An unknown gas effuses through an opening at a rate 3.53 times slower than nitrogen gas. What is the molecular mass of the unknown gas?
Pick a number for rate of the unknown gas. Let's say 10 mL/s. Then rate for N2 is 10 x 3.53 = 35.3 mL/s.
[(rate unk gas)/(rate N2)] = sqrt (mm N2/mm unknown)
Substitute and solve for mm (molar mass) unknown gas.
Post your work if you get stuck.
To find the molecular 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.
Let's assume the molar mass of nitrogen gas (N2) is M_nitrogen.
According to the given information, the rate of effusion of the unknown gas is 3.53 times slower than nitrogen gas. Therefore, the rate of effusion of the unknown gas is 1/3.53 times the rate of effusion of nitrogen gas.
According to Graham's law of effusion, the ratio of the rates of effusion is equal to the square root of the ratio of the molar masses:
(rate of effusion of unknown gas) / (rate of effusion of nitrogen gas) = √(M_nitrogen / M_unknown)
Substituting the values:
(1/3.53) = √(M_nitrogen / M_unknown)
Squaring both sides:
(1/3.53)^2 = (M_nitrogen / M_unknown)
1 / (3.53)^2 = M_nitrogen / M_unknown
1 / 12.4609 = M_nitrogen / M_unknown
M_unknown = M_nitrogen / (1 / 12.4609)
Therefore, to find the molecular mass of the unknown gas, you need to know the molecular mass of nitrogen gas (M_nitrogen).
To find the molecular mass of the unknown gas, we can 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 molecular mass.
Let's denote the rate of effusion of the unknown gas as R₁ and the rate of effusion of nitrogen gas as R₂. According to the problem, the unknown gas effuses 3.53 times slower than nitrogen gas, so we have the following relationship:
R₁ = R₂/3.53
Using Graham's law, we can also relate the rates of effusion to the square roots of the molecular masses:
√(Molecular mass of unknown gas) = √(Molecular mass of nitrogen gas) * (Rate of effusion of nitrogen gas) / (Rate of effusion of unknown gas)
Plugging in the values, we have:
√(Molecular mass of unknown gas) = √(28 g/mol) * (R₂) / (R₁)
Dividing both sides of the equation by √(28 g/mol) and then squaring both sides, we get:
(Molecular mass of unknown gas) = ((R₂ / R₁) ^ 2) * 28 g/mol
Now, we can substitute the given values into the equation to get the molecular mass of the unknown gas.