Question

The density of a gas is found to be $1.56g{L^{ - 1}}$ at $745mm$ pressure and ${65^ \circ }C$. What is the molecular mass of the gas?
A: $44.2u$
B: $4.42u$
C: $2.24u$
D: $22.4u$

Answer 1

Density of a substance is measured as mass of the substance per unit volume of that substance. Molecular mass of the substance is the mass of one molecule of that substance and molar mass is the mass of one mole of a substance.
Formula used: $P = \dfrac{{dRT}}{M}$
Where, $P$ is pressure in $atm$, $d$ is density in $g{L^{ - 1}}$, $R$ is gas constant in $Latm{K^{ - 1}}mo{l^{ - 1}}$, $T$ is temperature in $K$ and $M$ is molecular mass.

Complete step by step answer:
In this question we have given pressure, density and temperature of the gas and we have to find molecular mass of gas. Pressure that is given is $745mm$ but we need pressure in $atm$. We know that:
$1mm$ of $Hg = \dfrac{1}{{760}}atm$
Therefore, $745mm$ of $Hg = \dfrac{{745}}{{760}}atm$
This means pressure $\left( P \right)$ is $\dfrac{{745}}{{760}}atm = 0.98atm$
Given temperature $\left( T \right)$ is ${65^ \circ }C$ but we need temperature in Kelvin and we know:
${0^ \circ }C = 273K$
This means, ${65^ \circ }C = 273 + 65K = 338K$
So, temperature $\left( T \right)$ is $338K$
Value of gas constant $\left( R \right)$ is $0.0821Latm{K^{ - 1}}mo{l^{ - 1}}$
Density is $\left( d \right)$ $1.56g{L^{ - 1}}$ (given)
We have to find the molecular mass of the gas. This can be found by using the formula:
$P = \dfrac{{dRT}}{M}$
Substituting the values of known quantities:
$0.98 = \dfrac{{1.56 \times 0.0821 \times 338}}{M}$
$M = \dfrac{{1.56 \times 0.0821 \times 338}}{{0.98}}$
Solving this we get,
$M = 44.2$
This means molecular mass of gas is $44.2$.
So, the correct answer is option A that is $44.2u$.

Note:
The formula we used in this question is derived from the ideal gas equation. In this equation some assumptions are made and gas is assumed to be ideal. These assumptions are:
Gas consists of a very large number of molecules which are in random motion and obey newton’s law of motion.
Volume of particles is negligible as compared to the volume occupied by gas.
Only the force during elastic collision acts on molecules.