Graham's Law of Effusion
Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Mathematically:
Rate₁ / Rate₂ = √(M₂ / M₁)
Where:
* Rate₁ and Rate₂ are the rates of effusion of gases 1 and 2, respectively.
* M₁ and M₂ are the molar masses of gases 1 and 2, respectively.
Applying the Law
1. Identify the known values:
* Chlorine (Cl₂) has a molar mass of 70.90 g/mol.
* Chlorine diffuses 2.04 times faster than gas Q. This means:
* Rate₁ (Chlorine) = 2.04 * Rate₂ (Gas Q)
2. Set up the equation:
* 2.04 * Rate₂ / Rate₂ = √(M₂ / 70.90)
3. Simplify and solve for M₂:
* 2.04 = √(M₂ / 70.90)
* 2.04² = M₂ / 70.90
* M₂ = 2.04² * 70.90
* M₂ ≈ 294 g/mol
Therefore, the molecular weight of gas Q is approximately 294 g/mol.
