A sample of pure ammonia gas (\text{NH}_3) has a mass of 3.4\text{ g}. What is the total n… — JAMB UTME

A sample of pure ammonia gas ( $\text{NH}_3$ ) has a mass of $3.4\text{ g}$ . What is the total number of atoms contained in this sample? $[\text{N} = 14, \text{H} = 1, N_A = 6.02 \times 10^{23}\text{ mol}^{-1}]$

$4.816 \times 10^{23}$ Answer
B
$1.204 \times 10^{23}$
C
$3.612 \times 10^{23}$
D
$2.408 \times 10^{23}$

Answer

4.816 \times 10^{23}

atoms

The molar mass of ammonia (

\text{NH}_3

) is

17\text{ g/mol}

. A mass of

3.4\text{ g}

corresponds to

0.2\text{ moles}

\text{NH}_3

molecules, which contains

1.204 \times 10^{23}

molecules. Because one molecule of

\text{NH}_3

consists of

4

atoms (

1

nitrogen atom and

3

hydrogen atoms), multiplying

1.204 \times 10^{23}

4

gives

4.816 \times 10^{23}

total atoms.

Step-by-Step Solution

Calculate the molar mass of ammonia (

\text{NH}_3

)

\text{Molar Mass} = 14 + 3(1) = 17\text{ g/mol}

Molar mass is required to convert sample mass into moles.

Calculate the number of moles of

\text{NH}_3

\text{Moles} = \frac{3.4\text{ g}}{17\text{ g/mol}} = 0.2\text{ mol}

Dividing given mass by molar mass yields the mole quantity.

Determine the number of molecules of

\text{NH}_3

\text{Molecules} = 0.2\text{ mol} \times 6.02 \times 10^{23}\text{ mol}^{-1} = 1.204 \times 10^{23}\text{ molecules}

Multiplying moles by Avogadro's constant gives total molecules.

Calculate the total number of individual atoms

\text{Total atoms} = 1.204 \times 10^{23} \times 4 = 4.816 \times 10^{23}\text{ atoms}

Each

\text{NH}_3

molecule contains 1 nitrogen atom and 3 hydrogen atoms (4 atoms in total).

Key Concept

Converting mass to number of constituent atoms using Avogadro's constant and molecular stoichiometry.

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