Solution: A gas of unknown identity diffuses at a rate of 83.3 mL/s in a diffusion apparatus in which carbon dioxide diffuses at the rate of 102 mL/s. Calculate the molecular mass of the unknown gas.

Problem

A gas of unknown identity diffuses at a rate of 83.3 mL/s in a diffusion apparatus in which carbon dioxide diffuses at the rate of 102 mL/s. Calculate the molecular mass of the unknown gas.

Solution

Recall: Graham's Law of Effusion allows us to compare the rate of effusion of two gases. Graham's Law states that the rate of effusion of a gas is inversely proportional to its molar mass.

This means that when comparing two gases:

Let's designate CO2 as gas 1 and the unknown as gas 2. We're given:
rateCO2 = 102 mL/s                  MCO2 = 12.01 g/mol C + 2(16.00 g/mol O) = 44.01 g/mol
rateunk = 83.3 mL/s                  Munk = ?

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