Question

A container is filled with oxygen and helium at the same temperature. The molar mass of oxygen is 32 g/mol and that of helium is 4 g/mol. What is the ratio: average speed of oxygen molecules ________ average speed of helium molecules? A. 1 ----- √8 B. √8 C. 1 ------ 8 D. 8..​

Answer 1

Answer:

A) option  1 ----- √8

Explanation:

Answer 2

Given: A container is filled with oxygen and helium at the same temperature. The molar mass of oxygen is 32 g/mol and that of helium is 4 g/mol.

To find: Ratio of average speed of oxygen molecules and average speed of helium molecules

Explanation: Average speed of a molecule is directly proportional to the square root of the temperature at which the gas is kept and indirectly proportional to the molar mass of the gas.

The formula of the average speed is:

$\sqrt{ \frac{8Rt}{\pi \times m} }$

where R is gas constant, t is temperature of the gas and m is the molar mass of the gas.

Since the temperature for both gases is same and 8R/π is a constant, therefore the average speed depends inversely on the molar mass of gas.

Let average speed of oxygen be v1 and average speed of helium be v2.

Molar mass of oxygen (m1) = 32 g/mol

Molar mass of helium (m2) = 4 g/mol

Using formula:

=>$\frac{v1}{v2} = \sqrt{ \frac{m2}{m1} }$

=>$\frac{v1}{v2} = \sqrt{ \frac{4}{32} }$

=>$\frac{v1}{v2} = \sqrt{ \frac{1}{8} }$

Therefore the ratio of average speed of oxygen molecules and helium molecules is option (a) 1 : ✓8