Question

A sample of neon effuses from a container in 72 seconds. the same amount of an unknown noble gas requires 147 seconds. you may want to reference (pages 442 - 444) section 10.9 while completing this problem. part a identify the second gas.

Answer 1

Answer: The unknown noble gas is Krypton.

Step-by-step explanation:

Rate of effusion is defined as the amount of volume displaced per unit time.

`\text{Rate of effusion}=(V)/(t)`

To calculate the rate of diffusion of gas, we use Graham's Law.

This law states that the rate of effusion or diffusion of gas is inversely proportional to the square root of the molar mass of the gas. The equation given by this law follows the equation:

`\text{Rate of diffusion}\propto \frac{1}{\sqrt{\text{Molar mass of the gas}}}`

We are given:

Time taken by neon gas = 72 s

Time taken by unknown gas = 147 s

Molar mass of neon gas = 20.18 g/mol

By taking their ratio, we get:

`\frac{(V)/(t_(Ne))}{\frac{V}{t_{\text{unknown gas}}}}=\sqrt{\frac{M_(Ne)}{M_{\text{unknown gas}}}}\\\\\\(147)/(72)=\sqrt{\frac{M_{\text{unknown gas}}}{20.18}}\\\\M_{\text{unknown gas}}=84.11g/mol`

The noble gas having molar mass of 84.11 g/mol is Krypton

Hence, the unknown noble gas is Krypton.

Answer 2

The second gas is identified as follows

by Graham law formula
let the unknown gas be represented by letter y

=time of effusion of Neon/ time of effusion of y = sqrt (molar mass of neon/molar mass of y)

= 72 sec/ 147 sec = sqrt( 20.18 g/mol/ y g/mol)

square the both side to remove the square root sign

72^2/147^2 = 20.18 g/mol/y g/mol

=0.24 = 20.18g/mol/y g/mol

multiply both side by y g/mol
= 0.24 y g/mol = 20.18g/mol
divide both side by 0.24
y = 84 g/mol

y is therefore Krypton since it is the one with a molar mass of 84 g/mol