Question

A gas made up of atoms escapes through a pinhole 0.392 times as fast as Ne gas. Write the chemical formula of the gas.

Answer 1

Answer:  The chemical formula of the gas is Xenon.

Explanation:

From Graham's law of effusion rates, the rate of effusion of a gas is inversely proportional to the square root of its molar mass.

$\frac{rate_1}{rate_2}=\sqrt{\frac{M_2}{M_1}}$

Given: Rate of unknown gas = $0.392\times R_{Ne}$  

Putting the values in the formula:

$\frac{rate_X}{rate_{Ne}}=\sqrt{\frac{M_{Ne}}{M_X}}$

$0.392=\sqrt{\frac{20.17}{M_X}}$

Squaring both sides:

$0.154=\frac{20.17}{M_X}$

$M_X=131g/mol$

As Xenon (Xe) has molar mass of 131g/mol, Thus the chemical formula of the gas is Xenon.