An unknown gas Q requires 1.80 times as long to effuse under the same conditions as the same amount of nitrogen gas. What is the molar mass (g/mol) of Q?
Molecular size in real gases causes positive deviations from the PV/RT ratio of an ideal gas.
a. True
b. False
To find the molar mass of gas Q, we need to use 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.
Let's assume the molar mass of nitrogen gas (N2) is M and the molar mass of gas Q is x.
According to the problem, the unknown gas Q requires 1.80 times as long to effuse under the same conditions as the same amount of nitrogen gas. Mathematically, we can write this as:
Rate of effusion of Q / Rate of effusion of N2 = 1.80
Using Graham's law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass. So, we can write:
sqrt(x) / sqrt(M) = 1.80
To solve this equation, we can square both sides to eliminate the square root:
(x / M) = (1.80)^2
x / M = 3.24
Now, if we assume the molar mass of nitrogen gas (N2) as approximately 28 g/mol, we can set up a proportion:
28 g/mol / M = 3.24
Cross-multiplying, we get:
M = 28 g/mol / 3.24
M ≈ 8.64 g/mol
Therefore, the molar mass of gas Q is approximately 8.64 g/mol.