Final answer:
The molar mass of an unknown gas that effuses at 2.0 times the rate of Cl₂ is calculated using Graham's law of effusion to be approximately 17.725 g/mol, suggesting that the unknown gas might be methane (CH₄).
Step-by-step explanation:
Calculating Molar Mass Using Graham's Law
To find the molar mass of an unknown gas that effuses at a rate of 2.0 times the rate of Cl₂, we can use Graham's law of effusion. This law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass, which can be represented as:
Rate of effusion of gas 1 / Rate of effusion of gas 2 = sqrt(Molar mass of gas 2 / Molar mass of gas 1)
For chlorine gas (Cl₂), the molar mass is approximately 70.9 g/mol. Plugging the values into the equation:
2.0 / 1 = sqrt(70.9 g/mol / Molar mass of unknown gas)
Rearranging the equation to solve for the molar mass of the unknown gas, we get:
Molar mass of unknown gas = 70.9 g/mol / (2.0)^2
Molar mass of unknown gas = 17.725 g/mol
The molar mass of the unknown gas is therefore approximately 17.725 g/mol. By comparing this value to the molar masses of known gases, it is possible that the unknown gas could well be methane (CH₄), as this is the only gas with a molar mass very close to our calculated value.