A gas of unknown molecular mass was allowed to effuse through a small opening under constant-pressure conditions. It required 125 s for 1.0 L of the gas to effuse. Under identical experimental conditions it required 34 s for 1.0 L of O2 gas to effuse.

Part A
Calculate the molar mass of the unknown gas. (Remember that the faster the rate of effusion, the shorter the time required for effusion of 1.0 L; that is, rate and time are inversely proportional.)

450 g/mol

Explanation:

To solve the problem the problem, it is necessary to use Graham's Law of effusion
M1/32g(mol) = 120s/32s = 450/mol

A heavier gas will require more time to effuse than a lighter gas

oops!

It's 125 sec and 34 sec. I get something like 432 but you should confirm that.
(1/125)/(1/34) = sqrt(32/M)
M = 432

To calculate 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.

Let's denote the rate of effusion of the unknown gas as r1, and the rate of effusion of O2 gas as r2. We are given the following information:

- Time for the unknown gas to effuse: t1 = 125 s
- Time for the O2 gas to effuse: t2 = 34 s

According to Graham's law, the rate of effusion for each gas can be calculated as:

r1 = 1 / t1
r2 = 1 / t2

Let's calculate the rates of effusion for each gas:

r1 = 1 / 125 = 0.008
r2 = 1 / 34 = 0.029

Now we can set up a ratio using these rates of effusion:

r1 / r2 = sqrt(M2 / M1)

where M1 and M2 are the molar masses of the unknown gas and O2 gas, respectively.

Let's plug in the known values:

0.008 / 0.029 = sqrt(M2 / M1)

To simplify the calculation, let's square both sides of the equation:

(0.008 / 0.029)^2 = (sqrt(M2 / M1))^2
0.2181 = M2 / M1

Since we want to find the molar mass of the unknown gas (M1), let's rearrange the equation:

M1 = M2 / 0.2181

Now, we need to know the molar mass of O2 gas (M2). The molar mass of O2 is 32 g/mol.

Plugging in the values:

M1 = 32 g/mol / 0.2181
M1 ≈ 146.6 g/mol

Therefore, the molar mass of the unknown gas is approximately 146.6 g/mol.

To find the molar mass of the unknown gas, we can compare its rate of effusion to that of a known gas, in this case, oxygen (O2).

From the given information, we know that the rate of effusion for the unknown gas is inversely proportional to the time required for effusion. In other words, the faster the rate of effusion, the shorter the time required for effusion of 1.0 L.

Using this relationship, we can set up a proportion:

(rate of effusion of unknown gas) / (rate of effusion of O2) = (time for O2 to effuse) / (time for unknown gas to effuse)

Plugging in the given values:

(x) / (1.0) = (34) / (125)

Cross-multiplying and solving for x (rate of effusion of unknown gas):

x = (1.0) * (34) / (125)
x = 0.272 L/s

Now we can use the ideal gas law to relate the rate of effusion to the molar mass of the gas:

rate of effusion = (Molar mass)^(1/2) / (Square root of molar mass of O2)

Solving for the molar mass of the unknown gas:

(0.272) = (Molar mass of unknown gas)^(1/2) / (Square root of 32 g/mol)

Cross-multiplying and solving for Molar mass of unknown gas:

Molar mass of unknown gas = (0.272)^2 * (32 g/mol)
Molar mass of unknown gas = 0.238 g/mol

Therefore, the molar mass of the unknown gas is approximately 0.238 g/mol.