Question

The equation of state for $5\;{\rm{g}}$ of oxygen at a pressure $P$ and temperature $T$, when occupying a volume V, will be (where $R$ is the gas constant)
(A) $PV = \dfrac{5}{{32}}RT$
(B) $PV = 5RT$
(C) $PV = \dfrac{5}{{2}}RT$
(D) $PV = \dfrac{5}{{16}}RT$

Answer 1

Here, we will use the hypothetical ideal gas formula. The ideal gas formula requires the number of moles in a gas. We calculate the number of moles in the oxygen gas by dividing the total mass to the molar mass of the oxygen.

Complete step by step answer:
Given: The gas given in the question is Oxygen, the mass of the oxygen gas is $m = 5\;{\rm{g}}$, the pressure of the gas is $P$, the temperature of the gas is $T$ and volume occupied by the gas is $V$.
We write the equation for the ideal gas,
$PV = nRT$
Here, $R$ is the gas constant and $n$ is the number of moles in the oxygen gas.
Now, we write the formula to find the number of moles in oxygen gas,
$n = \dfrac{m}{M}$
Here, $M$ is the molecular mass of the oxygen gas.
There are two atoms in an oxygen molecule and the atomic number of the oxygen is $16$. Then, we calculate the molecular mass of oxygen by multiplying the number of atoms in an oxygen molecule to the atomic number of the oxygen.
$\begin{array}{l} M = 16 \times 2\\\ M = 32 \end{array}$
We put this value in the equation of number of moles,
$n = \dfrac{5}{{32}}$
Now, we have the value of number of moles in oxygen, then putting this value of $n$ in ideal gas equation,
$PV = \dfrac{5}{{32}}RT$

Therefore, the equation for the state of oxygen is $PV = \dfrac{5}{{32}}RT$.

So, the correct answer is “Option A”.

Note:
We should know that the ideal gas equation is also termed as the general gas equation. In the ideal gas equation, we can say that the pressure is proportional to the number of moles in a gas. This equation holds well as long as we keep the value of density as minimum.