Question

A gas made up of atoms escapes through a pinhole 3.16 times as fast as Ar gas. Write the chemical formula of the gas.

Answer 1

Apply Effusion rate law

Which relates rates and molar masses; inversely proportional to the squared root as follows:

Rate 1 / Rate 2 = sqrt(MW2/MW1)

for argon --> 39.948 g/mol

In this case, we do not have rate of 1 or 2

but we have a ratio of rates

Rate of Gas = 3.16 faster than Rate of Argon

then

Rate 1 / Rate 2 = sqrt(MW2/MW1)

1 / (3.16) = sqrt(Mw2/39.948 )

Solve for Mw2

(1 / (3.16) )^2 = Mw2/39.948

Mw2 =39.948 * (1 / (3.16) )^2

Mw2 = 4.000g/mol

This is most likely Helium, since molar mass = 4 G/mol approx

Helium chemical formula = He