Question

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

Answer 1

Hint: For a perfect gas, the general gas equation is given as $PV = nRT$. For the given question, we need to calculate the number of the mole of hydrogen. We are given the amount of gas from which number of moles can be calculated.

Formula used:
The ideal gas equation is given as
$PV = nRT$
where pressure is represented by P, volume is represented by V, n signifies the number of moles of the given gas while T is the temperature of the gas.

R is called the universal gas constant. Its value is given as

R$= 8.314J/mol{\text{ K}}$

No. of moles of the gas is given as

$n = \dfrac{m}{M}$

where m signifies the available amount of gas and M signifies the molar mass of the gas.

Detailed step by step solution:
We are given that we have 4 g of hydrogen gas. We need to calculate the number of moles of the gas.

$m = 4g$

The molar mass of a hydrogen atom is 1 g/mol. For hydrogen gas molecules, we have two hydrogen atoms. Therefore, for hydrogen gas, the molar mass is given as

$M = 2g/mol$

Now, we can calculate the number of moles of hydrogen gas as follows:
$n = \dfrac{m}{M} = \dfrac{4}{2} = 2mol$

Now we can write the ideal gas equation for 4 g of hydrogen gas as follows
$PV = 2RT$

Hence, the correct answer is option B.

Note: An ideal gas has no interactions within its particles. There particles of the gas possess kinetic energy but they do not have any potential energy. Practically, such types of gases do not exist. There are always some interactions between the particles of a gas.