Question

Equal volume of ${H_2}$, ${O_2}$ and the gases are at temperature and pressure. Which of these with large number of molecules:
A. ${H_2}$
B. ${O_2}$
C. He
D. All the gases will have same number of molecules

Answer 1

Hint: For the ideal gases hydrogen, oxygen and helium ideal gas equation is used to calculate the number of moles. The number of molecules present in the gases is calculated by multiplying the number of moles with the Avagadro’s number.

Complete step by step answer:
The ideal gas law deals with the ideal gases which is a combination of Boyle's law and Charles law.
Boyle's law states that for a particular mass of compound at constant temperature, the pressure of the gas is inversely proportional to the volume of gas.
The Charles law states that for a particular fixed mass of compound which is held at constant pressure, the volume of the gas is directly proportional to the temperature of the gas.
The combination of these laws, Ideal gas equation is determined which gives the relation between the pressure, volume, number of moles and temperature.
The ideal gas equation is given as shown below.
$PV = nRT$
Where,
P is the pressure
V is the volume
T is the temperature
n is the number of moles
R is the universal gas rate constant
From the above equation, the number of moles is calculated as shown below.
$\Rightarrow$ $n = \dfrac{{PV}}{{RT}}$
From the above equation, we can see that the number of moles remains the same under the same physical conditions as equal volumes are mixed at the same temperature and pressure.
The number of molecules is calculated as shown below.
$Number\;of\;molecules = n \times {N_A}$
Where,
${N_A}$ is Avagadro’s number.
Thus, the number of molecules will remain the same in all the gases.
So, the correct answer is “Option D”.

Note: Don’t get confused in the number of moles and number of molecules as both are different and have different formulas for calculating. As numbers of moles are the same, the number of molecules will also be the same as Avagadro’s law states that for similar conditions of temperature and pressure, the gases with the same volume contain the same number of molecules.