JEE Main 2022 — Some Basic Concepts Of Chemistry Question with Solution

First, determine the molar mass of the compound C${}_7$H${}_5$N${}_3$O${}_6$:

Carbon (C): 12 g/mol, and there are 7 C atoms: $7\times 12=84\text{ g/mol}$

Hydrogen (H): 1 g/mol, and there are 5 H atoms: $5\times 1=5\text{ g/mol}$

Nitrogen (N): 14 g/mol, and there are 3 N atoms: $3\times 14=42\text{ g/mol}$

Oxygen (O): 16 g/mol, and there are 6 O atoms: $6\times 16=96\text{ g/mol}$

Calculate the total molar mass:

${\text{Molar mass of C}}_7{\text{H}}_5{\text{N}}_3{\text{O}}_6=84+5+42+96=227\text{ g/mol}$

Calculate the number of moles of C${}_7$H${}_5$N${}_3$O${}_6$ in 681 grams:

${\text{Moles of C}}_7{\text{H}}_5{\text{N}}_3{\text{O}}_6=\frac{681\text{ g}}{227\text{ g/mol}}=3\text{ moles}$

Each molecule of C${}_7$H${}_5$N${}_3$O${}_6$ contains 3 nitrogen atoms. Thus, in 3 moles, the total moles of nitrogen atoms is:

$\text{Moles of N atoms}=3\times 3=9\text{ moles}$

Using Avogadro's number, calculate the number of nitrogen atoms:

$\text{Number of N atoms}=9\text{ moles}\times 6.02\times 10^{23}\text{ atoms/mole}$

$=54.18\times 10^{23}=5.418\times 10^{24}\text{ N atoms}$

Convert this number to the form $x\times 10^{21}$:

$5.418\times 10^{24}=5418\times 10^{21}$

Thus, the value of $x$ is:

$x=5418$