Chapter 2.3, Problem 18E

The Ideal Gas Law A mole of a chemical is a fixed number, like a dozen, of molecules (or atoms in the case of an element) of that compound. A mole of water, for example, is about 18 grams, or just over half an ounce in your kitchen. Chemists often use the mole as the measure of the amount of a chemical compound.

A mole of carbon dioxide has a fixed mass, but the volume $V$ that it occupies depends on pressure $p$ and temperature $T$; greater pressure tends to compress the gas into a smaller volume, whereas increasing temperature tends to make the gas expand into a larger volume. If we measure the pressure in atmospheres (1 atm is the pressure exerted by the atmosphere at sea level), the temperature in kelvins, and the volume in liters, then the relationship is given by the ideal gas law:

$pV=0.082T.$

a. Solve the ideal gas law for the volume $V.$

b. What is the volume of 1 mole of carbon dioxide under 3 atm of pressure at a temperature of 300 kelvins?

c. Solve the ideal gas law for pressure.

d. What is the pressure on 1 mole of carbon dioxide if it occupies a volume of 0.4 liter at a temperature of 350 kelvins?

e. Solve the ideal gas law for temperature.

f. At what temperature will 1 mole of carbon dioxide occupy a volume of 2 liters under a pressure of 0.3 atm?