Problem 1
A 20.0-L tank contains \(4.86 \times 10{^-}{^4}\) kg of helium at 18.0\(^\circ\)C. The molar mass of helium is 4.00 g/mol. (a) How many moles of helium are in the tank? (b) What is the pressure in the tank, in pascals and in atmospheres?
Problem 2
Helium gas with a volume of 3.20 L, under a pressure of 0.180 atm and at 41.0\(^\circ\)C, is warmed until both pressure and volume are doubled. (a) What is the final temperature? (b) How many grams of helium are there? The molar mass of helium is 4.00 g/mol.
Problem 3
A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.110 m\(^3\) of air at a pressure of 0.355 atm. The piston is slowly pulled out until the volume of the gas is increased to 0.390 m\(^3\). If the temperature remains constant, what is the final value of the pressure?
Problem 4
A 3.00-L tank contains air at 3.00 atm and 20.0\(^\circ\)C. The tank is sealed and cooled until the pressure is 1.00 atm. (a) What is the temperature then in degrees Celsius? Assume that the volume of the tank is constant. (b) If the temperature is kept at the value found in part (a) and the gas is compressed, what is the volume when the pressure again becomes 3.00 atm?
Problem 5
(a) Calculate the density of the atmosphere at the surface of Mars (where the pressure is 650 Pa and the temperature is typically 253 \(K\), with a \(CO_2\) atmosphere), Venus (with an average temperature of 730 \(K\) and pressure of 92 atm, with a \(CO_2\) atmosphere), and Saturn's moon Titan (where the pressure is 1.5 atm and the temperature is -178\(^\circ\)C, with a \(N_2\) atmosphere). (b) Compare each of these densities with that of the earth's atmosphere, which is 1.20 kg/m\(^3\). Consult Appendix D to determine molar masses.
Problem 6
You have several identical balloons. You experimentally determine that a balloon will break if its volume exceeds 0.900 L. The pressure of the gas inside the balloon equals air pressure (1.00 atm). (a) If the air inside the balloon is at a constant 22.0\(^\circ\)C and behaves as an ideal gas, what mass of air can you blow into one of the balloons before it bursts? (b) Repeat part (a) if the gas is helium rather than air.
Problem 7
A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one of the cylinders contains 499 cm\(^3\) of air at atmospheric pressure (1.01 \(\times\) 10\({^5}\) Pa) and a temperature of 27.0\(^\circ\)C. At the end of the stroke, the air has been compressed to a volume of 46.2 cm\(^3\) and the gauge pressure has increased to 2.72 \(\times\) 10\({^6}\) Pa. Compute the final temperature.
Problem 8
A welder using a tank of volume 0.0750 m\(^3\) fills it with oxygen (molar mass 32.0 g/mol) at a gauge pressure of 3.00 \(\times\) 10\({^5}\) Pa and temperature of 37.0\(^\circ\)C. The tank has a small leak, and in time some of the oxygen leaks out. On a day when the temperature is 22.0\(^\circ\)C, the gauge pressure of the oxygen in the tank is 1.80 \(\times\) 10\({^5}\) Pa. Find (a) the initial mass of oxygen and (b) the mass of oxygen that has leaked out.
Problem 9
A large cylindrical tank contains 0.750 m\(^3\) of nitrogen gas at 27\(^\circ\)C and 7.50 \(\times\) 10\({^3}\)Pa (absolute pressure). The tank has a tight-fitting piston that allows the volume to be changed. What will be the pressure if the volume is decreased to 0.410 m\(^3\) and the temperature is increased to 157\(^\circ\)C?
Problem 10
An empty cylindrical canister 1.50 m long and 90.0 cm in diameter is to be filled with pure oxygen at 22.0\(^\circ\)C to store in a space station. To hold as much gas as possible, the absolute pressure of the oxygen will be 21.0 atm. The molar mass of oxygen is 32.0 g/mol. (a) How many moles of oxygen does this canister hold? (b) For someone lifting this canister, by how many kilograms does this gas increase the mass to be lifted?
