Question 147: Thermodynamics & KTG

Question

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their
partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their
densities is

Accepted Answer

To determine the ratio of the densities of the two non-reactive monoatomic ideal gases, we can use the ideal gas law and the given information. The ideal gas law is given by:
$$ PV = nRT $$
Where:
P
is the pressure
V
is the volume
n
is the number of moles
R
is the gas constant
T
is the temperature
Given that the gases are monoatomic and non-reactive, their molecular masses are directly proportional to their atomic masses. Let the atomic masses of the two gases be $M_1$ and $M_2$, with $M_1 : M_2 = 2 : 3$.
The density ($ho$) of a gas is given by the formula:
$$ ho = \frac{m}{V} $$
Where $m$ is the mass and $V$ is the volume. Using the ideal gas law, we can relate density to pressure and temperature.
From the ideal gas law:
$$ PV = nRT $$
Since $ n = \frac{m}{M} $, where $M$ is the molar mass, we have:
$$ P = \frac{mRT}{MV} $$
Rearranging to solve for density ($ho\ = \frac{m}{V}$):
$$ ho = \frac{PM}{RT} $$
Thus, the density of a gas is directly proportional to its pressure and molar mass, and inversely proportional to the temperature. Given that the ratio of their partial pressures $P_1 : P_2 = 4 : 3$, we can write:
$$ ho_1 = \frac{P_1 M_1}{RT} $$
$$ ho_2 = \frac{P_2 M_2}{RT} $$
Taking the ratio of the densities:
$$ \frac{ho_1}{ho_2} = \frac{\left(\frac{P_1 M_1}{RT}ight)}{\left(\frac{P_2 M_2}{RT}ight)} = \frac{P_1 M_1}{P_2 M_2} $$
Substituting the given ratios, $ P_1 : P_2 = 4 : 3 $ and $ M_1 : M_2 = 2 : 3 $, into the equation, we get:
$$ \frac{ho_1}{ho_2} = \frac{4 	imes 2}{3 	imes 3} = \frac{8}{9} $$
Therefore, the ratio of their densities is $ \frac{8}{9} $, which corresponds to option D. Consequently, the answer is:
Option D: 8 : 9

Answer

1 : 4

Answer

1 : 2

Answer

6 : 9

Answer

8 : 9

Thermodynamics & KTG

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is

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