Question

Compute gram molecular weight of ${H_2}$ gas if 4 g of gas contains $24.09 \times {10^{23}}$ atoms:
(A) 4 g
(B) 3 g
(C) 2 g
(D) 1 g

Answer 1

Hint: First find the total number of moles of atoms present in a given number of atoms. Then we can easily find the gram molecular weight of hydrogen gas by using the concept of number of moles.

Complete Step-by-Step Solution:
Gram molecular weight is the molecular weight expressed in $gmo{l^{ - 1}}$ unit only. We will use the definition of moles to find the gram molecular weight of hydrogen gas.
- We know that one molecule of ${H_2}$ gas contains two atoms. So, one mole of ${H_2}$ gas will contain 2 moles of atoms.
- We know that $6.022 \times {10^{23}}$ atoms or molecules in one mole quantity.
- We can say that one mole of hydrogen gas contains $2 \times 6.022 \times {10^{23}}$ = $12.044 \times {10^{23}}$ number of atoms.
- We are given that the number of atoms present in the gas is $24.09 \times {10^{23}}$ .
So, we can say that the number of moles of the gas will be equal to the total number of atoms present divided by the number of atoms present in one mole of the gas.
So, we can say that
\[{\text{Number of moles of }}{{\text{H}}_2} = \dfrac{{{\text{Total atoms}}}}{{{\text{No}}{\text{. of atoms present in 1 mole of }}{{\text{H}}_2}}}\]
So, we can write that
\[{\text{Number of moles of }}{{\text{H}}_2} = \dfrac{{24.09 \times {{10}^{23}}}}{{12.04 \times {{10}^{23}}}} = 2\]
Thus, we obtained that the number of moles of hydrogen gas (${H_2}$) present is 2 moles.
Now, we can say that the weight of 2 moles of hydrogen gas is 4 g. So, the weight of 1 mole of hydrogen gas will be $\implies\dfrac{4}{2} = 2$ g.
- We know that molecular weight is the weight of 1 mole of any species.
Thus, we obtained that gram molecular weight of ${H_2}$ is 2 g.

So, the correct answer is (C).

Note: Here, a common mistake that can occur is we assume that a number of molecules is given to us. Actually the number of atoms present in the gas is provided. Thus, double the number of atoms will be present in the gas than the number of molecules as the gas is ${H_2}$.