Question

A sample of hydrogen gas has a density of ___ g/L at a pressure of 0.799 atm and a temperature of 47 °C. Assume ideal behavior.

Answer 1

Answer: The density of the given sample of hydrogen gas is 0.061 g/L

Explanation:

Assuming ideal gas behavior, the equation follows:

PV = nRT

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$

Rearranging the above equation:

$P=\frac{m}{M}\frac{RT}{V}$

We know that:

$\text{Density}=\frac{\text{Mass}}{\text{Volume}}$

Rearranging the above equation:

$P=\frac{dRT}{M}$     ......(1)

We are given:

P = pressure of the gas = 0.799 atm

d = density of hydrogen gas = ?

R = Gas constant = $0.0821\text{ L . atm }mol^{-1}K^{-1}$

T = temperature of the gas = $47^oC=[47+273]K=320K$

M = molar mass of hydrogen gas = 2 g/mol

Putting values in equation 1, we get:

$0.799atm=\frac{d\times 0.0821\text{ L.atm }mol^{-1}K^{-1}\times 320K}{2g/mol}\\\\d=\frac{0.799\times 2}{0.0821\times 320}=0.061g/L$

Hence, the density of the given sample of hydrogen gas is 0.061 g/L