Final answer:
The molecular mass of the unknown gas is approximately 8.46 g/mol.
Step-by-step explanation:
Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. In this case, the unknown gas effuses 1.754 times slower than C₂H₂. Since the effusion rate is inversely proportional to the square root of the molar mass, we can set up the following equation:
(Rate of unknown gas) / (Rate of C₂H₂) = sqrt(Molar mass of C₂H₂) / sqrt(Molar mass of unknown gas)
Plugging in the given values, we have:
1.754 / 1 = sqrt(26.04 g/mol) / sqrt(Molar mass of unknown gas)
Simplifying, we get:
Molar mass of unknown gas = (sqrt(26.04 g/mol))^2 / (1.754^2)
= 26.04 g/mol / 3.076516
= 8.46 g/mol
Therefore, the molecular mass of the unknown compound is approximately 8.46 g/mol.