Question

A sample of ammonium phosphate ${\left( {N{H_4}} \right)_3}P{O_4}$ contains 3.18 moles of H-atom. The number of moles of $O - atom$ in the sample is:
A) $0.265$
B) $0.795$
C) $1.06$
D) $3.18$

Answer 1

We know that mole is a fundamental unit for measuring the amount of substance. According to the mole concept, Number of atoms or molecules is given as,
Number of atoms and molecules $= \left( {{\rm{Number}}\,{\rm{of}}\,{\rm{Moles}}} \right) \times \left( {6.022 \times {{10}^{23}}} \right)$
And the relationship between the gram and the atomic mass unit (amu) is given as,

1 amu = $\dfrac{\text{1 gram}}{6.022 \times 10^{23}}$ = 1.66 $\times$ 10$^{-24}$ grams

Complete step-by-step solution:
Given, the sample of ammonium phosphate ${\left( {N{H_4}} \right)_3}P{O_4}$ contains 3.18 moles of H-atom.
Now, we can calculate the number of moles of $O - atom$ in the sample as follows,
${\rm{149}}\;{\rm{grams}}$ of ${\left( {N{H_4}} \right)_3}P{O_4}$ contains 12g of $H$.

Now, 3.18 moles of H-atom is present in $\dfrac{{{\rm{149 \times 3}}{\rm{.18}}}}{{{\rm{12}}}} = {\rm{39}}{\rm{.5}}\;{\rm{grams}}\;{\rm{of}}\;{\left( {{\rm{N}}{{\rm{H}}_{\rm{4}}}} \right)_{\rm{3}}}{\rm{P}}{{\rm{O}}_{\rm{4}}}$

${\rm{149}}\;{\rm{gram}}$ of ${\left( {N{H_4}} \right)_3}P{O_4}$ contains $\dfrac{{64 \times 39.5}}{{149}}\;{\rm{grams}}$ of Oxygen $= {\rm{16}}{\rm{.96}}\;{\rm{grams}}$ of Oxygen.

By this we now know that ${\rm{16}}{\rm{.96}}\;{\rm{grams}}$ of oxygen is present in the given sample.

$\therefore$Number of moles of oxygen $= \dfrac{{16.96}}{{16}} = 1.06\;{\rm{moles}}$

Hence, out of the given options, option C is correct.

Additional Information:
Some important formulas of mole concept are:

Mass of one mole of atoms $= {\rm{Ar}}\;{\rm{in}}\;{\rm{grams}}$

Number of moles of atoms ${\rm{ = }}\dfrac{{{\rm{Mass}}\,{\rm{of}}\,{\rm{the}}\,{\rm{element}}\,{\rm{in}}\,{\rm{grams}}}}{{{\rm{Relative}}\,{\rm{atomic}}\,{\rm{mass,}}\,{\rm{Ar}}}}$

Mass of 1 mole of molecules = Mr in grams

Number of moles of molecules${\rm{ = }}\dfrac{{{\rm{Mass}}\,{\rm{of}}\,{\rm{the}}\,{\rm{substance}}\,{\rm{in}}\,{\rm{grams}}}}{{{\rm{Relative}}\,{\rm{atomic}}\,{\rm{mass,}}\,{\rm{Mr}}}}$
Mass of substance containing 1 mole of particles = Molar mass

Note: The number of atoms in 1 mole is equal to the Avogadro’s number denoted as $\left( {{{\rm{N}}_{\rm{A}}}} \right)$. The value of Avogadro’s number is $6.022 \times {10^{23}}$. The molar mass is given as mass divided by mole that is,
${Molar\; mass}$ = $\dfrac{Mass}{Mole}$ = g/mol