Question

1. An unknown noble gas has a density of 5.84 g dm–3 at STP. Calculate its molar mass, and so identify the gas. 

Answer 1

Density of unknown gas($\rho$) = 5.84 g dm^-3 = 5.84 g/L

Let molar mass of unknown gas = M g/mol

At standard temperature and pressure conditions,

Temperature(T) = 273.15 K

Pressure(P) = 1 atm

Gas Constant(R) = 0.0821 L atm K^-1 mol^-1

From ideal gas equation,

$\Rightarrow PV= nRT$

$\Rightarrow PV= \dfrac{m}{M}RT$

$\Rightarrow M= \dfrac{m}{V}\dfrac{RT}{P}$

$\Rightarrow M = \rho \dfrac{RT}{P}$

$\Rightarrow M = 5.84 \times \dfrac {0.0821 \times 273.15}{1}$

$\Rightarrow M = 130.965g/mol \approx 131 g/mol$

Xenon has molar mass approximately equal to 131 g/mol