Question

The perfect gas equation for $4$grams of hydrogen gas is:
A. $PV = RT$
B. $PV = 2RT$
C. $PV = \dfrac{1}{2}RT$
D. $PV = 4RT$

Answer 1

Hint: The general equation of perfect gas is to be used. From the given values in question, after calculating the number of moles of the equation, the answer can be obtained.
By using formula: $I - $ideal perfect gas equation
$PV = nRT$
Where $P$indicates volume ,$n$ represents no. of moles,$R$ is a gas constant and $T$ is temperature.

Complete step by step answer:
We know that number of moles of a gas is given by
\[n = \dfrac{{given\,mass}}{{molar\,\,mass}} = \dfrac{m}{M}\]
Where $m$signifies available mass of gas and $M$signifies the molar mass of the gas. For hydrogen gas,
Molar mass, $M = 2g\,mol$
And given mass ,$m = 4g$
So, no of moles $\dfrac{4}{2} = 2\,moles$
Now, the ideal gas equation is given by $PV = nRT$
Where $P$denotes pressure, $V$ is volume, $n$ is no. of moles, $R$ is gas constant, $R = 3.314$ and $T$ is temperature.
For $4g$ of hydrogen gas,
No. of moles, $n = 2$
So, the ideal gas equation becomes
$PV = (2)RT$
$PV = 2RT$
Hence, the correct option is B.

Note:This can also be solved by unitary method to find numbers of moles of hydrogen gas. Molar mass of hydrogen gas $ = 2g/mol$. This means,
Corresponding $2g$of hydrogen gas, no. of moles $ = 1$mole
Corresponding to $1g$of hydrogen gas, no. of moles $ = \dfrac{1}{2}$mole
Corresponding to $4g$of hydrogen gas, no. of moles $ = \dfrac{4}{2} = 2moles$
So, $n = 2$moles,
Also, no gas is perfectly ideal as ideal gas has no interactions within its particles and thus no kinetic energy of particles which is not possible.