Respuesta :
To determine the molar mass of the unknown gas, we use Graham's Law of Effusion where it relates the effusion rates of two gases with their molar masses. It is expressed as r1/r2 = √M2/M1. We calculate as follows:
Let 1 = argon gas 2 = unknown gas
r2 = 0.91r1r1/r2 = 1/0.91
1/0.91 = √M2/M1 = √M2/40M2 = 48.30 g/mol
Let 1 = argon gas 2 = unknown gas
r2 = 0.91r1r1/r2 = 1/0.91
1/0.91 = √M2/M1 = √M2/40M2 = 48.30 g/mol
Answer : The molar mass of a gas is, 48.3 g/mole
Solution : Given,
Molar mass of argon gas = 40 g/mole
According to the Graham's law, the rate of effusion of gas is inversely proportional to the square root of the molar mass of gas.
[tex]R\propto \sqrt{\frac{1}{M}}[/tex]
or,
[tex]\frac{R_1}{R_2}=\sqrt{\frac{M_2}{M_1}}[/tex]
where,
[tex]R_1[/tex] = rate of effusion of a gas
[tex]R_2[/tex] = rate of effusion of argon gas
[tex]M_1[/tex] = molar mass of a gas
[tex]M_2[/tex] = molar mass of argon gas
As per question,
[tex]R_1=0.91\times R_2[/tex]
Now put all the given values in the above formula, we get the molar mass of a gas.
[tex]\frac{0.91\times R_2}{R_2}=\sqrt{\frac{40g/mole}{M_1}}[/tex]
[tex]M_1=48.30g/mole[/tex]
Therefore, the molar mass of a gas is, 48.3 g/mole
