MHTCET 5 May 2025 Shift 2 Paper

Concept:The number of atoms in a sample is found by first converting mass to moles, then multiplying by the number of atoms per molecule and Avogadro's number.Explanation:The molecular formula of urea is $\mathrm{H}_{2}\mathrm{N}-\mathrm{CO}-\mathrm{NH}_{2}$, which is $(\mathrm{NH}_{2})_{2}\mathrm{CO}$.The molar mass of urea is $60\ \mathrm{g\,mol}^{-1}$.Number of moles of urea in $5.4\ \mathrm{g}$:$$\text{moles} = \frac{5.4}{60} = 0.09\ \mathrm{mol}$$Each urea molecule contains $4$ hydrogen atoms.So, moles of hydrogen atoms in $0.09\ \mathrm{mol}$ urea:$$0.09 \times 4 = 0.36\ \mathrm{mol}$$Now, number of hydrogen atoms:$$0.36 \times 6.022 \times 10^{23} = 2.168 \times 10^{23}$$Thus, the number of hydrogen atoms is $2.168 \times 10^{23}$.Answer:Option C: $2.168 \times 10^{23}$