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# The volume of mole of a perfect gas at NTP is:A) $22.4$ $litres$B) $2.24$ $litres$C) $100$ $litres$D) None of these

Last updated date: 20th Jun 2024
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Hint: In chemistry the mole is an amount unit. One mole of substance is defined as the amount of substance containing the same number of discrete atoms as the number of atoms in a sample of pure $12C$ weighing exactly $12 g$. Experimentally it was determined that one mole of a substance comprises $6.02214179 \times {10^{23}}$ atoms. This number is known as Avagadro’s number.

Complete step by step answer:
We know that the equation for state of an ideal gas is given by,
$PV = nRT$
Where. P is absolute pressure of the gas, V is the volume of gas, T is the temperature of the gas in kelvin. N is the number of moles of the gas and R is the universal gas constant which has a value of $8.314 J/mol-K$. Hence, volume of an ideal gas can be determined by the following equation
$V = \dfrac{{nRT}}{P}$………….(1)
We know that. At N.T.P, temperature is $T$ = $293.15 K \left( {{{20}^o}C} \right)$ and and pressure is $P$ = $1 atm$ = $101.325 kPa$, putting these values along with the value of universal gas constant ($R = 8.314 J/mol-K$) in equation (1), for one mole of ideal gas (n = 1) we get,
$V = \dfrac{{1 \times 8.314 \times 293.15}}{{101.325}}$
$V = 24.054 l$
Hence, at N.T.P the volume of an ideal gas is $24.05$ $litres$. Therefore, we can say that none of the given options are in agreement with our solution.

Hence option D is the correct answer option.

Note: There is a difference between N.T.P and S.T.P and it is mentioned below.
S.T.P stands for standard temperature and pressure. At S.T.P the temperature is $T = {0^o}C$ and pressure is $P = 100 kPa$.
N.T.P stands for normal temperature and pressure. At N.T.P the temperature is $T = {20^o}C$ and pressure is $P =101.325 kPa$.