Answer to Question #151105 in General Chemistry for lewynn

Question

What is the mass of gas at a pressure of 500 kPa and a temperature of 50 °C if it occupies a volume of 0.10 m3? The gas has a characteristic gas constant of 189 J kg-1 K-1

Answer 1

A characteristic gas constant is the universal gas constant divided by the molar mass of the gas:

$R_c = \frac{R}{M}$ .

The ideal gas law links the number of the moles of the gas , its volume, temperature and pressure:

$pV = nRT$ .

Finally, the mass of gas is its number of the moles times molar mass:

$m = n\cdot M$ .

Using these equations, the mass of the gas is:

$m = n\cdot M = \frac{pV}{RT}\cdot M = \frac{pV}{R_cT}$

$m = \frac{500\cdot10^3\cdot 0.10}{189 \cdot(50+273.15)} = 0.819$ kg.

Remark: the units in the equation cancel and give kg as the result.

Answer: the mass of the gas is 0.819 kg.