Question

How many grams of hydrogen is present in $8.5g{\text{ }}NH3$?
(a) $1.5$
(b) $0.5$
(c) $0.08$
(d) None of the above

Answer 1

The gram atoms is the atomic mass of a substance expressed in grams. In a compound, gram atom of a substance can be calculated as:
$Gram{\text{ }}atom = {\text{ }}Atomic{\text{ }}mass{\text{ }}of{\text{ }}the{\text{ }}substance \times {\text{ }}number{\text{ }}of{\text{ }}moles{\text{ }}of{\text{ }}compound$

Complete step by step answer:
As we know that the atomic mass of an element is the number of times an atom of the element is heavier than an atom of a carbon taken as$12$ . The atomic mass of an atom expressed grams is called Gram Atomic Mass. The amount of the element is called one gram atom. A mole is defined as that amount of the substance which has mass equal to gram atomic mass if the substance is atomic or gram molecules are masked if the substance is molecular.
i.e. $Number{\text{ }}of{\text{ }}moles{\text{ }}of{\text{ }}substance = \dfrac{{Given{\text{ }}mass{\text{ }}of{\text{ }}substance}}{{Molecular{\text{ }}mass{\text{ }}of{\text{ }}substance}}{\text{ }}$ -(i)
Molecular mass of a substance is the number of times the molecules of the substance are heavier than $1/12th$ mass of an atom of $carbon - 12$ isotope.
The molecular mass of substance expressed in grams is called gram molecular mass.
Now firstly we have to calculate the molecular mass of $N{H_3}$ which can be calculated as:
$molar{\text{ }}mass{\text{ }}of{\text{ }}N{H_3} = {\text{ }}1 \times {\text{ }}Atomic{\text{ }}mass{\text{ }}of{\text{ }}N{\text{ }} + {\text{ }}3 \times {\text{ }}Atomic{\text{ }}mass{\text{ }}of{\text{ }}H$
We know that gram atomic mass of $N$ is $14{\text{ }}gram$ and that of $H$ is$1$ .So on putting values in above equation, we get
$Molar{\text{ }}mass{\text{ }}of{\text{ }}N{H_3} = {\text{ }}1 \times {\text{ }}14 + {\text{ }}3 \times 1{\text{ }} = 17g$
The given mass of $N{H_3}$ is $8.5{\text{ }}g$. So the number of moles of $N{H_3}$ present can be calculated by equation (i), we get
$Number{\text{ }}of{\text{ }}moles{\text{ }}of{\text{ }}N{H_3} = \dfrac{{given{\text{ }}mass{\text{ }}of{\text{ }}N{H_3}}}{{Molar{\text{ }}mass{\text{ }}of{\text{ }}N{H_3}}}{\text{ }} \\\ Number{\text{ }}of{\text{ }}moles{\text{ }}of{\text{ }}N{H_3} = \dfrac{{8.5g}}{{17g}} = 0.5mole \\\$
The gram atoms of an element present in the molecule can be calculated as:
$Gram{\text{ }}atoms{\text{ }}of{\text{ }}substance = Atomic{\text{ }}mass{\text{ }}of{\text{ }}the{\text{ }}element \times Number{\text{ }}of{\text{ }}moles{\text{ }}of{\text{ }}molecules\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;$ -(ii)
We have to find the gram atoms of hydrogen in $N{H_3}$ having atomic mass $1$. Since $3$ atoms of hydrogen is present, so the combined atomic mass of hydrogen is $3$ and the number of moles of $N{H_3}$ present is $0.5{\text{ }}mole$ . So putting value in equation (ii) we get
$Gram{\text{ }}atom{\text{ }}of{\text{ }}H{\text{ }}in{\text{ }}N{H_3} = {\text{ }}3 \times 0.5 = {\text{ }}1.5{\text{ }}gram{\text{ }}atoms$
So $1.5{\text{ }}g{\text{ }}atom{\text{ }}of{\text{ }}H{\text{ }}is{\text{ }}present{\text{ }}in{\text{ }}8.5{\text{ }}g{\text{ }}of{\text{ }}N{H_3}$ .

So, the correct answer is Option A.

Note: Number of gram atoms and number of atoms in a substance both are different things number of atoms can be expressed as
$Number\; Of \;Atoms = 6.022{{ \times }}{10^2}^3{{ \times }}number\;of\;gramatoms$