Answer : The molar mass of unknown gas is, 41 g/mole
Solution : Given,
Diffusion rate of neon gas = 7 cm/s
Diffusion rate of unknown gas = 4.9 cm/s
Molar mass of neon gas = 20 g/mole
According to the Graham's law, the rate of effusion of a gas is inversely proportional to the square root of the molar mass of the gas.
Formula used :
\(\frac{R_1}{R_2}=\sqrt{\frac{M_2}{M_1}}\)
where,
\(R_1\) = diffusion rate of neon gas
\(R_2\) = diffusion rate of unknown gas
\(M_1\) = molar mass of neon gas
\(M_2\) = molar mass of unknown gas
Now put all the given values in the above formula, we get the molar mass of unknown gas.
\(\frac{7cm/s}{4.9cm/s}=\sqrt{\frac{M_2}{20g/mole}}\)
\(M_2=40.81g/mole=41g/mole\)
Therefore, the molar mass of unknown gas is, 41 g/mole
