Question

A container is filled with oxygen and helium at the same temperature. The molar mass of oxygen is 32 Q169 g/mol and that of helium is 4 g/mol . What is the ratio: average speed of oxygen molecules average speed of helium molecules I B 18​

Answer 1

Answer:

Molecular weight of Helium M

1

=4

Molecular weight of O

2

M

2

=32

Assuming their root mean square velocities to be equal, we get

V

rms2

V

rms1

=

P

2

M

1

P

1

M

2

(∵V=constatnt)

Assuming their V

rms

velocities to be equal

1=

P

2

(4)

P

1

(32)

P

2

=8P

1

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

Now, temperature is constant and 8R/π has a constant value for all gases. Therefore, the speed depends only on molar mass of the gas.

Let average speed of oxygen and its molar mass be v1 and m1 respectively and average speed and molar mass of helium be v2 and m2 respectively.

m1 = 32 g/ mol

m2 = 4 g/mol

Using formula:

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

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

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

=>$\frac{v1}{v2} = \frac{1}{2.83}$

=>v1 : v2 = 1: 2.83

Therefore, the ratio of the average speed of oxygen and helium molecules is in the ratio 1 : 2.83.