# The Ideal Gas Law Practice Problems

A bio sauna operates at a temperature of 55˚C with an average relative humidity of 65%. The vapor pressure of water at 55.0°C is 1.78 × 10^{4} Pa. Calculate the partial pressure of water vapor inside the sauna. Relative humidity is the ratio of water vapor partial pressure in air to the vapor pressure of water at the same temperature.

Fixed-volume containers can be used as thermometers. The temperature of a sample is reported in terms of absolute pressure. If such a thermometer displays an absolute pressure of 420 mm Hg at the triple point of carbon dioxide (CO_{2}), determine the pressure displayed at the boiling point of ethanol.

The triple point for carbon dioxide occurs at -57°C and 5.2 atm. The pressure of a gas sample at this triple point is 3.8 atm. If the volume does not change, determine the pressure of the gas sample at the boiling point of nitrogen.

A sealed light bulb is filled with argon molecules at normal atmospheric pressure of 1 atm and a temperature of 293 K. What is the average spacing between two argon molecules?

During an experiment, a researcher measures the pressure of nitrogen gas and the temperature inside the cryostat chamber and finds that the pressure is 10^{-7} mbar and the temperature is 50 K. The volume of the cryostat chamber is 10 cm^{3}. How many nitrogen molecules (N) are present inside the cryostat chamber?

The mass of a molecule of substance K is 1.297 ×10^{-22} g. Calculate the molar mass (M) of substance K.

During a chemical vapor deposition experiment, a cylinder containing 10 kg of diatomic nitrogen (N_{2}) is used. Calculate the number of i) N_{2} moles (n) and ii) N_{2} molecules inside the cylinder. The molar mass of nitrogen is 28.0 g/mol.

What is the radius (R) of a sphere containing 200 billion helium gas molecules at 300 K and at a pressure of 10^{5 }Pa?

The pressure of the air inside an insulation system of volume 10 cm^{3} is 10^{-8} atm. The air temperature is 250 K. The pressure rises to 10^{-4} atm due to a system malfunction. Compare the number of molecules that would be present at the same temperature inside the system before and after the system stopped working properly.

A container with a movable piston is filled with SO_{2} of molar mass 64.07 g/mol. The movable piston keeps the pressure inside the container at a constant 924 Pa. The container is moved back and forth between 100°C and -10°C. Determine the ranges of the density (in mol/m^{3}) of the SO^{2}.

The service ceiling is the maximum operating altitude of an aircraft. A military helicopter has a service ceiling of 8,000 m, where the air temperature is -36.9°C, and the density equals 0.53 kg/m^3. At that altitude, what is the atmospheric pressure (p)?

A balloon made of rubber and filled with air has a volume of 1 m^{3} under standard conditions of pressure and temperature. What is the volume of the balloon (V_{Mars}) if it is placed outside a Martian station where the pressure and temperature are 600 Pa and -60 °C, respectively? Assume that the balloon will not burst on Mars.

A laboratory technician entraps 2 ml of air at a pressure of 0.300 atm inside the barrel of a syringe with a tightly closed hub during an experiment. He increases the volume of the air to 6 ml by gradually moving the plunger back. The temperature of the air inside the barrel decreases from 25°C to 20°C. What is the pressure's final value (p_{f})?

Find the density of the air (ρ) inside a truck tire filled with air where the pressure is 7.58 × 10^{5} Pa and the temperature is 25 °C. Assume that the average molar mass of air is 28.97 g/mol.

An ideal carbon monoxide (CO) gas has initially a temperature of 290 K and a pressure of 3 atm. The gas undergoes an expansion from 0.5 m^{3} to 1 m^{3}. The CO final pressure is 4 atm. Carbon monoxide's molar mass is 28.0 g/mol. What is the mass (m) of CO?

A worker uses a hand air pump to inflate an air mattress. The worker notices that the volume of the mattress is 160 liters. The temperature of the air inside the mattress is 25°C, and the absolute pressure inside the mattress is 1.0272 atmospheres. What is the mass of air in the mattress?

The piston-cylinder assembly of an engine initially contains 0.5 mol of an ideal gas at a pressure of 1 atm. The gas inside the cylinder expands slowly and isothermally until the volume of the cylinder is doubled. What is the final pressure (p_{f}) inside the cylinder?

A balloon contains 7 × 10^{-3} m^{3} of argon gas. The initial pressure and temperature are 1 atm and 290 K, respectively. The balloon is cooled until both its volume and pressure are halved. Find the final temperature (T_{f}).

An empty aerosol sprayer of volume 0.3 liters is filled with 0.3 g of carbon dioxide gas at a temperature of 25 °C. The molecular mass of carbon dioxide is 44 g/mol. Find the pressure (p) inside the sprayer. Express your answer i) in pascals and ii) in atmospheres.

A diver uses a scuba oxygen cylinder of 12 liters filled with 16 kg of diatomic oxygen gas (O_{2}). The molar mass of O_{2} is 32.00 g/mol. How many moles of oxygen (n) are present in the cylinder?

Ethanol's data sheet shows that its critical density is 280 kg/m^{3}. Ethanol density at room temperature is 789 kg/m^{3}. Calculate the ratio (V_{critical }/V_{room temperature}) of the volume occupied by one mole of ethanol at the critical point to that at room temperature. Ethanol's molecular mass is 46 g/mol.