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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.