The rate of effusion of unknown gas X is found to be about 1.5 times that of SF6 gas (MW=146 g/mol) at the same conditions of temperature and pressure. What is the molecular weight of gas X?
Answer in units of g/mol
Well, the rate of effusion is directly proportional to the square root of the molar mass. Since the rate of effusion of gas X is 1.5 times that of SF6, we can say that (molar mass of X) / (molar mass of SF6) = (rate of effusion of X)^2 / (rate of effusion of SF6)^2.
Given that the molar mass of SF6 is 146 g/mol, we can simplify the equation to (molar mass of X) / 146 = (1.5)^2 / 1^2.
Simplifying further, we get (molar mass of X) = 146 * (1.5^2). Solving this, we find that the molar mass of gas X is approximately 328.5 g/mol.
So, the molecular weight of gas X is approximately 328.5 g/mol. But remember, this is no laughing matter... except for the clown, of course! 🤡
To solve this problem, we can use Graham's law of effusion, which states that the rates of effusion of two gases are inversely proportional to the square roots of their molar masses.
Let's denote the rate of effusion of unknown gas X as Rx and the rate of effusion of SF6 gas as Rsf6.
According to the given information, Rx = 1.5 * Rsf6.
Using Graham's law of effusion:
Rx / Rsf6 = sqrt(Msf6 / Mx)
where Msf6 is the molar mass of SF6 gas and Mx is the molar mass of unknown gas X.
Squaring both sides of the equation gives:
(Rx / Rsf6) ^ 2 = (Msf6 / Mx)
Substituting the known values:
(1.5 * Rsf6 / Rsf6) ^ 2 = (146 g/mol / Mx)
Simplifying:
2.25 = 146 g/mol / Mx
Multiplying both sides of the equation by Mx:
2.25 * Mx = 146 g/mol
Finally, dividing both sides by 2.25:
Mx = 146 g/mol / 2.25
Calculating this expression:
Mx ≈ 64.89 g/mol
Therefore, the molecular weight of gas X is approximately 64.89 g/mol.
To find the molecular weight of gas X, we can use Graham's Law of Effusion. According to Graham's Law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
The equation for Graham's Law is:
Rate₁ / Rate₂ = √(M₂ / M₁)
Where:
Rate₁ and Rate₂ are the rates of effusion of gases X and SF6 respectively
M₁ and M₂ are the molecular weights of gases X and SF6 respectively
We are given that the rate of effusion of gas X is 1.5 times that of SF6. So we can set it up as follows:
1.5 / 1 = √(M_SF6 / M_X)
Squaring both sides of the equation, we get:
2.25 = (M_SF6 / M_X)
Now, we can substitute the known molecular weight of SF6 which is 146 g/mol:
2.25 = (146 g/mol) / M_X
Rearranging the equation to solve for M_X:
M_X = (146 g/mol) / 2.25
Calculating this gives:
M_X ≈ 64.89 g/mol
Therefore, the molecular weight of gas X is approximately 64.89 g/mol.