Understanding diffusion

As the temperature rises, the average speed at which the molecules are moving increases. 

When a molecule's energy is sufficient break the interactions with its neighbors, it can escape from liquid phase - it is transformed into a gas.

In a gas, there are essentially no interaction between molecules.

We can see the effects of these collisions in a visible phenomena known Brownian motion.

In 1827, the English botanist Robert Brown watched the jerky motion of pollen grains in water -- they moved in a distinctive pattern known as a random walk.

What drives these movements? In 1905, Albert Einstein published a paper that explained these motions in terms of molecular collisions between the visible particles with the invisible solvent molecules.

Because of this constant and random bombardment, sometimes a particle is pushed one way, sometimes another.

Smaller particles move more than larger ones and motions increase with increasing temperature.

The vScope is a virtual microscope with a temperature-controlled stage.

Temperature is proportional to the average velocity at which the solvent molecules move.

where k is a constant, m is the mass of the particles, v is their velocity and the bar indicates the average of all particles. 

You may recognize the 1/2(mv²) term as the kinetic energy of a particle. 

By increasing the temperature, we increase the force of the molecular collisions between solvent molecules and suspended particles.

In fact, particles can be kept dispersed in a solution by this constant molecular bombardment.   A solution of discrete particles maintained in a suspended state is known as a colloid.

It can also "trap" the particles a small volume using the back to origin button.

The left hand screen slider lets you control the vScope's magnification.

The right-hand slider controls the temperature of the system.

The graph zoom in button expands the graph that displays the average distance the set of particles have moved from their original position.

click to use the vScope

The distance is displayed in micrometers (µm).  Use the start/stop button to control the tracker; the reset button starts a new experiment.

Open the vScope and see if you can get the buttons to work – what happens if you set the temperature to "0"? What is the maximum temperature that the vScope can reach?

You will use the vScope to study a two basic properties of diffusion. These are

• the relationship between time and the average distance the particles have traveled.
• the relationship between temperature and a specific distance the particles have traveled.

To determine the relationship between time and the average distance traveled by the particles, pick 10ºC, 15ºC or 20ºC – you will keep this temperature constant through your first set of experiments.

Use the particle trap to move the particles so that the distance traveled at time 0 to 0 µm. 

Perform at least three independent experiments using the vScope.  Each experiment should be at least 30 seconds long.   The simplest approach is to let the experiment run for about 33 second; stop it and then determine distance traveled at various time points (e.g. at 5, 10, 15, 20, 25 and 30 seconds).  Make a table of your data. 

For each set of measurements, calculate the mean distance travelled and standard deviation for each time point.

Plot these points, together with +/– the standard deviations on a graph of distance (y-axis) versus time (x-axis).   Hand in your graph with your report. 

If the relationship between time (t) and the average distance the particles have moved (D) where "linear" then it will follow the simple rule D = kt, where k a constant.

If the relationship between time and distance is linear, then when the time is doubled, the average distance traveled will be doubled.

Next, we will examine the relationship between temperature and the time it takes to travel a specific distance (in our case 200 µm), using the vScope. 

Choose at least four temperatures (we suggest 5, 10, 15, 20 and 30ºC).   Perform at least 3 trials for each temperature, some may have to be longer than 30 seconds.  For each trial, at each temperature, note the time it takes for the average distance travelled to reach 200 µm. Calculate the mean and standard deviation for each temperature, and plot these points on a graph of time (y-axis) versus temperature (x-axis).   Hand in your graph with your report. 

Experiment 2 and 3 write-up: answer these questions individually

• Q1:  Is the relationship between time and average distance traveled linear? 
• Q2: Is the relationship between time to travel a set distance and temperature linear?
• Q3: Would changing the distance travelled change your answer?
• Q4: In your experiments why did you not get exactly the same value for each measurement?  what was the source of the variation? 
• Q5: Does the presence of variation mean that the system cannot be described mathematically?
• Q6: How would decreasing the number of diffusing particule from 30 (as it is) to 5 alter your measurements?
• Q7: How would increasing the number of diffusing particule from 30 to 1000 alter your measurements?
• Q8: Einstein hypothesized that invisible particles were responsible for Brownian motion – was this scientific, postulating invisible particles?