Respuesta :
Answer: The molar mass of unknown gas is 367.12 g/mol
Explanation:
Rate of a gas is defined as the amount of gas displaced in a given amount of time.
[tex]\text{Rate}=\frac{V}{t}[/tex]
To calculate the rate of diffusion of gas, we use Graham's Law.
This law states that the rate of effusion or diffusion of gas is inversely proportional to the square root of the molar mass of the gas. The equation given by this law follows the equation:
[tex]\text{Rate of effusion}\propto \frac{1}{\sqrt{\text{Molar mass of the gas}}}[/tex]
So,
[tex]\left(\frac{\frac{V_{X}}{t_{X}}}{\frac{V_{O_2}}{t_{O_2}}}\right)=\sqrt{\frac{M_{O_2}}{M_{X}}}[/tex]
We are given:
Volume of unknown gas (X) = 1.0 L
Volume of oxygen gas = 1.0 L
Time taken by unknown gas (X) = 105 seconds
Time taken by oxygen gas = 31 seconds
Molar mass of oxygen gas = 32 g/mol
Molar mass of unknown gas (X) = ? g/mol
Putting values in above equation, we get:
[tex]\left(\frac{\frac{1.0}{105}}{\frac{1.0}{31}}\right)=\sqrt{\frac{32}{M_X}}\\\\M_X=367.12g/mol[/tex]
Hence, the molar mass of unknown gas is 367.12 g/mol
