Question

What is the density of hydrogen gas using the ideal gas law?

Answer 1

Hint : The ideal gas law, also known as the general gas equation, is the equation of state for a hypothetical ideal gas. Although it has several shortcomings, it is a rational estimate of the behaviour of such gases under a variety of conditions.

Complete Step By Step Answer:
The chemical element with atomic number $1$ and an atomic mass of \[1.00794\]$amu$, the lightest of all known atoms, is hydrogen, the most common element in the universe. It occurs in the form of a diatomic gas.
To find the density of hydrogen gas we use the ideal gas law.
The Ideal gas law states that:
$PV = nRT$
Here,
$P$is the absolute pressure of a gas,
$V$is the volume it occupies,
$n$is the number of atoms and molecules in the gas
And $T$is its absolute temperature.
It is known to us that$n = \dfrac{m}{M}$, $M$is the molar mass and $m$is the mass of the substance measured in the grams.
Substituting the above equation in the gas law, we get:
$pV = \dfrac{m}{M}RT$
$ \Rightarrow pM = \dfrac{m}{V}RT$
We know that the density of the compound $\rho = \dfrac{m}{V}$. Thus, by substituting this relation in the above equation becomes:
$ \Rightarrow pM = \rho RT$
Therefore,
$ \Rightarrow \rho = \dfrac{{pM}}{{RT}}$
To find the density of hydrogen gas, we use the standard conditions of $P = 1$$atm$and $T = 298K$.
We know that the molar mass of ${H_2} = 2.012gmo{l^{ - 1}}$
Substituting the values to the above equation,
${\rho _{{H_2}}} = \dfrac{{1 \cdot atm \times 2.016 \cdot g \cdot mo{l^{ - 1}}}}{{0.0821 \cdot \dfrac{{L \cdot atm}}{{K \cdot mol}} \times 298 \cdot K}} \cong 0.1 \cdot g \cdot {L^{ - 1}}$
Thus, the density of hydrogen gas found using the ideal gas law is $0.1g{L^{ - 1}}$

Note :
The term "ideal gas" refers to a hypothetical gas composed of molecules that follow a series of rules: The molecules of an ideal gas are neither attracted nor repellent to one another. The only interaction ideal gas molecules can have will be an elastic collision when they collide with each other or the container's sides.