Carefully pour the agar solution into silicone ice-cube molds or a small glass baking pan. Make sure the agar block(s) will be at least 3 cm deep when they solidify. If you don’t have enough solution, make more using the ratio of 0.8 g agar-agar powder to 100 ml water.

Place a few millileters of the pH indicator into a small container ( either bromothymol blue or phenolphthalein ). Using a dropper, add a few drops of vinegar. What do you notice?

As an acid, vinegar has a large number of hydrogen ions. When the hydrogen ions come into contact with the pH indicator, the solution changes color.

Fill a clear container with vinegar to a 3-cm depth. Place one agar cube of each size in the vinegar, making sure the blocks are submerged. The untreated blocks (one of each size) will be used for comparison. What do you think will happen to each cube?

Determine the surface area and volume of each cube. To find the surface area, multiply the length of a side of the cube by the width of a side of the cube. This will give you the area of one face of the cube. Multiply this number by 6 (the number of faces on a cube) to determine the total surface area. To find the volume, multiply the length of the cube by its width by its height. Then determine the surface-area-to-volume ratios by dividing the surface area by the volume for each cube.

How will you know if hydrogen ions are moving into the cube? How long do you think it will take the hydrogen ions to diffuse fully into each of the cubes? Why? How would you be able to tell when the vinegar has fully penetrated the cube?

After 5 minutes, remove the cubes from the vinegar with a plastic spoon, and place them on white paper or on a white plate. Compare the treated cubes to the untreated cubes and observe any color changes.

How much vinegar has been absorbed by each treated cube? One way to measure this is to calculate the percentage of the volume of the cube that has been penetrated by the vinegar. (Hint: It may be easier to first consider the volume that has not been penetrated by the vinegar—the portion that has not yet changed color.) Do you want to adjust any of your predictions for the diffusion times? What are your new predictions?

Carefully return all of the treated cubes to the vinegar. Continue checking the vinegar-soaked cubes every 5 minutes by removing them to determine the percentage of the cube that has been penetrated by the vinegar. Continue this process until the vinegar has fully penetrated the cubes. Make a note of the time when this occurs.

What do you notice about the percentage of penetration for each of the cubes at the different time intervals? What relationships do you notice between surface area, volume, surface-area-to-volume ratio, and percentage penetration? What does this say about diffusion as an object gets larger?

Biological cells can only survive if materials can move in and out of them. In this Snack, you used cubes of agar to visualize how diffusion changes depending on the size of the object taking up the material.

Diffusion occurs when molecules in an area of higher concentration move to an area of lower concentration. As hydrogen ions from the vinegar move into the agar cube, the color of the cube changes allowing you to see how far they have diffused. While random molecular motion will cause individual molecules and ions to continue moving back and forth between the cube and the vinegar solution, the overall concentrations will remain in equilibrium, with equal concentrations inside and outside the agar cube.

How did you find the percentage of the cube that was penetrated by the hydrogen ions at the various time intervals? One way to do this is to start with the volume of the cube that has not been penetrated—in other words, the part in the center that has not yet changed color. To determine the volume of this inner cube, measure the length of this inner cube and multiply it by the width and height. Subtract this from the original volume of the cube and you obtain the volume of the cube that has been penetrated. By dividing this number by the original volume and multiplying by 100%, you can determine the percentage penetration for each cube.

You may have noticed that the bigger the vinegar-soaked cube gets, the time it takes for additional vinegar to diffuse into the cube also increases—but not in a linear fashion. In other words, if the cube dimensions are doubled, the time it takes for the hydrogen ions to completely diffuse in more than doubles. When you triple the size, the time to diffuse MUCH more than triples. Why would this happen?

As the size of an object increases, the volume also increases, but by more than you might think. For example, when the cube doubles from a length of 1 cm to a length of 2 cm, the surface area increase by a factor of four, going from 6 cm 2 (1 cm x 1 cm x 6 sides) to 24 cm 2 (2 cm x 2 cm x 6 sides). The volume, though, increases by a factor of eight, increasing from 1 cm 3 (1cm x 1 cm x 1 cm) to 8 cm 3 (2 cm x 2 cm x 2 cm).

Because the volume is increasing at a greater factor than the surface area, the surface-area-to-volume ratio decreases. As the cube size increases, the surface-area-to-volume ratio decreases (click to enlarge the table below). The vinegar can only enter the cube through its surface, so as that ratio decreases, the time it takes for diffusion to occur throughout the whole volume increases significantly.

$$\begin{array}{|c|c|c|c|} \hline \begin{array}{c} \text { Cube Side } \\ \text { Length } \end{array} & \text { Surface Area } & \text { Volume } & \begin{array}{c} \text { Surface-area- } \\ \text { to-volume ratio } \end{array} \\ \hline 1 \mathrm{~cm} & 6 \mathrm{~cm}^2 & 1 \mathrm{~cm}^3 & 6 \mathrm{~cm}^{-1} \\ \hline 2 \mathrm{~cm} & 24 \mathrm{~cm}^2 & 8 \mathrm{~cm}^3 & 3 \mathrm{~cm}^{-1} \\ \hline 3 \mathrm{~cm} & 54 \mathrm{~cm}^2 & 27 \mathrm{~cm}^3 & 2 \mathrm{~cm}^{-1} \\ \hline \end{array}$$

Anything that comes into a cell (such as oxygen and food) or goes out of it (such as waste) must travel across the cell membrane. As cells grow larger, the ratio of surface area to volume decreases dramatically, just like in your agar cubes. Larger cells must still transport materials across their membranes, but have a larger volume to supply and a proportionately smaller surface area through which to do so.

Bacterial cells are fairly small and have a comparatively larger surface-area-to-volume ratio. Eukaryotic cells, such as those in plants and animals, are much larger, but have additional structures to help them conduct the required amount of transport across membranes. A series of membrane-bound structures continuous with the plasma membrane, such as the endoplasmic reticulum, provide additional surface area inside the cell, allowing sufficient transport to occur. Even with these strategies, though, there are upper limits to cell size.

While this Snack investigates how the size of an agar cube impacts diffusion, the shape of each cube remains consistent. Biological cells, however, come in different shapes. To see how different shapes of “cells” affect diffusion rates, try various shapes of agar solids. Ice-cube molds can be found in spherical and rod shapes in addition to cubes. How does the shape impact the surface-area-to-volume ratios?

This Snack fits well into a series of investigations on osmosis and diffusion. The Naked Egg Snack will allow students to explore how concentration gradients power movement of materials into and out of cells. The Cellular Soap Opera Snack will help students consider the types of materials that move through cell membranes.

To help students better understand the concepts of surface area, volume, and surface-area-to-volume ratio, have them build models with plastic centimeter cubes. Physical models can help make these ideas more concrete. Students can also graph class data to better understand the mathematical relationships involved.

If there’s not enough time within a class period for the largest cubes to be fully penetrated by the hydrogen ions present in the vinegar, students can make note of the percentage of the cube that has been penetrated by the vinegar and use that data to extrapolate a result. Alternatively, students in the following period may be able to note the time for the previous class.

Agar-agar comes as a powder and can be purchased online or at markets featuring Asian foods. Unflavored gelatin can be used as a substitute, but is more difficult to handle. To make cubes from gelatin, add boiling water (25% less than the amount recommended on the package) to the gelatin powder, stir, and refrigerate overnight. You may need to experiment with the ratio of water to gelatin to achieve the perfect consistency.

Cabbage juice can be used as an inexpensive alternative to commercial pH indicator solutions. To make cabbage juice indicator, pour boiling water over chopped red cabbage and let it sit for 10 minutes. Strain out the cabbage, and use the remaining purple water to mix with the agar powder.

Related Snacks

Diffusion I: Random molecular movement and influences on diffusion rate

by Heather MacNeill Falconer, M.A./M.S., Gina Battaglia, Ph.D., Anthony Carpi, Ph.D.

Listen to this reading

Did you know that the process of diffusion is responsible for the way smells travel from the kitchen throughout the house? In diffusion, particles move randomly, beginning in an area of higher concentration and ending in an area of lower concentration. This principle is fundamental throughout science and is very important to how the human body and other living things function.

Diffusion is the process by which molecules move through a substance, seemingly down a concentration gradient, because of the random molecular motion and collision between particles.

Many factors influence the rate at which diffusion takes place, including the medium through with a substance is diffusing, the size of molecules diffusing, the temperature of the materials, and the distance molecules travel between collisions.

The diffusion coefficient, or diffusivity, provides a relative measure at specific conditions of the speed at which two substances will diffuse into one another.

If you’ve ever made cookies and left the kitchen door open, you’re probably aware that the aroma spreads throughout the house. It is strongest in the kitchen, where the cookies are baking, a little less in the dining or living room, and least in the upstairs corner bedroom. And if the door is closed in the corner bedroom, the cookie scent is even weaker.

This is a delicious example of diffusion , or the movement of matter from a region of high concentration (the cookie pan in the kitchen) to a region of low concentration (the corner bedroom). This principle of diffusion is fundamental throughout science, from gas exchange in the lungs to the spread of carbon dioxide in the atmosphere to the movement of water from one side of a cell’s plasma membrane to the other. However, the concept of diffusion is rarely as simple as molecules moving from one place to another. Temperature, the size of the molecules involved, the distance molecules need to travel, the barriers they may encounter along the way, and other factors all influence the rate at which diffusion takes place.

• Random walk: Molecular movement through a given space

The universe is in constant motion: from the orbiting of planets around the sun, to the movement of particles from one area to another. And while on a grand scale it may appear that there is a rationale to this movement – for example, the planets in our solar system have regular revolutions that can be predicted – in truth there is a great deal of motion that occurs randomly.

When we learn about diffusion , we often hear about the movement of particles from an area of high concentration to an area of low concentration, as if the particles themselves are somehow motivated to move in this direction. But this movement is in fact a by-product of what scientists refer to as the “random walk” of particles. Molecules do not move in straight paths from Point A to Point B. Instead, they interact with their environment , bumping into other molecules and barriers encountered along their way, as well as interacting with the medium through which they are moving.

The observation of the spontaneous, random movement of small particles was first recorded in the first century BCE . Lucretius, a Roman poet and philosopher, described the dust seen in sunbeams coming through a window (Figure 1):

You will see a multitude of tiny particles mingling in a multitude of ways... their dancing is an actual indication of underlying movements of matter that are hidden from our sight... It originates with the atoms which move of themselves [i.e., spontaneously]… So the movement mounts up from the atoms and gradually emerges to the level of our senses, so that those bodies are in motion that we see in sunbeams, moved by blows that remain invisible.

While Lucretius’s “dancing” particles were likely dust particles or pollen grains that are affected by air currents and other phenomenon, his description is a wonderfully accurate assessment of what goes on at the molecular level. Many scientists have explored this random molecular motion in a variety of contexts, most famously by the Scottish botanist Robert Brown in the 19 th century.

In 1828, while observing pollen granules suspended in water under a microscope, Brown discovered that the motion of the granules were “neither from currents in the fluid , nor from its gradual evaporation , but belonged to the particle itself.” After suspending various organic and inorganic substances in water and seeing this same inherent , random movement, he concluded that this random walk of particles – later termed Brownian motion in his honor – was a general property of matter that is suspended in a liquid medium. However, it would take nearly a century for scientists to mathematically quantify Brownian motion and demonstrate that this random movement of molecules dictates diffusion .

Comprehension Checkpoint

• What causes random molecular movement?

About the same time that Brown was making his observations , a group of scientists including the French engineer Sadi Carnot and German physicist Rudolph Clausius were establishing a whole new field of scientific study: the field of Thermodynamics (see our Thermodynamics I module for more information). Clausius’s work in particular led to the development of the kinetic theory of heat – the idea that atoms and molecules are in motion and the speed of that motion is related to a number of things, including the heat of the substance. The molecules of a solid are generally considered to be locked in place (though they vibrate); however, the molecules of a liquid or a gas are free to move around, and they do: bumping in to one another or the walls of their container like balls on a pool table.

As molecules in a liquid or gas move through space, they bump into one another and follow random paths – moving in a straight line until something blocks their way and then bouncing off of that thing. This random molecular movement is constantly occurring and can be measured, giving a molecule’s mean free path – or, the average distance a particle moves between impacts with other particles.

It is this spontaneous and random motion that leads to diffusion . For example, as the scent molecules from baking cookies move into the air, they interact with air molecules – crashing into them and changing direction. Over time, these random processes will cause the scent molecules to disperse throughout the room. Diffusion is presented as a process in which a substance moves down a concentration gradient – from an area of high concentration to an area of low concentration. However, it is important to recognize that there is no directional force at play – the scent molecules are not pushed to the edge of the room because the concentration is lower there. It is the random movement of these molecules within the roomful of moving air molecules that causes them to evenly spread out throughout the entire space – bouncing off walls, moving through doors, and eventually moving through the whole house. In this way, it appears to move along a concentration gradient – from the kitchen oven to the most distant rooms of the house.

• How concentration gradients work

It may sound like a paradox – the movement of molecules are random, yet at the same time appear to occur along a gradient – but in practice, it’s actually quite logical. A simple illustration of this process can be seen using a glass of water and food coloring. When a drop of food coloring enters the water, the food coloring molecules are highly concentrated at the location where the dye molecules meet the water molecules, giving the water in that area a very dark color (Figure 2). The bottom of the glass initially has few or no food coloring molecules and so remains clear. As the food coloring molecules begin to interact with the water molecules, molecular collisions cause them to move randomly around the glass. As collisions continue, the molecules spread out, or diffuse , over space.

Figure 2 : Diffusion of a purple dye in a liquid.

Eventually, the molecules spread throughout the entire glass, becoming evenly distributed and filling the space. At this point, the molecules have reached a state of equilibrium in which no net diffusion is taking place and the concentration gradient no longer exists. In this state, the molecules are still moving haphazardly and colliding with each other; we just can’t see that motion because the water and color molecules are evenly dispersed throughout the space. Once equilibrium has been reached, the probability that a molecule will move from the top to the bottom is equal to the probability a molecule will move from the bottom to the top.

• Temperature and other factors influencing the rate of diffusion

We know that diffusion involves the movement of particles from one place to another; thus, the speed at which those particles move affects diffusion. Since molecular motion can be measured by the heat of an object, it follows that the hotter a substance is the faster diffusion will take place in that substance. (Click the animation below to see how temperature affects diffusion.) If you were to repeat your food coloring and water experiment comparing a glass of cold to a glass of hot water, you would see that the color disperses much more quickly in the hot water. But what other factors influence the speed, or rate, at which diffusion takes place?

Interactive Animation: The Effect of Temperature on Diffusion

• Size matters

In 1829, the Scottish physical chemist Thomas Graham first quantified diffusion behavior before the idea of atoms and molecules was widely established. Basing his observations on real-life “substances,” Graham measured the diffusion rates of gases through plaster plugs, fine tubes, and small orifices that were meant to slow down the diffusion process so that he could quantify it. One of his experiments , detailed in Figure 3, used an apparatus with the open end of a tube sitting in a beaker of water and the other end sealed with a plaster stopper containing holes large enough for gases to enter and leave the tube. Graham filled the open end of the tube with various gases (as indicated by the red tube in Figure 3), and observed the rate at which the gases effused , or escaped through the plaster plug. If the gas effused from the tube faster than the air outside of the tube moved in, the water level in the tube would rise. On the other hand, if the outside air moved through the plaster faster than the gas in the tube escaped to the outside, the water level in the tube would go down. He used the rate of change in the water level to determine the relative rate at which the different gases diffused into air.

Figure 3 : Thomas Graham's experiment to measure the diffusion rates of gases.

Graham experimented with many combinations of different gases and published his findings in an 1829 publication of the Quarterly Journal of Science, Literature, and Art titled “A Short Account of Experimental Researches on the Diffusion of Gases Through Each Other, and Their Separation by Mechanical Means.” He stated that when gases come into contact with each other, “indefinitely minute volumes” of the gases spontaneously intermix with each other until they reach equilibrium (Graham, 1829). However, he discovered that different types of gases did not mix at the same rate – rather, the rates at which two gases diffuse is inversely proportional to the square root of their densities, a relationship now known as Graham’s law . Although Graham’s original relationship used density , or mass per unit volume , the modern form of the equation uses molar mass, or the mass of one mole of a substance.

What Graham showed was that the molecular weight of a molecule directly affects the speed at which that molecule can move. Graham’s work actually helped lay the foundations of kinetic molecular theory because it recognized that at a given temperature, a heavy molecule would move more slowly than a light molecule. In other words, more kinetic energy is needed to move a large molecule at the same speed as a small molecule. You can think of it this way: A small push will get a tennis ball rolling quickly; however, it takes a much harder push to move a bowling ball at the same speed. At a given temperature, small molecules move faster, and will diffuse more quickly than large ones. View the animation below to see how atomic mass affects diffusion .

Interactive Animation: The Effect of Atomic Mass on Diffusion

• Solution properties

Graham later studied the diffusion of salts into liquids and discovered that the diffusion rate in liquids is several thousand times slower than in gases. This seems relatively obvious to us today, as we know that the molecules of a gas move faster and are more spread out than molecules in a liquid. Therefore, the movement of one substance within a gas occurs more freely than in a liquid. Diffusion in liquids is proportional to temperature, as it is in gases, as well as to the viscosity of the specific liquid into which the material is diffusing. (View the animation below to compare diffusion in gases and liquids.) Diffusion, in fact, can even take place in solids . While this is a very slow process , Sir William Chandler Roberts-Austen, a British metallurgist, fused gold plates to the end of cylindrical rods made of lead. He analyzed the lead rods after a period of 31 days and actually found that gold atoms had “flowed” into the solid rods.

Interactive Animation: The Effect of State on Diffusion: Gases versus Liquids

• Concentration and the diffusion coefficient

While we have talked extensively about diffusion and concentration gradients, it was not until the mid-1800s when a German-born physicist and physiologist named Adolf Fick built upon Graham’s work and introduced the notion of a diffusion coefficient, or diffusivity, to characterize how fast molecules diffuse .

In his 1855 publication “On Diffusion” in Annalen der Physik , Fick described an experimental setup in which he connected cylindrical and conical tubes with solid salt crystals at the bottom to an “infinitely large” reservoir filled with freshwater (Figure 4). The solid salt crystals dissolved into the water in the tubes and diffused toward the water reservoir. A stream of freshwater swept the saltwater out of the reservoir. This stream of water kept the salt concentration at the very top of the tubes (the point where the salt solution met the water reservoir) close to zero. The dissolving salt at the bottom of the tube maintained a high salt concentration in the water at that end of the tube. Because the tubes had a different shape (conical versus cylindrical), the concentration gradient in the tubes differed, setting up a system in which diffusion could be compared in relation to a concentration gradient.

Figure 4 : Fick's experimental setup in which he connected cylindrical and conical tubes to a reservoir filled with freshwater. (Image from the 1903 publication, Collected Works, I . Stahel’sche Verlags-Anstalt, Würzburg: Germany.)

Fick then calculated the diffusion rate of the salt by measuring the amount of salt that passed through the top of the respective tubes (just before they met the freshwater in the reservoir) within a given time period. He discovered that the movement rate of the salt solution into the water reservoir depended on the concentration difference between the solution at the bottom of the tube and the concentration of the solution leaving the tube and entering the reservoir. In other words – the higher the concentration of salt at the top of the tube, the faster it diffused into the water reservoir. You can see how concentration affects diffusion in the animation below.

Interactive Animation: The Effect of Concentration on Diffusion

After studying the phenomenon, Fick hypothesized that the relationship between the concentration gradient and the diffusion rate was similar to what Joseph Fourier, a French mathematician and physicist, found in his study of heat conduction in 1822. Fourier had described the rate of heat transfer through a substance as proportional to the difference in temperature between two regions. Heat moves from warmer to cooler objects, and the greater the temperature difference between the two objects, the faster the heat moves. (This is why your mug of hot coffee cools off much faster outside on a cold morning than when you leave it in your heated apartment). Using Fourier’s law of thermal conduction as a model , Fick created a mathematical framework for the movement of salt into the water, proposing that the diffusion rate of a substance is proportional to the difference in concentration between the two regions. What this means for diffusion of a substance is that if the concentration of a given substance is high in relation to the substance it is diffusing into (e.g., food coloring into water), it will diffuse faster than if the concentration difference is low (e.g., food coloring into food coloring). The application of a successful principle from one branch of science to another is not uncommon, and Fick was a classic example of this process . Fick knew of Fourier’s work because he had modeled his experimental apparatus on that of Fourier. Thus it was natural for him to apply Fourier’s law to diffusion. While he had no way to know that the underlying mechanism of heat conduction and diffusion were both based on atomic collisions (in fact, some researchers at the time still doubted the existence of atoms), he had a feeling. That feeling, and the existence of atoms themselves, would be mathematically proven some 50 years later when Albert Einstein published his seminal work, Investigations on the Theory of the Brownian Movement (Einstein, 1905).

The diffusion coefficient, or diffusivity D , defined by Fick is a proportionality constant between the diffusion rate and the concentration gradient. The diffusion coefficient is defined for a specific solute-solvent pair, and the higher the value for the coefficient, the faster two substances will diffuse into one another. For example, at 25°C the diffusivity of gaseous air into gaseous water is 0.282 cm 2 /sec (Cussler, 1997). At the same temperature, the diffusivity of dissolved air into liquid water is 2.00 x 10 -5 cm 2 /sec, a much lower number than that for the two gases, representing the much slower diffusion rate in liquids compared to gases. And the diffusivity of dissolved helium into liquid water at 25°C is 6.28 x 10 -5 cm 2 /sec – higher than that of dissolved air, representing the smaller size of helium atoms compared to the nitrogen and oxygen molecules in air.

• Distance molecules travel

Yet another factor that influences the rate at which diffusion occurs is the distance a molecule travels before bumping into something (referred to as a molecule’s mean free path). Imagine taking a container filled with a gas and putting it under pressure so that the molecules in the gas are squeezed together. This would slow the rate of diffusion through the gas because the molecules travel a shorter distance before colliding with something else and changing direction. (The animation below shows the effect of pressure on diffusion.)

Interactive Animation: The Effect of Pressure on Diffusion

This is an important factor affecting the difference in diffusion rates in gases versus liquids versus solids ; because gas particles are the most spread out of the three, molecules travel the furthest between collisions and diffusion occurs most rapidly in this state (Figure 5).

Figure 5 : The three states of matter at the atomic level: gas, liquid, and solid.

To fully understand why we can smell the cookies baking in the kitchen from the bedroom we also have to consider another process at work here – advection . Advection involves the transfer of a material or heat due to the movement of a fluid . So, because people walk through the rooms of your house and because heat rises from your radiators, the air is constantly moving, and that movement carries and mixes the scent molecules in your house. In many situations (such as your house), the effects of advection exceed those of diffusion , but these processes work in tandem to bring you the cookie smell.

From the traveling smells of cookies to the dissolving of salt into water, diffusion is a process happening around (and within!) us every second of every day. It is a process that is critical to moving oxygen across the membranes of our lungs, moving nutrients through soil to be taken up by plants, dispersing pollutants that are released into the atmosphere , and a whole host of other events that are necessary for life to exist.

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Practical: Investigating the Rate of Diffusion ( OCR A Level Biology )

Revision note.

Biology & Environmental Systems and Societies

Practical: Investigating the Rate of Diffusion

• It is possible to investigate the effect of certain factors on the rate of diffusion
• Different apparatus can be used to do this, such as Visking tubing and cubes of agar

Practical 1: Investigating the rate of diffusion using visking tubing

• Visking tubing (sometimes referred to as dialysis tubing) is a non-living partially permeable membrane made from cellulose
• Pores in this membrane are small enough to prevent the passage of large molecules (such as starch and sucrose ) but allow smaller molecules (such as glucose ) to pass through by diffusion
• Filling a section of Visking tubing with a mixture of starch and glucose solutions
• Suspending the tubing in a boiling tube of water for a set period of time
• Testing the water outside of the visking tubing at regular intervals for the presence of starch and glucose to monitor whether the diffusion of either substance out of the tubing has occurred
• The results should indicate that glucose, but not starch, diffuses out of the tubing

An example of how to set up an experiment to investigate diffusion

• Comparisons of the glucose concentration between the time intervals can be made using a set of colour standards (produced by known glucose concentrations) or a colorimeter to give a more quantitative set of results
• A graph could be drawn showing how the rate of diffusion changes with the concentration gradient between the inside and outside of the tubing

Practical 2: Investigating the rate of diffusion using agar

• The effect of surface area to volume ratio on the rate of diffusion can be investigated by timing the diffusion of ions through different sized cubes of agar
• Purple agar can be created if it is made up with very dilute sodium hydroxide solution and Universal Indicator
• Alternatively, the agar can be made up with Universal Indicator only
• The acid should have a higher molarity than the sodium hydroxide so that its diffusion can be monitored by a change in colour of the indicator in the agar blocks
• The time taken for the acid to completely change the colour of the indicator in the agar blocks
• The distance travelled into the block by the acid (shown by the change in colour of the indicator) in a given time period (eg. 5 minutes)
• These times can be converted to rates (1 ÷ time taken)
• A graph could be drawn showing how the rate of diffusion (rate of colour change) changes with the surface area to volume ratio of the agar cubes

An example of how to set up an experiment to investigate the effect of changing surface area to volume ratio on the rate of diffusion

When an agar cube (or for example a biological cell or organism) increases in size, the volume increases faster than the surface area, because the volume is cubed whereas the surface area is squared. When an agar cube (or biological cell / organism) has more volume but proportionately less surface area, diffusion takes longer and is less effective. In more precise scientific terms, the greater the surface area to volume ratio , the faster the rate of diffusion !

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Author: Alistair

Alistair graduated from Oxford University with a degree in Biological Sciences. He has taught GCSE/IGCSE Biology, as well as Biology and Environmental Systems & Societies for the International Baccalaureate Diploma Programme. While teaching in Oxford, Alistair completed his MA Education as Head of Department for Environmental Systems & Societies. Alistair has continued to pursue his interests in ecology and environmental science, recently gaining an MSc in Wildlife Biology & Conservation with Edinburgh Napier University.

12.7 Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes

Learning objectives.

By the end of this section, you will be able to:

• Define diffusion, osmosis, dialysis, and active transport.
• Calculate diffusion rates.

There is something fishy about the ice cube from your freezer—how did it pick up those food odors? How does soaking a sprained ankle in Epsom salt reduce swelling? The answer to these questions are related to atomic and molecular transport phenomena—another mode of fluid motion. Atoms and molecules are in constant motion at any temperature. In fluids they move about randomly even in the absence of macroscopic flow. This motion is called a random walk and is illustrated in Figure 12.20 . Diffusion is the movement of substances due to random thermal molecular motion. Fluids, like fish fumes or odors entering ice cubes, can even diffuse through solids.

Diffusion is a slow process over macroscopic distances. The densities of common materials are great enough that molecules cannot travel very far before having a collision that can scatter them in any direction, including straight backward. It can be shown that the average distance x rms x rms that a molecule travels is proportional to the square root of time:

where x rms x rms stands for the root-mean-square distance and is the statistical average for the process. The quantity D D is the diffusion constant for the particular molecule in a specific medium. Table 12.2 lists representative values of D D for various substances, in units of m 2 /s m 2 /s .

Note that D D gets progressively smaller for more massive molecules. This decrease is because the average molecular speed at a given temperature is inversely proportional to molecular mass. Thus the more massive molecules diffuse more slowly. Another interesting point is that D D for oxygen in air is much greater than D D for oxygen in water. In water, an oxygen molecule makes many more collisions in its random walk and is slowed considerably. In water, an oxygen molecule moves only about 40 μ m 40 μ m in 1 s. (Each molecule actually collides about 10 10 10 10 times per second!). Finally, note that diffusion constants increase with temperature, because average molecular speed increases with temperature. This is because the average kinetic energy of molecules, 1 2 mv 2 1 2 mv 2 , is proportional to absolute temperature.

Example 12.11

Calculating diffusion: how long does glucose diffusion take.

Calculate the average time it takes a glucose molecule to move 1.0 cm in water.

We can use x rms = 2 D t x rms = 2 D t , the expression for the average distance moved in time t t , and solve it for t t . All other quantities are known.

Solving for t t and substituting known values yields

This is a remarkably long time for glucose to move a mere centimeter! For this reason, we stir sugar into water rather than waiting for it to diffuse.

Because diffusion is typically very slow, its most important effects occur over small distances. For example, the cornea of the eye gets most of its oxygen by diffusion through the thin tear layer covering it.

The Rate and Direction of Diffusion

If you very carefully place a drop of food coloring in a still glass of water, it will slowly diffuse into the colorless surroundings until its concentration is the same everywhere. This type of diffusion is called free diffusion, because there are no barriers inhibiting it. Let us examine its direction and rate. Molecular motion is random in direction, and so simple chance dictates that more molecules will move out of a region of high concentration than into it. The net rate of diffusion is higher initially than after the process is partially completed. (See Figure 12.21 .)

The net rate of diffusion is proportional to the concentration difference. Many more molecules will leave a region of high concentration than will enter it from a region of low concentration. In fact, if the concentrations were the same, there would be no net movement. The net rate of diffusion is also proportional to the diffusion constant D D , which is determined experimentally. The farther a molecule can diffuse in a given time, the more likely it is to leave the region of high concentration. Many of the factors that affect the rate are hidden in the diffusion constant D D . For example, temperature and cohesive and adhesive forces all affect values of D D .

Diffusion is the dominant mechanism by which the exchange of nutrients and waste products occur between the blood and tissue, and between air and blood in the lungs. In the evolutionary process, as organisms became larger, they needed quicker methods of transportation than net diffusion, because of the larger distances involved in the transport, leading to the development of circulatory systems. Less sophisticated, single-celled organisms still rely totally on diffusion for the removal of waste products and the uptake of nutrients.

Osmosis and Dialysis—Diffusion across Membranes

Some of the most interesting examples of diffusion occur through barriers that affect the rates of diffusion. For example, when you soak a swollen ankle in Epsom salt, water diffuses through your skin. Many substances regularly move through cell membranes; oxygen moves in, carbon dioxide moves out, nutrients go in, and wastes go out, for example. Because membranes are thin structures (typically 6 . 5 × 10 − 9 6 . 5 × 10 − 9 to 10 × 10 − 9 10 × 10 − 9 m across) diffusion rates through them can be high. Diffusion through membranes is an important method of transport.

Membranes are generally selectively permeable, or semipermeable . (See Figure 12.22 .) One type of semipermeable membrane has small pores that allow only small molecules to pass through. In other types of membranes, the molecules may actually dissolve in the membrane or react with molecules in the membrane while moving across. Membrane function, in fact, is the subject of much current research, involving not only physiology but also chemistry and physics.

Osmosis is the transport of water through a semipermeable membrane from a region of high concentration to a region of low concentration. Osmosis is driven by the imbalance in water concentration. For example, water is more concentrated in your body than in Epsom salt. When you soak a swollen ankle in Epsom salt, the water moves out of your body into the lower-concentration region in the salt. Similarly, dialysis is the transport of any other molecule through a semipermeable membrane due to its concentration difference. Both osmosis and dialysis are used by the kidneys to cleanse the blood.

Osmosis can create a substantial pressure. Consider what happens if osmosis continues for some time, as illustrated in Figure 12.23 . Water moves by osmosis from the left into the region on the right, where it is less concentrated, causing the solution on the right to rise. This movement will continue until the pressure ρ gh ρ gh created by the extra height of fluid on the right is large enough to stop further osmosis. This pressure is called a back pressure . The back pressure ρ gh ρ gh that stops osmosis is also called the relative osmotic pressure if neither solution is pure water, and it is called the osmotic pressure if one solution is pure water. Osmotic pressure can be large, depending on the size of the concentration difference. For example, if pure water and sea water are separated by a semipermeable membrane that passes no salt, osmotic pressure will be 25.9 atm. This value means that water will diffuse through the membrane until the salt water surface rises 268 m above the pure-water surface! One example of pressure created by osmosis is turgor in plants (many wilt when too dry). Turgor describes the condition of a plant in which the fluid in a cell exerts a pressure against the cell wall. This pressure gives the plant support. Dialysis can similarly cause substantial pressures.

Reverse osmosis and reverse dialysis (also called filtration) are processes that occur when back pressure is sufficient to reverse the normal direction of substances through membranes. Back pressure can be created naturally as on the right side of Figure 12.23 . (A piston can also create this pressure.) Reverse osmosis can be used to desalinate water by simply forcing it through a membrane that will not pass salt. Similarly, reverse dialysis can be used to filter out any substance that a given membrane will not pass.

One further example of the movement of substances through membranes deserves mention. We sometimes find that substances pass in the direction opposite to what we expect. Cypress tree roots, for example, extract pure water from salt water, although osmosis would move it in the opposite direction. This is not reverse osmosis, because there is no back pressure to cause it. What is happening is called active transport , a process in which a living membrane expends energy to move substances across it. Many living membranes move water and other substances by active transport. The kidneys, for example, not only use osmosis and dialysis—they also employ significant active transport to move substances into and out of blood. In fact, it is estimated that at least 25% of the body’s energy is expended on active transport of substances at the cellular level. The study of active transport carries us into the realms of microbiology, biophysics, and biochemistry and it is a fascinating application of the laws of nature to living structures.

• 3 At 20°C and 1 atm

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Diffusion in dilute gases is in some ways more complex, or at least more subtle, than either viscosity or thermal conductivity . First, a mixture is necessarily involved, inasmuch as a gas diffusing through itself makes no sense physically unless the molecules are in some way distinguishable from one another. Second, diffusion measurements are rather sensitive to the details of the experimental conditions. This sensitivity can be illustrated by the following considerations.

Light molecules have higher average speeds than do heavy molecules at the same temperature . This result follows from kinetic theory, as explained below, but it can also be seen by noting that the speed of sound is greater in a light gas than in a heavy gas. This is the basis of the well-known demonstration that breathing helium causes one to speak with a high-pitched voice. If a light and a heavy gas are interdiffusing, the light molecules should move into the heavy-gas region faster than the heavy molecules move into the light-gas region, thereby causing the pressure to rise in the heavy-gas region. If the diffusion takes place in a closed vessel , the pressure difference drives the heavy gas into the light-gas region at a faster rate than it would otherwise diffuse, and a steady state is quickly reached in which the number of heavy molecules traveling in one direction equals, on the average, the number of light molecules traveling in the opposite direction. This method, called equimolar countercurrent diffusion, is the usual manner in which gaseous diffusion measurements are now carried out.

The steady-state pressure difference that develops is almost unmeasurably small unless the diffusion occurs through a fine capillary or a fine-grained porous material. Nevertheless, experimenters have been able to devise clever schemes either to measure it or to prevent its development. The first to do the latter was Graham in 1831; he kept the pressure uniform by allowing the gas mixture to flow. The results of this work now appear in elementary textbooks as Graham’s law of diffusion . Most of these accounts are incorrect or incomplete or both, owing to the fact that the writers confuse the uniform-pressure experiment either with the equal countercurrent experiment or with the phenomenon of effusion (described below in the section Kinetic theory of gases ). Graham also performed equal countercurrent experiments in 1863, using a long closed-tube apparatus he devised. This sort of apparatus is now usually called a Loschmidt diffusion tube after Loschmidt , who used a modified version of the tube in 1870 to make a series of accurate diffusion measurements on a number of gas pairs.

A quantitative description of diffusion follows. A composition difference in a two-component gas mixture causes a relative flow of the components that tends to make the composition uniform. The flow of one component is proportional to its concentration difference, and in an equal countercurrent experiment this is balanced by an equal and opposite flow of the other component. The constant of proportionality is the same for both components and is called the diffusion coefficient, D 12 , for that gas pair. This relationship between the flow rate and the concentration difference is called Fick’s law of diffusion . The SI units for the diffusion coefficient are square metres per second (m 2 /s). Diffusion, even in gases, is an extremely slow process, as was pointed out above in estimating molecular sizes and collision rates. Gaseous diffusion coefficients at one atmosphere pressure and ordinary temperatures lie largely in the range of 10 -5 to 10 -4 m 2 /s, but diffusion coefficients for liquids and solutions lie in the range of only 10 -10 to 10 -9 m 2 /s. To a rough approximation, gases diffuse about 100,000 times faster than do liquids.

Diffusion coefficients are inversely proportional to total pressure or total molar density and are therefore reported by convention at a standard pressure of one atmosphere. Doubling the pressure of a diffusing mixture halves the diffusion coefficient, but the actual rate of diffusion remains unchanged. This seemingly paradoxical result occurs because doubling the pressure also doubles the concentration, according to the ideal gas equation of state , and hence doubles the concentration difference, which is the driving force for diffusion. The two effects exactly compensate .

Diffusion coefficients increase with increasing temperature at a rate that depends on whether the pressure or the total molar density is held constant as the temperature is changed. If the rate increases as T s at constant molar density (where s usually lies between 1 / 2 and 1), then it will increase as T 1 + s at constant pressure, according to the ideal gas equation of state.

Perhaps the most surprising property of gaseous diffusion coefficients is that they are virtually independent of the mixture’s composition, varying by at most a few percent over the whole composition range, even for very dissimilar gases. A trace of hydrogen , for example, diffuses through carbon dioxide at virtually the same rate that a trace of carbon dioxide diffuses through hydrogen. Liquid mixtures do not behave this way, and liquid diffusion coefficients may vary by as much as a factor of 10 from one end of the composition range to the other. The lack of composition dependence of gaseous diffusion coefficients is one of the odder properties to be explained by kinetic theory.

If a temperature difference is applied to a uniform mixture of two gases, the mixture will partially separate into its components, with the heavier, larger molecules usually (but not invariably) concentrating at the lower temperature. This behaviour was predicted theoretically before it was observed experimentally, but a rather elaborate explanation was required because simple theory suggests no such phenomenon. It was predicted in 1911–12 by David Enskog in Sweden and independently in 1917 by Sydney Chapman in England, but the validity of their theoretical results was questioned until Chapman (who was an applied mathematician) enlisted the aid of the chemist F.W. Dootson to verify it experimentally.

Thermal diffusion can be used to separate isotopes . The amount of separation for any reasonable temperature difference is quite small for isotopes, but the effect can be amplified by combining it with slow thermal convection in a columnar arrangement devised in 1938 by Klaus Clusius and Gerhard Dickel in Germany. While the apparatus is quite simple, the theory of its operation is not: a long cylinder with a diameter of several centimetres is mounted vertically with an electrically heated hot wire along its central axis. The thermal diffusion occurs horizontally between the hot wire and the cold wall of the cylinder, and the convection takes place vertically to bring new gas regions into contact.

There is also an effect that is the inverse of thermal diffusion, called the diffusion thermoeffect, in which an imposed concentration difference causes a temperature difference to develop. That is, a diffusing gas mixture develops small temperature differences, on the order of 1° C, which die out as the composition approaches uniformity. The transport coefficient describing the diffusion thermoeffect must be equal to the coefficient describing thermal diffusion, according to the reciprocal relations central to the thermodynamics of irreversible processes.

What is the effect of temperature on the rate of diffusion?

Temperature: we define temperature as the average kinetic energy of all the atoms or molecules of a substance. it is the measure of hotness or coldness expressed in terms of scales like fahrenheit and celsius. with the increase in temperature the kinetic energy of the particle increases and as a result the rate of diffusion, i.e., the movement of particles from one medium to another takes place at a faster rate. the rate of diffusion increases with the increase in temperature..

What is the effect of temperature on the rate constant of a reaction? How can this temperature effect on rate constant be represented quantitatively?

Explain the effects of temperature and pressure on the rate of diffusion.

Define diffusion explain the rate of order of diffusion in solids liquids and gases and state the effect of temperature on diffusion