What is the total number of nitrogen atoms contained in a 5.60\text{ dm}^3 sample of dinit… — JAMB UTME

What is the total number of nitrogen atoms contained in a $5.60\text{ dm}^3$ sample of dinitrogen monoxide gas ( $\text{N}_2\text{O}$ ) measured at standard temperature and pressure ( $\text{STP}$ )? $[N_A = 6.02 \times 10^{23}\text{ mol}^{-1}\text{; Molar volume of gas at STP } = 22.4\text{ dm}^3\text{mol}^{-1}]$

$3.01 \times 10^{23}$ Answer
B
$2.81 \times 10^{23}$
C
$1.51 \times 10^{23}$
D
$4.52 \times 10^{23}$

Answer

3.01 \times 10^{23}

nitrogen atoms

The correct answer of

3.01 \times 10^{23}

is calculated by determining the amount in moles of dinitrogen monoxide gas (

5.60\text{ dm}^3 / 22.4\text{ dm}^3\text{mol}^{-1} = 0.25\text{ mol}

), multiplying by 2 because there are two nitrogen atoms per

\text{N}_2\text{O}

molecule (

0.50\text{ mol}

of N atoms), and multiplying by Avogadro's constant (

0.50 \times 6.02 \times 10^{23} = 3.01 \times 10^{23}

Step-by-Step Solution

Calculate the moles of dinitrogen monoxide gas at STP

\text{Moles of N}_2\text{O} = \frac{5.60\text{ dm}^3}{22.4\text{ dm}^3\text{mol}^{-1}} = 0.25\text{ mol}

At STP, one mole of any ideal gas occupies a molar volume of 22.4 dm³.

Determine the number of moles of nitrogen atoms

\text{Moles of N atoms} = 0.25\text{ mol} \times 2 = 0.50\text{ mol}

Each formula unit of dinitrogen monoxide (N₂O) contains 2 atoms of nitrogen.

Convert moles of nitrogen atoms to the total number of atoms using Avogadro's constant

\text{Number of N atoms} = 0.50\text{ mol} \times 6.02 \times 10^{23}\text{ atoms/mol} = 3.01 \times 10^{23}\text{ atoms}

Avogadro's constant provides the number of particles per mole of substance.

Key Concept

Mole Concept and Avogadro's Constant applied to Gas Molar Volume

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