Biophysical Chemistry I

due on 1995/10/20

HOMEWORK#1

1. Photosynthesis by land plants leads to the fixation each year of about 1 kg of carbon on the average for each square meter of an actively growing forest. The atmosphere is approximately 20 % O2 and 80 % N2 but contains 0.046 % CO2 by weight.

(a) What volumn of air (250C, 1atm) is needed to provide this 1 kg of carbon?
(b) How much carbon is present in the entire atmosphere lying above each square meter of the earth's surface? (Hint : Remember that atmospheric pressure is the consequence of the force exerted by all the air above the surface; 1 atm is equivalent to 1.033 x 104 kg m-2.)
(c) At the current rate of utilization, how long would it take to use all the CO2 in the entire atmosphere directly above the forest? (This assumes that atmosphere circulation and replacement from the oceans, rocks, combustion of fuels, respiration of animals, and decay of biological meterials are cut off.)

2. Calculate the work (in joules) done on the systemfor each of the following examples. Specify the sign of the work. The system is given in italics.

(a) A box of groceries weighing 10 kg is carried up 3 flights of stairs (10 m altogether).
(b) A 6.0-V storage battery is charged by a power supply for 2 hr with a current of 5.5 A.
(c) A muscle of 1 square cm cross section and 10 cm length exerts a force of 5 N when it is stretched by 5 % of its length by a mass M. The mass is increased sufficiently to stretch the muscle by 10 persent of its original length. (Assume that muscle behaves like a spring that follows Hooke's law.)

3. Recently, biological organisms have been discovered living at great depths at the bottom of the ocean. The properties of common substances are greatly altered there because of enormous hydrostatic pressures caused by the weight of the ocean lying above. The organisms need to equilibrate their internal pressures with this external hydrostatic pressure to prevent being crushed.

(a) Calculate the hydrostatic pressure in the ocean at depth 2500 m.
(b) Except near sources of heat, such as vents of hot gases coming from the earth's mantle, the temperature is close to 40C is 49.5 x 10-6 atm-1.
(c) Consider a balloon filled with O2, at 1 atm pressure and occupying a 10L volumn at 293 K. Assuming ideal gas behavior, what would be its volumn at depth of 2500 m under the ocean surface at 277 K? What is the persentage increase in density of the O2?
(d) Repeat the calculation of part (c) for O2 gas taking into acount its deviation from ideal behavior. The van der Waals constants for O2 are: a=1.360 L2 atm mol-1 and b=3.183 x 10-2 L mol-1.

4. Calculate the heat (in joules) absorbed by the system for each of the following examples. specify the sign of the heat.

(a) 100 ml of liquid water is heated from 00C to 1000C at 1 atm.
(b) 100 ml of liquid water is frozen to ice at 00C at 0.01 atm.
(c) 100 ml of liquid water is evaporated to steam at 1000C at 1 atm.

5. Human beings expend energy during expansion and contraction of their lungs in breathing. Each exhalation from the lungs of an adult involves pushing out about 0.5L of gas against 1 atm pressure. This occurs about 15,000 times in a 24hr day.

(a) Estimate the amount of work in breathing done by each person in the course of 24 hr.
(b) To get a feeling for how much this represents, imagine using it to raise a mass to the top of a 30-story building (about 100 m). First make a guess at how large a weight could be raised by this amount of work: 1 kg, 100 kg, 1000kg. Now do the calculation and draw some conclusions about how much your body is working even when you are "resting".