How to calculate the molar mass of an unknown gas

Asked by admin @ 22/11/2021 in Chemistry viewed by 285 People

The molar mass of unknown gas was measured by effusion experiment. it was found that it took 63s for the gas to effuse, whereas nitrogen gas required 48s. what is the molar mass of the gas?a) 32g/molb) 37g/molc) 24g/mold) 16g/mole) 48g/mol

Answered by admin @ 22/11/2021

Answer: Option (e) is the correct answer.

Explanation:

According to Graham's law, time taken for effusion is directly proportional to square root of molar mass.

$\frac{T_{N_{2}}}{T_{Gas}} = \sqrt{\frac{M_{N_{2}}}{M_{Gas}}}$

where, $T_{N_{2}}$ = Time taken by the nitrogen gas

$T_{Gas}$ = Time taken by the other gas

$M_{N_{2}}$ = molar mass of nitrogen

$M_{Gas}$ = molar mass of other gas

Therefore, we will calculate the molar mass of unknown as follows.

$\frac{T_{N_{2}}}{T_{Gas}} = \sqrt{\frac{M_{N_{2}}}{M_{Gas}}}$

$\frac{48 sec}{63 sec} = \sqrt{\frac{28 g/mol}{M_{Gas}}}$

Squaring on both the sides,

$M_{Gas} = (\frac{63}{48})^{2} \times 28$

= $\frac{3969}{2304} \times 28$

= 48.2 g/mol

Thus, we can conclude that molar mass of the given gas is 48 g/mol.

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