The molar mass of the unknown gas is 17.75 g/mol
R ∝ [tex]\frac{1}{\sqrt{M}}[/tex]
Expanding further, we have
[tex]\frac{R_{1} }{R_{2} } = \sqrt{\frac{M_{2}}{M_{1}} }[/tex]
Where
R₁ and R₂ are the rate of diffusion of the individual gas
M₁ and M₂ are the molar masses of the individual gas.
With the above information in mind, we can obtain the molar mass of the unknown gas as follow:
Let R₁ be the rate of the unknown gas
Let R₂ be rate of Cl₂ gas
Let M₁ be the molar mass of the unknown gas
Let M₂ be the molar mass of the Cl₂ gas
From the question given above, we were obtained the following:
Rate of the unknown gas = 2 times the rate of Cl₂ i.e
Molar mass of Cl₂ (M₂) = 2 × 35.5 = 71 g/mol
[tex]\frac{R_{1} }{R_{2} } = \sqrt{\frac{M_{2}}{M_{1}} }\\\\\\\frac{2R_{2}}{R_{2} } = \sqrt{\frac{7 1}{M_{1}} }\\\\2 = \sqrt{\frac{7 1}{M_{1}} }[/tex]
[tex]2^{2} = \frac{71}{M_{1}} \\\\4 = \frac{71}{M_{1}}[/tex]
4 × M₁ = 71
[tex]M_{1} = \frac{71}{4}[/tex]
Therefore, the molar mass of the unknown gas is 17.75 g/mol
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