Question

densities of two gases are in the ratio 1:2 and their temperature are in the ratio 2:1 then the ratio of their respective molar mass at certain pressure is

Answer 1

Here is the answer to the question..
Hope you got it

Answer 2

Answer: The ratio of their molar masses is 1 : 1

Explanation:

Assuming ideal gas behavior, the equation follows:

PV = nRT

where,

P = pressure of the gas

V = volume of the gas

n = number of moles of the gas

R = Gas constant

T = temperature of the gas

We know that:

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$

Rearranging the above equation:

$P=\frac{m}{M}\frac{RT}{V}$

We know that:

$density=\frac{Mass}{Volume}$

Rearranging the above equation:

$M=\frac{dRT}{P}$

Pressure and Gas constant are taken as constant in accordance to the question, so:

$M=d\times T$

We are given:

$\frac{d_1}{d_2}=\frac{1}{2}$

$\frac{T_1}{T_2}=\frac{2}{1}$

Taking the ratio of molar masses of both the gases, we get:

$\frac{M_1}{M_2}=\frac{1}{2}\times \frac{2}{1}=\frac{1}{1}$

Hence, the ratio of their molar masses is 1 : 1