Respuesta :
Answer: The molar mass of the gas is 9.878 g/mol.
Explanation:
According to Graham's law, the rate of diffusion is inversely proportional to square root of molar mass of gas.
[tex]Rate = \frac{1}{\sqrt{M}}[/tex]
where,
M = molar mass of gas
As given gas diffuses 1/7 times faster than hydrogen gas. So, its molar mass is calculated as follows.
[tex]\frac{R_{1}}{R_{2}} = \sqrt{\frac{M_{2}}{M_{1}}}\\[/tex]
where,
[tex]M_{1}[/tex] = molar mass of hydrogen gas
[tex]M_{2}[/tex] = molar mass of another given gas
[tex]R_{1}[/tex] = rate of diffusion of hydrogen
[tex]R_{2}[/tex] = rate of diffusion of another given gas = [tex]\frac{1}{7}R_{1}[/tex]
Substitute the values into above formula as follows.
[tex]\frac{R_{1}}{R_{2}} = \sqrt{\frac{M_{2}}{M_{1}}}\\\frac{R_{1}}{\frac{1}{7}R_{1}} = \sqrt{\frac{M_{2}}{2}}\\7 \times 1.414 = M_{2}\\M_{2} = 9.878 g/mol[/tex]
Thus, we can conclude that the molar mass of the gas is 9.878 g/mol.
