The rate of effusion of a particular gas was measured and found to be 25.0 mL/min. Under the same conditions, the rate of effusion of pure methane (CH4) gas is 46.4 mL/min. What is the molar mass of the unknown gas?
(rate1/rate2) = sqrt(M2/M1)
Solve for the one unknown.
55.1
To calculate the molar mass of the unknown gas, we can use Graham's law of effusion. According to Graham's law, the ratio of the rates of effusion of two gases is equal to the square root of the ratio of their molar masses.
The formula is:
Rate1 / Rate2 = sqrt(MolarMass2 / MolarMass1)
Let's substitute the given values into the formula:
25.0 mL/min (Rate1) / 46.4 mL/min (Rate2) = sqrt(MolarMass2 / MolarMass1)
Now, we can rearrange the formula to solve for the unknown molar mass:
sqrt(MolarMass2 / MolarMass1) = 25.0 mL/min / 46.4 mL/min
Taking the square root of both sides:
sqrt(MolarMass2 / MolarMass1) = 0.5388
Now, let's isolate the ratio of molar masses on one side by squaring both sides of the equation:
(MolarMass2 / MolarMass1) = 0.5388^2
(MolarMass2 / MolarMass1) = 0.2907
Now, rearrange the equation to solve for the molar mass of the unknown gas:
MolarMass2 = MolarMass1 * 0.2907
We don't know the molar mass of the methane (CH4), but we can use its molar mass as a reference. The molar mass of methane (CH4) is approximately 16.04 g/mol.
MolarMass2 = 16.04 g/mol * 0.2907
MolarMass2 ≈ 4.65 g/mol
Therefore, the molar mass of the unknown gas is approximately 4.65 g/mol.
To determine the molar mass of the unknown gas, 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 formula is as follows:
Rate1 / Rate2 = sqrt(Molar Mass2 / Molar Mass1)
Where:
- Rate1 is the rate of effusion of the unknown gas
- Rate2 is the rate of effusion of pure methane
- Molar Mass1 is the molar mass of the unknown gas (what we want to find)
- Molar Mass2 is the molar mass of pure methane (16.04 g/mol)
We are given:
- Rate1 = 25.0 mL/min
- Rate2 = 46.4 mL/min
- Molar Mass2 = 16.04 g/mol
First, let's convert the rates of effusion from mL/min to L/min:
Rate1 = 25.0 mL/min = 0.0250 L/min
Rate2 = 46.4 mL/min = 0.0464 L/min
Now, let's plug the values into the formula and solve for Molar Mass1:
0.0250 L/min / 0.0464 L/min = sqrt(16.04 g/mol / Molar Mass1)
Simplifying the equation:
0.539 = sqrt(16.04 g/mol / Molar Mass1)
To solve for Molar Mass1, we square both sides of the equation:
0.539^2 = 16.04 g/mol / Molar Mass1
0.290821 = 16.04 g/mol / Molar Mass1
Now, isolate Molar Mass1 by multiplying both sides of the equation by Molar Mass1:
0.290821 * Molar Mass1 = 16.04 g/mol
Dividing both sides of the equation by 0.290821, we find:
Molar Mass1 = 16.04 g/mol / 0.290821
Molar Mass1 = 55.152 g/mol
Therefore, the molar mass of the unknown gas is approximately 55.152 g/mol.