Question

What is the mass of a molecule of $C{H}_4$ ?
A. 16 gm
B. $26.6\times {10}^{22}gm$
C. $2.66\times {10}^{-23}gm$
D. $16N_{A}gm$

Answer 1

Hint: We should know gram atomic masses of Carbon and Hydrogen.
The complete gram molecular mass of $C{H}_4$ will be for one mole substance.
Calculate for a molecule of $C{H}_4$ using Avogadro number.

Complete step by step answer:
First of all we must know the Gram Atomic mass of Carbon and Hydrogen, which is 12 gm and 1 gm respectively.
Now we find gram molecular mass of $C{H}_4$ by the following formula:
Gram molecular mass of $C{H}_4$ = gram atomic mass of Carbon + 4 $\times$ gram atomic mass of Hydrogen.
Gram molecular mass of $C{H}_4$ = 12 + 4 X 1
Gram molecular mass of $C{H}_4$ = 12 + 4
Gram molecular mass of $C{H}_4$ = 16 gm.
Now we know that 16 gm is gram molecular mass of $C{H}_4$ , that is the mass of 1 mole $C{H}_4$ is 16 gm.
But it is asked to us to calculate the mass of a molecule of $C{H}_4$ .
Mass of 1 mole $C{H}_4$ = 16 gm
We know 1 mole $C{H}_4$ = $$6.022\times {10}^{23}$$ molecules of $C{H}_4$.

Therefore, mass of 1 molecule of $C{H}_4$ = ${\displaystyle \frac{16}{6.022\times {10}^{23}}}=2.66\times {10}^{-23}gm$

So option (C) $2.66\times {10}^{-23}gm$ is correct.

Additional information: Alternative method:
We can calculate the mass of 1 molecule of $C{H}_4$ in amu.
So, Mass of 1 molecule of $C{H}_4$ = mass of 1 atom of Carbon + 4 $\times$ mass of 1 atom of Hydrogen.
Mass of 1 molecule of $C{H}_4$ = 12 + 4 X 1
Mass of 1 molecule of $C{H}_4$ = 16 amu
We know 1 amu = $1.67\times {10}^{-24}gm$
$$\therefore 16amu=16\times 1.67\times {10}^{-24}gm=2.66\times {10}^{-23}gm$$

So, the correct answer is “Option C”.

Note: It is very likely and common mistake to take gram molecular mass as mass of 1 molecule.
But we should know these terms clearly, and gram molecular mass is mass of 1 mole substance, not mass of one molecule.