Question

1.674×10-4 mol of an unidentified gaseous substance effuses through a tiny hole in 86.6 s. Under identical conditions, 1.715×10-4 mol of argon gas takes 84.5 s to effuse. What is the molar mass of the unidentified substance (in g/mol)?

Answer 1

The molar mass of the unidentified gaseous substance can be determined by applying Graham's law of effusion, using known effusion times and the molar mass of argon.

Step-by-step explanation:

To calculate the molar mass of an unidentified gaseous substance using effusion times, we'll apply Graham's law of effusion. Graham's law states that the rate of effusion for a gas is inversely proportional to the square root of its molar mass.

Let's denote the unknown gas as gas U, and argon as gas A. Since we know the molar mass of argon (39.948 g/mol), we can set up a ratio according to Graham's law:

(Effusion rate of A / Effusion rate of U) = (Square root of molar mass of U / Square root of molar mass of A)

By rearranging the equation, we get:

Molar mass of U = Molar mass of A * (Effusion rate of U / Effusion rate of A)2

First, we find the effusion rates, which are inversely proportional to the effusion times:

Effusion rate of U = 1.674×10−4 mol / 86.6 s

Effusion rate of A = 1.715×10−4 mol / 84.5 s

Now we calculate the molar mass of the unknown gas U:

Molar mass of U = (39.948 g/mol) * (×10−4 mol / 86.6 s / ×10−4 mol / 84.5 s)2

By plugging in the numbers and solving, we obtain the molar mass of the unidentified substance.

Answer 2

44.06 g/mol

Step-by-step explanation:

We are given;

• Number of moles of unidentified gas as 1.674×10^-4 mol
• Time of effusion of unidentified gas 86.6 s
• Number of moles of Argon gas as 1.715×10^-4 mol
• Time of effusion of Argon gas is 84.5 s

We are supposed to calculate the molar mass of unidentified gas

Step 1: Calculate the effusion rates of each gas

Effusion rate = Number of moles/time

Effusion rate of unidentified gas (R₁)

= 1.674×10^-4 mol ÷ 86.6 s

= 1.933 × 10^-6 mol/s

Effusion rate of Argon gas (R₂)

= 1.715×10^-4 mol ÷ 84.5 sec

= 2.030 × 10^-6 mol/s

Step 2: Calculate the molar mass of unidentified gas

• Assuming the molar mass of unidentified gas is x;
• We can use the Graham's law of effusion to find x;
• According to Graham's law of diffusion;

`(R_(1))/(R_(2))}=\frac{\sqrt{MM_(Ar)}}{√(X)}`

But, Molar mass of Argon is 39.948 g/mol

Therefore;

`(1.933*10^-6mol/s)/(2.030*10^-6mol/s)}=(√(39.948))/(√(X))`

`0.9522=(√(39.948))/(√(X))`

Solving for X

x = 44.06 g/mol

Therefore, the molar mass of the identified gas is 44.06 g/mol