a sample of hydrogen effuses through a porous container about 9 times faster than an unknown gas. Estimate the molar mass of the unknown gas.
Answer 164
To estimate the molar mass of the unknown gas, we can use Graham's Law of Effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
According to the given information, the rate of effusion of hydrogen (H2) is 9 times faster than the unknown gas. Let's denote the molar mass of the unknown gas as M.
Graham's Law of Effusion can be written as:
(rate of effusion of unknown gas) / (rate of effusion of hydrogen gas) = √(molar mass of hydrogen) / √(molar mass of unknown gas)
Using the given information, we can substitute the values:
(rate of effusion of unknown gas) / 1 = √2 / √M
Squaring both sides of the equation, we get:
(rate of effusion of unknown gas)^2 = 2 / M
Since the rate of effusion of hydrogen gas is 9 times slower, the rate of effusion of the unknown gas is 9.
Substituting this value into the equation, we have:
9^2 = 2 / M
81 = 2 / M
Cross-multiplying the equation, we get:
81M = 2
Dividing both sides by 81:
M = 2 / 81
Therefore, the estimated molar mass of the unknown gas is approximately 0.0247 g/mol.
To estimate the molar mass of the unknown gas, we can use Graham's Law of effusion.
Graham's Law states that the rate of effusion (or diffusion) of a gas is inversely proportional to the square root of its molar mass.
Let's denote the hydrogen gas as H2, and the unknown gas as X.
According to the problem, the rate of effusion of hydrogen gas (H2) is 9 times faster than the rate of effusion of the unknown gas (X).
Using Graham's Law, we can set up the following equation:
(H2 effusion rate) / (X effusion rate) = sqrt((X molar mass) / (H2 molar mass))
Since we are given the effusion rate ratio (9), we can rewrite the equation as:
9 = sqrt((X molar mass) / (H2 molar mass))
Squaring both sides to eliminate the square term:
81 = (X molar mass) / (H2 molar mass)
We know the molar mass of hydrogen (H2) is approximately 2 g/mol.
Let's assume the molar mass of the unknown gas (X) is equal to M g/mol.
Substituting the values into the equation:
81 = M / 2
Multiplying both sides by 2 to isolate M:
M = 81 * 2
M = 162 g/mol
Therefore, the estimated molar mass of the unknown gas is 162 g/mol.