Understanding Graham's Law
Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. In simpler terms, lighter gases effuse (or diffuse) faster than heavier gases.
The Formula
The formula for Graham's Law is:
Rate₁ / Rate₂ = √(M₂ / M₁)
Where:
* Rate₁ is the rate of effusion of gas 1
* Rate₂ is the rate of effusion of gas 2
* M₁ is the molar mass of gas 1
* M₂ is the molar mass of gas 2
Solving the Problem
1. Identify the knowns:
* Rate₁ (unknown gas) = 1 (we'll assume it's 1, since it diffuses slower)
* Rate₂ (H₂) = 2.92
* M₂ (H₂) = 2.016 g/mol
2. Set up the equation:
1 / 2.92 = √(2.016 g/mol / M₁)
3. Solve for M₁ (the molar mass of the unknown gas):
* (1/2.92)² = 2.016 g/mol / M₁
* M₁ = 2.016 g/mol / (1/2.92)²
* M₁ ≈ 17.0 g/mol
Therefore, the molar mass of the unknown gas is approximately 17.0 g/mol.
Important Note: This assumes the unknown gas is behaving ideally and that the temperature and pressure are constant.
