Question

Select one correct statement. In the gas equation, $PV=nRT$.
(a)- n is the number of molecules of a gas
(b)- n moles of the gas has a volume V
(c)- V denotes the volume of one mole of the gas
(d)- P is the pressure if the gas when only one mole of gas is present

Answer 1

Hint: If the ideal gas equation is written as $PV=nRT$ then all the properties are for n mole of gas. If the ideal gas equation is written as $PV=RT$ then all the properties are for 1 mole of gas.

Complete step by step answer:
$PV=nRT$is an ideal gas equation that is used for calculating a certain property of the gas at specified conditions.
The ideal gas equation is directly by combining all the statements of gas laws like Boyle’s law, Charles Law, and Avogadro’s Law, which follows as:
Boyle’s law states that:
$V\propto \dfrac{1}{P}$ at constant T
Charles law states that:
$V\propto T$ at constant P
Avogadro’s law states that:
$V\propto n$ at constant T and P
In these, all statements n is the number of moles at V (volume) and P (pressure) of the gas at T (temperature).
So, by combining all these, we get:
$V\propto \dfrac{1}{P}\text{ x T x n}$
Removing the proportionality, we introduce a constant known as gas constant and is denoted with R.
So, the equation is:
$V=\dfrac{RTn}{P}$
$PV=nRT$.

So, the correct answer is an option (b)- n moles of the gas have a volume V.

Note: If it is specified that the number of moles is 1 then, the equation is $PV=RT$. It is also known as the equation of state. Some values of gas constant (R) taken are $0.0821\text{ l atm de}{{\text{g}}^{-1}}\text{ mo}{{\text{l}}^{-1}}$, $8.314\text{ x 1}{{\text{0}}^{7}}\text{ ergs de}{{\text{g}}^{-1}}\text{ mo}{{\text{l}}^{-1}}$, $8.314\text{ J}{{\text{K}}^{-1}}\text{ mo}{{\text{l}}^{-1}}$ etc.