SA/V Ratio and Rate of Diffusion

Kirk Brown
Tracy Joint Union HS
Tracy, California
[email protected]

This activity is designed to enable students to determine the relationship between surface area to volume ratio and the rate of diffusion. This activity is very inexpensive and requires little. The Phenopthalien Agar can be mixed and poured into small paper cups and allowed to solidify overnight. This activity can be completed in a single class period of approximately one hour.

In this lab you will be looking at how surface area and volume effect the rate of diffusion of gases into or out of a cell. In this exercise the student will calculate the effect that surface area to volume ratio has on the rate of diffusion. The method is explained and then the student explores how changes in shape affect the SA/V ratio and the rate of diffusion.

Type of Entry
Lesson/Class Activity

Type of Activity
Hands on Activity
Authentic Assessment
Review and Reinforcement of Concepts
Group or Cooperative Activity

Target Audience
Advanced Biology/Advanced Placement/International Baccalaureate
Integrated Science

Required of Students
Students will be cutting various shapes out of the phenopthalien agar and calculating the SA/V ratio and volume of the shape. Following the calculations the students lower the shapes into a cup of ammonia water. After a minute the students remove the shape and cut it in half. A measurement is made to determine the amount of diffusion that has taken place. Students then calculate the volume of the amount not diffused and subtract that volume from the initial volume to determine the volume diffused. After that they divide the final volume by the initial x 100 to determine the % diffusion.

Preparation time needed
The day before the laboratory exercise the students should be given the prelab instructions. They should be calculating the volumes and surface area of shapes to review the formulas. They will also come up with a useful hypothesis to guide their experiment.

To make the phenopthalien agar take 15 grams of agar and mix with 500 ml water. Place in microwave and heat on medium power for 7 minutes or until transparent. Allow it to cool to the touch.

Add 1 gram of solid phenopthalien or 10 ml of a premixed phenopthalien solution. Pour 3 cm deep into small cups. Old sample cups, paper cups or any other small container will work.

Take large paper clips and bend a small triangle at the end and bend it 90 degrees to make a dipper with a platform. Place some scotch tape on the platform so the small shapes won't fall through. Get enough cups to place about 1/2 full of ammonia water.

To make ammonia water, get sudsing ammonia from a grocery store and add about 1 cm of that and fill with water to almost the top of a small cup ( This can be mixed in a gallon milk container and then students pour from that).

Class Time Needed
This activity takes from 50 minutes to multiple class periods depending upon the level of student involvement.

What question does this activity answer for students?
This activity enables students to explore the relationship between Surface Area to volume ratio and the rate of diffusion. This activity is appropriate to introduce the student to the area of cell transport. This activity can be paired with another on potato core osmosis. The students should have control over what shapes and size of objects to enable them to determine if size has a relationship to SA/V.

Diagram of setup

  1. Review the formulas for calculating the surface area and volume of a cubes, rectangles, triangles, and cylinders.

    2r x length + r2 x 2 = Surface area of cylinder
    r2 x length = volume of a cylinder
    L x W x H = volume of a cube
    L x W x number of sides = surface area of cube
    1/2 b x h x length of prism = volume of a triangular prism
    1/2 b x h x 2 + area of sides = surface area of a prism.

  2. Draw two different sizes of each shape mentioned above and calculate the Surface Area and Volume of each. Show all work.

  3. Read the Procedures and come up with at least one hypothesis that will guide your experiment.

  1. Agar impregnated with Phenopthalien
  2. Razor blade
  3. Metric ruler
  4. Ammonia solution
  5. Beaker

  1. Obtain a block of Agar and Cut a cube about 1 cm on all sides. Calculate the surface area and volume of the block. Use this to calculate the SA/V ratio.

  2. Place your 1 cm cube into the beaker and wait 1 minute and remove the cube and cut the cube in half and measure the amount of diffusion into the block by the change in color.

  3. Calculate the new volume of the area not turned pink and then subtract from the initial volume to determine the amount of diffusion.

  4. Calculate the % diffusion by using the formula final volume/initial X 100.

  5. Develop a series of experiments to determine the effect of SA/V on the rate of diffusion.

  • How does surface area to volume ratio effect how fast diffusion can take place?

  • How does your body use surface area to volume ratio to help exchange gases?

  • How do single celled animals maintain efficient gas diffusion?

  • Why can't certain cells like bacteria get the size of a small fish?

  • What was the most effective shape that you tested? Draw the shape below.

  • What limitations would this shape have in a living system?

Method of Assessment/Evaluation
Each student should write a laboratory report that explains the relationship between surface area to volume ratio and the rate of diffusion. Each lab group can present their findings and show how they determined their rates. They can graph the information to correlate SA/V with rate of diffusion. In an advanced class students should be able to complete these tasks using a computer and complete the statistical analysis using a program like excel. This activity is very successful and easy to do.

Morholt, Evelyn and Paul Brandwein Sourcebook for the Biological Sciences California State Department of Education 1967

Some of Kirk's other favorite classroom activities
Agarose Gel Quantitation
Plant Transpiration

Find out more about Kirk Brown

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