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
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]
Rearranging the above equation:
[tex]P=\frac{m}{M}\frac{RT}{V}[/tex]
We know that:
[tex]\text{Density}=\frac{\text{Mass}}{\text{Volume}}[/tex]
Rearranging the above equation:
[tex]P=\frac{dRT}{M}[/tex] ......(1)
We are given:
P = pressure of the gas = 0.799 atm
d = density of hydrogen gas = ?
R = Gas constant = [tex]0.0821\text{ L . atm }mol^{-1}K^{-1}[/tex]
T = temperature of the gas = [tex]47^oC=[47+273]K=320K[/tex]
M = molar mass of hydrogen gas = 2 g/mol
Putting values in equation 1, we get:
[tex]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[/tex]
Hence, the density of the given sample of hydrogen gas is 0.061 g/L