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Unit 4 Math Practice
Name___________________________
Volume of a Sphere: V = 4/3 π r3
Volume of a Cube: V = l w h
Surface Area of a Sphere: A = 4 π r2
Surface Area of a Cube: A = 6 a2
1) Cells throughout the world have variable shapes and sizes. Because of this, and because structure is designed
around function, certain shapes are optimal for certain processes.
Analyze the following cells and determine the following…
Cell 1 (spherical) where the radius is 3 mm
Cell 2 (cube) where each side is 2 mm
Cell 3 (cube) where each side is 8 mm
A) What is the surface area to volume ratio of both cells?
How to calculate
Surface Area?
Cell 1:
Surface area
Volume
113.04 mm2
How to calculate
Volume?
V = 4/3 π r3
113.04 mm3
Surface area to
Volume Ratio
1:1
Cell 2:
24 mm2
V=lwh
8 mm3
3:1
Cell 3:
384 mm2
V=lwh
512 mm3
1:1.3 (or 3:4)
B) Compare the ratios and explain why one cell would be more efficient than another.
The more surface area a cell has relative to volume, the more efficiently a cell can transport particles in
and out of the cell to provide for all cellular functions taking place within the volume (cytoplasm) of the
cell.
C) Are you made of lots of large cells or lots of small cells? Why?
Lots of small cells—higher surface area to volume ratios in smaller cells  higher efficiency.
2) The phosphorylation of glucose occurs via dehydration synthesis as follows:
glucose + Pi  glucose-6-phosphate + H2O ΔG = +4.0 kcal/mole
The breakdown of ATP occurs via hydrolysis as follows:
ATP + H2O  ADP + Pi
ΔG = -7.3 kcal/mole
Calculate the total ΔG of the reaction. Does the hydrolysis of ATP provide sufficient energy to power the
synthesis of glucose-6-phosphate? Why or why not?
ΔG = -3.3 kcal/mole; yes, since the overall ΔG is less than zero, the coupled reaction will “work”—the
exergonic hydrolysis of ATP provides more than enough energy to power the endergonic phosphorylation of
glucose reaction.
3) Catalase is an enzyme found in peroxisomes that facilitates the breakdown of hydrogen peroxide (H2O2), a
toxic by-product of cellular respiration, into oxygen and water. An experiment was conducted to measure the
reaction rate of catalase under ideal enzymatic conditions. Using the data collected and recorded below,
properly create and label a line graph depicting the results of the experiment.
Time (seconds)
Total H2O2broken
down by catalase
0
0.0 mL
30
1.5 mL
60
3.0 mL
90
4.0 mL
120
4.5 mL
150
5.0 mL
 What is the approximate reaction rate for the catalase in this experiment between 0-90 seconds? Label your
reaction rate with the proper units! ___0.044 mL/second____
4)
1.5M sucrose
0.8M starch
0.4M NaCl
0.6M sucrose
1.2M starch
1.6M NaCl
The initial concentration of Side A and Side B are indicated above on either side of the U-tube. The membrane
shown is permeable to sucrose and NaCl but not starch.
Initially,
which side is hypertonic? __B__
what is the total molarity of the hypotonic side? _2.7 M_
Please use the correct letters to fill in the blanks below.
In order to reach equilibrium:
sucrose will move from side __A_ to side __B__.
starch will move from side __---__ to side _---__. (too big to pass through membrane)
NaCl will move from side __B_ to side __A__.
water will move from side __A__ to side __B__.
After this system reaches equilibrium:
what is the total molarity of each side? A = _3.05 M_ B = _3.05 M_
1. Three funnels containing three different starch solutions were placed for 24 hours into a beaker that
contained a starch solution of UNKNOWN concentration. The end of each funnel was covered by a
selectively permeable membrane.
a. What can you say about the concentration of the solution in the beaker based on the results shown in
the diagram?
Selectively
Permeable
Membrane
Tap
Water
2% Starch
Solution
4% Starch
Solution
UNKNOWN
Solution
START
AFTER 24 HOURS
2. A U-tube is divided into 2 halves, A and B, by a membrane which is freely permeable to water and salt, but
NOT to glucose. Side A is filled with a solution of 8% salt and 2% glucose, while side B is filled with 2%
salt and 8% glucose.
a. In terms of glucose concentration,
which side is a hypotonic solution?
b. What could you say about the water
concentration on side A relative to side B?
8% Salt
2% Salt
2% Glucose
8% Glucose
Side A
Side B
c. Which molecule(s) will move across the
membrane and in which net direction(s)?
d. Notice that the levels of liquid in both A
and B are equal. Do you think they will appear this
way when the system reaches equilibrium? Explain.
3. Flasks X, Y, and Z contain solutions with different concentrations of the solute NaCl. Flask X has 0.5%
NaCl, flask Y has 0.9% NaCl, and flask Z has 1.5% NaCl. Red blood cells (0.9% NaCl) will be placed into
each flask.
a. Predict what will happen to red blood cells in flask X (hint: draw out the situation)
b. Predict what will happen to the red blood cells in flask Y (hint: draw out the situation).
c. Predict what will happen to the red blood cells in flask Z (hint: draw out the situation).
4.
In the U-tube diagram below, the membrane is permeable to solute A; however, it is NOT permeable to
solute Z.
a. What is going to happen to solute A (both
direction and percentages)?
b. What is going to happen to solute Z (both
direction and percentages)?
Side 1
Side 2
20% A
10% Z
6% A
40% Z
c. What is going to happen to the water levels, specifically?
90% Water
10% Starch
5. Study the diagrams of the beakers to the right, noting
the concentrations of various substances in the beakers
and in the cellulose bags. Water molecules can pass
through the cellulose, but starch cannot pass through.
a. Draw arrows in the diagrams to show the
direction in which water will move.
b. Which of the beakers contains a solution that is
hypertonic relative to the bag’s contents?
c. What will eventually happen to the
concentrations in beaker 2?
1
90% Water
10% Starch
2
100% Water
80% Water
20% Starch
6. The direction in which water molecules move during osmosis depends on where the water molecules are
more highly concentrated. Study the diagrams below.
a. Decide whether the solution in each beaker is hypotonic, isotonic, or hypertonic in relation to the
solution inside the cellulose bag, then write your answer below each beaker.
b. Draw arrows to indicate the direction in which the water will move in each case.
90% Water
10% Starch
80% Water
20% Glucose
80% Water
20% Glucose
100% Water
90% Water
10% Starch
90% Water
10% Starch
7. Intravenous solutions must be prepared so that they are isotonic to red blood cells. A 0.9% salt solution is
isotonic to red blood cells.
a. Explain what will happen to a red blood cell placed in a solution of 99.3% water and 0.7%
salt.
b. What will happen to a red blood cell placed in a solution of 90% water and 10% salt?
8. What is the approximate overall rate of respiration of Organism A? (Use appropriate units.)
9. Calculate the approximate overall rate of ATP production based upon sugar concentration.