Question

The mass of a hydrogen molecule is 2.016 amu. Therefor the number of hydrogen molecules in 4.032gm of hydrogen will be:
A. \[6.023\times {{10}^{21}}\]
B. \[2\times 6.023\times {{10}^{23}}\]
C. \[4\times 6.023\times {{10}^{23}}\]
D. \[2\times 6.023\times {{10}^{21}}\]

Answer 1

Hint: So, the atomicity of hydrogen is two and the atomic weight of a hydrogen molecule is 1.08 amu. And we know that 1 amu = \[1.6603\times {{10}^{-24}}gms\], so by using this information we can find the number of hydrogen molecules.

Complete-step- by- step answer:
We know by the atomicity of hydrogen that the formula of a hydrogen molecule is: \[{{H}_{2}}\]. Atomic Mass Units (amu): a mass exactly equal to one-twelfth mass of carbon-12 atom. One amu is the average of the proton rest mass and the neutron rest mass. The mass of an atom in AMU is roughly equal to the sum of the number of protons and neutrons in the nucleus.
And we know that the mass of the hydrogen atom = 1.08 amu
So, the mass of one hydrogen molecule is (also given) = 2 x 1.08 amu
                                                                                        = 2.016 amu
We know that,
1 amu = \[1.6603\times {{10}^{-24}}gms\].
Mass of one hydrogen molecule (in gms) = \[2.016\times 1.6603\times {{10}^{-24}}gms\]
                                                                = 3.3472\[\times {{10}^{-24}}gms\]

So, 3.3472\[\times {{10}^{-24}}gms\]of hydrogen contains one molecule of hydrogen.
\[3.3472\times {{10}^{-24}}gms\to \] 1 molecule

So, in 4.032gm of hydrogen:
\[4.032gms\to \] \[\dfrac{1\times 4.032}{3.3472\times {{10}^{-24}}}\]
Number of hydrogen molecules in 4.032gm = \[\dfrac{1\times 4.032}{3.3472\times {{10}^{-24}}}\]

= 1.2046 \[\times {{10}^{24}}\] molecules =\[2\times 6.023\times {{10}^{23}}\]

So, the correct option is “B”.

Note: Here, in this problem you should know the conversion factor of amu in grams. And also we should know the atomicity of the hydrogen molecule which is two.