Question

Given a $4g$ sample each of ${H_2}\left( g \right)$ and $He\left( g \right)$, in separate containers. Which of the following statements is true? (Assume STP)
A: The sample of hydrogen gas will occupy $44.8{\text{ }}liters$ and the sample of helium will contain $6.02 \times {10^{23}}$ molecules.
B: The sample of hydrogen gas will occupy ${\text{22}}{\text{.4 }}liters$ and the sample of helium will contain $3.02 \times {10^{23}}$ molecules.
C: The sample of hydrogen gas will occupy $44.8{\text{ }}liters$ and the sample of helium will contain $1.202 \times {10^{24}}$ molecules.
D: The sample of hydrogen gas will occupy $44.8{\text{ }}liters$ and the sample of helium will contain $6.0 \times {10^{23}}$ molecules.
E: None of the above statement

Answer 1

STP stands for standard temperature and pressure conditions. Temperature, pressure and volume of a gas is defined at this condition. STP temperature is $273.15K$ and pressure is ${10^5}Pa$. Volume of one mole of gas at STP is $22.4L$.
Formula used: number of moles$= \dfrac{{{\text{given mass}}}}{{{\text{molecular mass}}}}$
Volume of gas at STP$= 22.4L$
Number of particles of gas at STP$= 6.02 \times {10^{23}}$

Complete step by step answer:
In this question we have given $4g$ of hydrogen and helium at STP conditions and we have to find the volume of hydrogen gas and number of molecules of helium gas. For this first we have to find out the number of moles of a gas at STP and volume of gas at STP.
At STP one mole of a gas occupy $22.4L$ of volume. Mass of one mole of gas is equal to the molecular mass of the gas. Molecular mass of hydrogen gas is two gram. Given mass of hydrogen gas is $4g$. From this we can calculate number of moles of hydrogen gas using the formula:
Number of moles$= \dfrac{{{\text{given mass}}}}{{{\text{molecular mass}}}}$
Here, molecular mass is $4g$ and given mass is $2g$. Substituting these values in above formula:
Number of moles$= \dfrac{4}{2} = 2$
So, the number of moles of hydrogen gas is two. We know that one mole of gas at STP occupies $22.4L$. Therefore, two moles of gas will occupy,
Volume of two moles of hydrogen gas$= 2 \times 22.4 = 44.8L$
So, the volume of hydrogen gas is $44.8{\text{ }}liters$.
Now, the molecular mass of helium is $4g$ and the given mass of helium is also $4g$. So number of moles f helium gas is,
Number of moles$= \dfrac{4}{4} = 1$
Number of moles of helium gas is one and we know there are $6.0 \times {10^{23}}$ particles in one mole of a gas. Therefore the number of molecules of helium gas is $6.0 \times {10^{23}}$.
So, the correct answer is option .

Note:
The volume of one mole of any gas at STP conditions is $22.4L$ and the number of molecules in one mole of any gas is $6.02 \times {10^{23}}$. Number of molecules of a gas in one mole doesn’t depend on temperature, pressure and volume. Number of molecules in one mole is always constant, that is $6.02 \times {10^{23}}$.