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. $16\;{N_A}\;gm$

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 $C{H_4}$ = $\dfrac{{16}}{{6.022 \times {{10}^{23}}}} = 2.66 \times {10^{ - 23}}\;gm$

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.