Larger Is Not Always Better Examining Cell Size and Rates of Diffusion

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RBiology

Larger Is Not Always BetterExamining Cell Size and Rates of Diffusion

About this Lesson

This lesson visually emphasizes the effi ciency of small cell size due to a high surface area-to-volume ratio. Three differently sized cubes of agar that have been made with phenolphthalein are placed in an acid solution where the students can observe diffusion occurring as the cells change from pink to colorless.

This lesson is included in the LTF Biology Module 2.

Objectives

Students will:• Investigate the relationship between cell size and the total surface area-to-volume ratio• Investigate the rate of diffusion and its relationship to cell size

Level

Biology

Common Core State Standards for Science Content

LTF Science lessons will be aligned with the next generation of multi-state science standards that are currently in development. These standards are said to be developed around the anchor docu-ment, A Framework for K–12 Science Education, which was produced by the National Research Council. Where applicable, the LTF Science lessons are also aligned to the Common Core Stan-dards for Mathematical Content as well as the Common Core Literacy Standards for Science and Technical Subjects.

Code Standard Level of Thinking

Depth of Knowledge

(LITERACY)RST.9-10.3

Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to spe-cial cases or exceptions defi ned in the text.

Apply II

(MATH)A-CED.4

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Apply II

(MATH)A-CED.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Apply II

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RTeacher Overview – Larger Is Not Always Better

Code Standard Level of Thinking

Depth of Knowledge

(MATH)S-ID.6a

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fi tted to data to solve problems in the context of the data. Use given functions or choose a func-tion suggested by the context. Emphasize linear, quadratic, and exponential models.

Apply II

(LITERACY)RST.9-10.7

Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart)and translate information expressed visually or mathematically (e.g., in an equation) into words.

Apply II

Connections to AP*

AP Biology: This lesson addresses concepts contained in Big Idea 2 in the revised AP Biology curriculum under the following sections: 2.A.3.b and 2.B.2.a*Advanced Placement and AP are registered trademarks of the College Entrance Examination Board. The College Board was not involved in the production of this product.

Materials and Resources

Assessments

The following types of formative assessments are embedded in this lesson:• Visual assessment of measurement skills, calculations and graph made during the activity

Each lab group will need the following:

aprons beaker, 250 mL calculator goggles paper towels gloves, disposable 2 knives, plastic ruler, clear metric 2 spoons, plastic agar blocks with phenolphthalein hydrochloric acid, 0.1%

Additional teacher materials:

beaker, 1000 mLhot platecontainer, square edgedpipette, thin stemagarhydrochloric acid, 1 Mphenolphthalein, solidsodium hydroxide, 1 M

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Teaching Suggestions

The day before class, prepare enough phenolphthalein agar to make at least 14 blocks measuring 6 cm × 3 cm × 3 cm. (Standard dimensions given here are in length × width × height.) Do not prepare the agar more than one day in advance, as the carbon dioxide in the air will combine with the water in the cubes, forming carbonic acid and turning the pink cubes white.

Phenolphthalein Agar

Mix 30 g plain agar per liter of water and bring to a boil while stirring continuously. Continue boiling until the agar granules disappear and the solution is clear rather than cloudy. Let the mixture cool, but before it solidifi es stir in 1 g phenolphthalein powder per liter of agar solution made. Intensify the pale pink color by slowly adding 0.1 M sodium hydroxide until it is a deep pink.

If you do not have enough 0.1 M sodium hydroxide, more can be made by dissolving 4 g sodium hydroxide pellets in enough water to make 1.0 L of solution. Take care in mixing this solution as sodium hydroxide is a strong base.

Pour the agar mixture into a fl at-bottomed pan to a depth of 3 cm. When the agar has solidifi ed, cut it into blocks measuring 6 cm × 3 cm × 3 cm and refrigerate until ready to use. If your agar becomes too pale pink prior to use, soak it in a 0.1 M sodium hydroxide solution for several min-utes to re-establish the deep pink color.

Plastic containers that measure 10 in. × 7 in. × 2 in. (or 25 cm × 18 cm × 4 cm) can be purchased at some discount stores. This size allows for 18 blocks of agar to be cut measuring approximately 6 cm × 3 cm × 3 cm.

Alternative Preparation

A quantity of 1.5 L agar must be prepared to make enough agar blocks to fi ll your container, which can be prepared using a microwave. Mix 45 g plain agar with 1.5 L water and place into a 2 L beaker or similar microwaveable container. Heat the mixture on high power and stir the mixture every 3 minutes until it begins to boil, which usually takes about 15–20 minutes. Allow the mixture to cool for a few minutes before stirring in 1.5 g phenolphthalein powder.

Intensify the pale pink color by slowly adding 0.1 M sodium hydroxide until a deep pink color appears. Pour this mixture into the plastic container and allow it to solidify. When the agar has solidifi ed, cut it into 6 cm × 3 cm × 3 cm blocks.

Hydrochloric Acid Solution

Use proper safety precautions when making the 0.1 M hydrochloric acid solution. Prepare this solution in a fume hood while wearing a face shield over goggles and nitrile rubber gloves.

Slowly add 4 mL concentrated hydrochloric acid to 1 L distilled water. Repeat two more times to make 3 L of 0.1 M hydrochloric acid. If hydrochloric acid is unavailable or undesirable, a dilute vinegar solution may be used as the acid for this activity. Prepare the dilute vinegar solution by adding 250 mL vinegar to 750 mL water.

v. 2.0, 2.0

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Answer Key

Data and Observations

Table 1: Surface Area-to-Volume RatioCube Dimension

(cm)Surface Area

(cm2)Volume

(cm3) Simplest Ratio

0.01 0.0006 0.000001 600:1

1 6 1 6:1

2 24 8 3:1

3 54 27 2:1

Table 2: Diffusion of Hydrochloric AcidCube Dimension

(cm)Distance Diffused

(cm)Rate of Diffusion

(cm/min)Distance from

Center (cm)1 0.5 0.05 0.1

2 0.5 0.05 0.5

3 0.5 0.05 1.0

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Answer Key (continued)

Analysis

Graph 1: Surface Area-to-Volume Ratio vs. Length of Cube Side

Conclusion Questions

1. The cube with the greatest surface area is the cube measuring 3 cm on a side, and the cube with the greatest volume is also the cube measuring 3 cm on a side.

2. Question 1 points out that the cube with the greatest surface area and volume is the cube measuring 3 cm on a side. However, the cube with the greatest total surface area-to-volume ratio is the hypothetical cell measuring 0.01 cm on a side, with a ratio of 600:1.

In examining the data in Table 1, it is obvious that the surface area does not increase as fast as the volume. The volume of a cell grows at a faster rate than does its surface area.

3. The cube turned from pink to white because phenolphthalein is an indicator that turns from pink to colorless in acid solutions. As the acid diffused into the cube, the agar turned colorless.

4. The acid diffused approximately 0.5 cm into the 1 cm cube, and the acid almost reached the center. In the 2 cm cube it still had 0.5 cm to go before reaching the center, and in the 3 cm cube the acid still had 1 cm to go before reaching the center.

5. For all three cubes, the rate of diffusion was the same at 0.05 cm/min. This implies that the larger the cell, the longer it takes for substances to diffuse to the center of that cell.

Surface Area - to - Volume Ratio vs. Length of Cube Side

x

x

x

0 1 2 3 40

2

4

6

8

10

Cube side length (cm)

Ratio

(cm

2/cm3

)

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Biology

Larger Is Not Always BetterExamining Cell Size and Rates of Diffusion

During the course of natural selection as cells evolved from prokaryotic to eukaryotic, cells increased in size. The average size of a prokaryotic cell is approximately 1 μm in diameter whereas the average size of eukaryotic cell usually ranges from 10 μm to 100 μm in diameter.

There are some cells that are exceptionally large. For example, a nerve cell can be meters long and an ostrich egg is technically one single cell. In these exceptions, the cells have modifi cations that allow them to still function effectively. A nerve cell is long but the diameter is small so that all of the cytoplasm is close to the surface. Although an ostrich egg is very large in three dimen-sions, the vast majority of the ostrich egg is inert. By having only a small area on the surface of the egg that is metabolically active, the cell can still function despite its large size.

There are two generally accepted reasons why cells remain small. First, a given amount of meta-bolically active cytoplasm requires a minimum amount of cell membrane for the exchange of materials. As a cell increases in size, the volume does not increase as fast as the cell membrane. Mathematically, as the radius of a hypothetical sphere is doubled, the surface area is squared whereas the volume is cubed. This explanation for cell size limitation is known as the surface-volume hypothesis.

The second reason why cells remain small has to do with the rate of diffusion and the distance materials must travel to reach the center of the cell. The rate of diffusion of materials in a liquid will remain constant as cells increase in size. This means that it will take a longer period of time for needed materials to reach the center of the cell, and it will also take a longer period of time for materials to exit the cell.


Student Activity – Larger Is Not Always Better

Purpose

This activity investigates how the rate of diffusion and the total surface area-to-volume ratio are related to cell size. Three cubes of agar each cut to different dimensions are used to represent cells of varying sizes.

Materials

Each lab group will need the following:

apronsbeaker, 250 mLcalculatorgogglespaper towelsgloves, disposable

2 knives, plastic ruler, clear metric 2 spoons, plastic agar blocks with phenolphthalein hydrochloric acid, 0.1%

SAFETY ALERT!

» Wear safety goggles and gloves during this activity. » Sodium hydroxide and hydrochloric acid are irritants. Avoid

skin and eye contact, and do not ingest. Both can stain clothing and cause a reaction on bare skin. Immediately fl ush any contaminated area with water for 10 minutes and notify your teacher.



Procedure

1. Write two hypotheses for this experiment. In your fi rst hypothesis, predict what will happen to the surface area-to-volume ratio that occurs as the volume of a cube increases. In your second hypothesis, predict what will happen to the rate of diffusion when the volume of a cube increases. Record both hypotheses in the space provided on your student answer page.

2. Obtain a block of agar from your teacher. Be sure to wear gloves while handling this block. The agar has been prepared to include phenolphthalein, C20H14O4, which is an indicator that turns from pink to colorless in the presence of an acid. The pink color of the phenolphthalein is enhanced by a 0.1 M sodium hydroxide solution, NaOH, which is a strong base.

3. Using the plastic knife, cut the block into three pieces. The fi rst pieces should be a cube 3 cm on each side, the second a cube 2 cm on each side, and the last a cube 1 cm on each side.

4. To test the diffusion in the agar, a weak acid solution of 0.1 M hydrochloric acid, HCl, is used.Place all three cubes into a beaker and cover with the hydrochloric acid solution. Allow the cubes to remain in the solution for 10 minutes. Stir the solution occasionally with the plastic spoon, taking care not to damage your cubes.

5. During this 10 minute wait, calculate the surface area, volume, and total surface area-to-volume ratio of four cubes (the three you have prepared plus a hypothetical cube measuring 0.01 cm on each side). Record your answers in the space provided in Table 1 on your student answer page.

a. Remember that the formula for area is A = length × width, and that there are six faces to a cube.

b. Remember that the formula for volume is V = length × width × height.

c. The total surface area-to-volume ratio is calculated as

surface arearatio of surface area to volume = volume

d. This ratio also may be written as surface area:volume. The ratio should be expressed in its simplest form (for example, 3:1 rather than 24:8).



Procedure (continued)

6. Using the data for the 1 cm, 2 cm, and 3 cm cubes from Table 1, prepare a graph that illustrates the relationship between the length of one side of the cube (on the x-axis) versus the simplest ratio of surface area to volume (on the y-axis).

7. Use the plastic spoon to remove the agar cubes from the hydrochloric acid solution after 10 minutes. Blot them dry with the paper towels. Continue wearing your gloves and avoid handling the cubes until they are completely dry.

8. Use the plastic knife to slice each cube in half. Record your observations of each of the sliced surfaces.

9. Measure the depth of diffusion of the hydrochloric acid in each of the three cubes by measuring the depth of the white margin. Record this data in Table 2 on your student answer page.

10. Measure the distance remaining that the acid would have to continue diffusing to reach the center of the cube by measuring from the inner edge of the white margin to the center of the cube. Record this data in Table 2 on your student answer page.

11. Calculate the rate of diffusion for all three cubes and record your answers in Table 2. Be sure to include units. The formula for the rate of diffusion is

distance the acid traveledrate of diffusion = time in the acid

12. Dispose of the acid as directed by your teacher, and place the agar cubes in the trash.



Hypotheses

Data and Observations

Table 1: Surface Area-to-Volume RatioCube Dimension

(cm)Surface Area

(cm2)Volume

(cm3) Simplest Ratio

0.01

1

2

3

Table 2: Diffusion of Hydrochloric AcidCube Dimension

(cm)Distance Diffused

(cm)Rate of Diffusion

(cm/min)Distance from

Center (cm)1

2

3



Analysis

Graph 1: ________________________________________________________

(title)



Conclusion Questions

1. Which cube had the greatest surface area? Which cube had the greatest volume? Be sure to consider the hypothetical cube as well.

2. Which cube had the greatest total surface area-to-volume ratio? Write a statement describing the relationship between the total surface area-to-volume ratio and increasing cell size. Be sure to consider the hypothetical cube as well.

3. What physical evidence was observed that suggests the acid entered the cell?

4. What is the distance the acid traveled into the three agar cubes? How much farther did the acid have to travel to reach the center of the cube?

5. Determine the rate of diffusion for each of the agar cubes. Write a statement describing the relationship between the rate of diffusion and cell size.

Larger Is Not Always Better Examining Cell Size and Rates of Diffusion

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