Question

A sample of neon effuses from a container in 76 seconds. the same amount of an unknown noble gas requires 155 seconds. part a identify the gas.

Answer 1

The  rate  of  gas effusion  or diffusion is  inversely  proportional  to  the square root of molar  mass 
molar mass  of  neon  is  20
let  the  molar  mass of  unknown gas  be  y
155/76=sqrs of y/20
square both  side  to  remove  the square root  sign
155^2/76^2 =y/20
by cross multiplication  y={(24025  x  20)/5776}=83.18

the  gas  is  krypton  since  83 is  one  isotope  of krypton

Answer 2

Answer: The other gas is Krypton (Kr).

Explanation: The rate of effusion of gas is given by Graham's Law.

Graham's Law states that the rate of effusion of gas is inversely proportional to the square root of their atomic masses.

Mathematically,

$\text{Rate of effusion}=\frac{1}{\sqrt{\text{Molar mass}}}$

Rate of effusion is the amount of gas effused in a given time 't'

Mathematically,

$\text{Rate of effusion}=\frac{V}{t}$

As per the question:

For Neon:

$t_1=76sec\\M_1=20$

For unknown gas:

$t_2=155sec\\M_2=?$

$V_{neon}=V_{\text{unknown gas}}$

Putting values in rate of effusion formula, we get:

$\frac{\frac{V_{neon}}{t_1}}{\frac{V_{\text{unknown gas}}}{t_2}}=\sqrt{\frac{M_2}{M_1}}$

$\frac{155}{76}=\sqrt{\frac{M_2}{20}}$

$M_2=83.150$

This mass corresponds to the mass of Krypton noble gas.