It takes 19.6 mins for a 10.0mL sample of an unknown gas to effuse through a pinhole.

A 10.0mL sample of He, required 5.05mins. What is the molar mass of the unknown gas?

I got that you have to do :
effuse rate of He/Effuse rate of Mx = Square root of (Mx/MHe) but then im stuck here.

Thank you!!:)

unk = 10/19.6 = approx 0.5 mL/min

He = 10/5.05 = appxox 2 mL/min

(2/0.5) = sqrt(M/4)
Square both sides.
(4/0.25) = M/4
Now solve for M.

To solve this problem, 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 say the unknown gas has a molar mass of Mx and helium has a molar mass of MHe.

We can set up the following equation using Graham's law:

Effusion rate of He/Effusion rate of Mx = √(Mx/MHe)

We are given that the effusion rate of helium is 10.0mL/5.05mins. Let's call this value Effusion rate of He.

We are also given that the effusion rate of the unknown gas is 10.0mL/19.6mins. Let's call this value Effusion rate of Mx.

Now we can substitute the given values into the equation:

10.0mL/5.05mins / (10.0mL/19.6mins) = √(Mx/MHe)

Simplifying, we get:

(10.0mL/5.05mins) * (19.6mins/10.0mL) = √(Mx/MHe)

Calculating the left side of the equation:

(10.0 * 19.6) / (5.05 * 10.0) = 4.625

Now we have:

4.625 = √(Mx/MHe)

To find the value of Mx, we need to square both sides of the equation:

(4.625)^2 = (√(Mx/MHe))^2

Simplifying:

21.390625 = Mx/MHe

Now we can solve for Mx:

Mx = 21.390625 * MHe

The molar mass of the unknown gas (Mx) is equal to 21.390625 times the molar mass of helium (MHe). Therefore, to find the molar mass of the unknown gas, you need to multiply the molar mass of helium (MHe) by 21.390625.