Under identical conditions, separate samples of O2 and an unknown gas were allowed to effuse through identical membranes simultaneously. After a certain amount of time, it was found that 4.92 mL of O2 had passed through the membrane, but only 3.04 mL of of the unknown gas had passed through. What is the molar mass of the unknown gas?

Question

Under identical conditions, separate samples of O2 and an unknown gas were allowed to effuse through identical membranes simultaneously. After a certain amount of time, it was found that 4.92 mL of O2 had passed through the membrane, but only 3.04 mL of of the unknown gas had passed through. What is the molar mass of the unknown gas?

Answer 1

I got to 1.62 = sqrt(M unknown/M O2)

I know that the molar mass of O2 is 32

So I squared both sides of the equation to get 2.6244 = M unknown/ 32g O2

Multiplied 2.6244 x 32 = 83.98g/molunknown

Answer 2

I differ slightly (84.82) probably because you rounded to 1.62 while I kept everything in the calculator until the final answer. But to three significant figures I would round the answer to 83.8 (probably krypton).

Answer 3

Well, that's quite a "gas-tly" situation! Let's figure it out together, shall we?

To find the molar mass of the unknown gas, we can use Graham's Law of Effusion. According to this law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass.

So, we can set up a ratio to compare the rates of effusion for the two gases:

(√molar mass of O2)/(√molar mass of the unknown gas) = (rate of effusion of O2)/(rate of effusion of the unknown gas).

Given that 4.92 mL of O2 and 3.04 mL of the unknown gas have passed through the membrane, we can see that the rate of effusion of O2 is greater.

Hence, we can rewrite the ratio as:

(√molar mass of O2)/(√molar mass of the unknown gas) = 4.92 mL / 3.04 mL.

By cross-multiplying and solving for the unknown gas's molar mass, we find:

(√molar mass of the unknown gas) = (√molar mass of O2) * (3.04 mL / 4.92 mL).

Calculating (√molar mass of the unknown gas) gives us:

(√molar mass of the unknown gas) = (√32 g/mol) * (3.04 mL / 4.92 mL).

Finally, squaring both sides of the equation gives us the molar mass of the unknown gas:

Molar mass of the unknown gas = (molar mass of O2) * (3.04 mL / 4.92 mL) * (3.04 mL / 4.92 mL).

So, put on your gas mask, grab a calculator, and calculate away!

Answer 4

To find the molar 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 molar mass.

Let's denote the molar mass of O2 as M1 and the molar mass of the unknown gas as M2. We can set up the following ratio using Graham's law:

(rate of effusion of O2) / (rate of effusion of unknown gas) = √(M2/M1)

We know that the rate of effusion of O2 (R1) is 4.92 mL and the rate of effusion of the unknown gas (R2) is 3.04 mL. Plugging in these values, we get:

(4.92 mL) / (3.04 mL) = √(M2/M1)

Simplifying the equation, we have:

(4.92/3.04)^2 = M2/M1

Now we need to know the molar mass of O2, which is 32 g/mol. Substituting this value, we can solve for M2:

(4.92/3.04)^2 = M2/32

(1.6184)^2 = M2/32

2.6159 = M2/32

Multiplying both sides by 32, we get:

M2 = 83.63 g/mol

Therefore, the molar mass of the unknown gas is approximately 83.63 g/mol.

Answer 5

(rate1/rate2) = sqrt(M2/M1)

Substitute and solve for molar mass.