Question

The sample of ammonium phosphate ${\left( {N{H_4}} \right)_3}P{O_4}$ contains 3.18 moles of H atoms. The number of moles of O atoms in the sample is:
$(a){\text{ 0}}{\text{.265}} \\\ (b){\text{ 0}}{\text{.795}} \\\ (c){\text{ 1}}{\text{.06}} \\\ (d){\text{ 3}}{\text{.18}} \\\$

Answer 1

Hint – In this question compute the total mass of one mole of ammonium phosphate ${\left( {N{H_4}} \right)_3}P{O_4}$, using the individual masses of $\left[ {{\text{mass of }}N{\text{ }} = {\text{ }}14,{\text{ }}H{\text{ }} = {\text{ }}1,{\text{ }}P{\text{ }} = {\text{ }}31{\text{ and }}O{\text{ }} = 16} \right]$. One mole of ${\left( {N{H_4}} \right)_3}P{O_4}$ contains 12 moles of hydrogen so compute the total weight of ${\left( {N{H_4}} \right)_3}P{O_4}$for 3.18 moles of H atoms. Using this, compute the moles of oxygen for this weight of ${\left( {N{H_4}} \right)_3}P{O_4}$.
Formula used – number of moles of oxygen = $\dfrac{{{\text{mass of oxygen present in the sample}}}}{{{\text{mass of one mole of oxygen}}}}$ moles.

Complete answer:

As we know that number of moles for any substance is the ratio of mass of substance to mass of one mole.
So number of moles of oxygen = $\dfrac{{{\text{mass of oxygen present in the sample}}}}{{{\text{mass of one mole of oxygen}}}}$ moles................. (1)
Now as we know that mass of one mole of oxygen = 16 gm.
Now the total mass of given sample is
${\left( {N{H_4}} \right)_3}P{O_4} = 3 \times \left( {14 + 4 \times 1} \right) + 31 + 4 \times 16 = 149$ gm, $\left[ {\because {\text{mass of }}N{\text{ }} = {\text{ }}14,{\text{ }}H{\text{ }} = {\text{ }}1,{\text{ }}P{\text{ }} = {\text{ }}31{\text{ and }}O{\text{ }} = 16} \right]$
And the sample contains 12 gm of hydrogen (H).
Now it is given that 3.18 moles of H is present.
So the mass of H present in the sample = $3.18 \times 1 = 3.18$ gm.
So the sample has $\dfrac{{149 \times 3.18}}{{12}} = 39.485$ gm of ${\left( {N{H_4}} \right)_3}P{O_4}$.
Now the gm of oxygen atom present in 39.485 gm of ${\left( {N{H_4}} \right)_3}P{O_4}$is
$= \dfrac{{64 \times 39.485}}{{149}} = 16.96$ gm of oxygen.
Now from equation (1) we have,
Number of moles of oxygen = $\dfrac{{{\text{mass of oxygen present in the sample}}}}{{{\text{mass of one mole of oxygen}}}} = \dfrac{{16.96}}{{16}} = 1.06$ moles.
So this is the required answer.
Hence option (C) is the correct answer.

Note – In such a type of question the trick point is to get the weight of the sample corresponding to the given moles of its individual components. It is generally done using a unitary method. Mole is a unit of measurement for an amount of substance. A mole of a substance or a mole of particles is defined as exactly $6.02214076 \times {10^{23}}$ particles.