If two gases have molar masses M1, and M2 Graham’s law states that the ratio R of their rates of effusion through a small opening is given by The effusion rate of an unknown gas through a small opening is Measured to be 1.66 ± 0.03 times greater than the effusion rate of carbon dioxide. The molar mass of carbon dioxide may be taken to be 44 g/mol with negligible uncertainty.

a. Estimate the molar mass of the unknown gas, and find the uncertainty in the estimate.

b. Find the relative uncertainty in the estimated molar mass.

Solution 10SE

Step1 of 3:

Let us consider be the molar mass of unknown gas and

be the molar mass of carbon dioxide.

We have Graham’s law and it states that the ratio R of their rates of effusion through a small opening is given by

R =

And also we have the effusion rate of an unknown gas through a small opening is Measured to be 1.66 ± 0.03 times greater than the effusion rate of carbon dioxide.

That is effusion rate of carbon dioxide is R = 1.66,g/mol.

Here our goal is:

a).We need to estimate the molar mass of the unknown gas, and find the uncertainty in the estimate.

b).We need to find the relative uncertainty in the estimated molar mass.

Step2 of 3:

a).

Let us consider the equation:

=

= 442.7556

= 121.2464

Hence,

Consider

Differentiate above equation with respect to R we get

= 2(44)(1.66)

= 146.08

Hence, = 146.08.

Now

= (146.08)(0.03)

= 4.3824

Hence, = 4.3824.

Therefore, The molar mass of the unknown gas is

Step3 of 3:

b).

From part (a), we have The molar mass of the unknown gas is

Now, the relative uncertainty in the estimated molar mass is given by

= (0.0362)100

Therefore, The relative uncertainty in the estimated molar mass is 3.62%.

Conclusion:

a).The molar mass of the unknown gas is

b).The relative uncertainty in the estimated molar mass is 3.62%.