A cylinder of volume 1810 dm³ contains gas at a pressure of 197 atm and temperature of 25°C.  Assuming that the gas behaves as a perfect gas, calculate the amount of gas contained in the cylinder.

A pressure vessel contains a gaseous mixture made up of 2.34 kg silane, SiH₄, and 55.4 kg argon, Ar.  Determine the mole fraction of silane.

The partial pressure of ethanol in the air above a sample of liquid ethanol is 1400 Pa.  Assuming the air to be at normal pressure, calculate the mole fraction of ethanol in the air.

Calculate the root-mean-squared speed of methane, CH₄, molecules in a sample of at 25 °C.

Calculate the mean speed of oxygen molecules, O₂, in air at 25 °C.

Calculate the mean free path of carbon dioxide molecules, CO₂, in a sample of gas at standard ambient temperature and pressure.  The collision cross section of a carbon dioxide molecule is 0.52 nm².

Calculate the compression factor for carbon dioxide at its critical point given that T_c = 31 °C, p_c = 72.9 atm and V_c = 94.0 cm³ mol^-1.

The second virial coefficient of ammonia, NH₃, is –40.4 cm³ mol^-1 at 600 K.  What does this imply about the nature of the interactions between the molecules at this temperature?

Use the virial equation to calculate the pressure exerted by exactly 1 mol of hydrogen held in a cylinder of volume 0.250 dm³ at a temperature of 1000 K.  The value of the second virial coefficient of hydrogen at this temperature is +22.54 cm³ mol^-1.

Use the van der Waals equation of state to calculate the pressure exerted by exactly1 mol of gaseous ammonia, NH₃, held at a temperature of 1000 K in a vessel of volume 2.50 dm³. The values of the van der Waals parameters for ammonia are a = 422.5 kPa dm⁶ mol^-2 and b = 3.71 x 10^-2 dm³ mol^-1.