A solid having density of $9 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ forms face centred cubic crystale of edge length $200 \sqrt{2} \mathrm{pm}$. What is the molar mass of the solid? [Avogadro constant $\cong 6 \times 10^{23}$ and $\mathrm{mol}^{-1}, \pi \cong 3$ ]

(C) $0.0305 \mathrm{~kg} \mathrm{~mol}^{-1}$

(A) $0.0432 \mathrm{~kg} \mathrm{~mol}^{-1}$

(B) $0.0216 \mathrm{~kg} \mathrm{~mol}^{-1}$

(D) $0.4320 \mathrm{~kg} \mathrm{~mol}^{-1}$

JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Solid State

A solid having density of

9 \times 1 0^{3} kg m^{- 3}

forms face centred cubic crystale of edge length

2002 pm

. What is the molar mass of the solid?
[Avogadro constant

≅ 6 \times 1 0^{23}

and

mol^{- 1}, π ≅ 3

]

Answer: (C)

For a face-centred cubic cell

Z = 4

, and density relates to molar mass through

ρ = \frac{Z M}{N _{A} a ^{3}}

. The edge is

a = 2002 pm = 2002 \times 1 0^{- 12} m

, so

a^{3} = (2002)^{3} \times 1 0^{- 36} = 2.26 \times 1 0^{7} \times 1 0^{- 36} = 2.26 \times 1 0^{- 29} m^{3}

. Then

M = \frac{ρ N _{A} a ^{3}}{Z} = \frac{9 \times 1 0 ^{3} \times 6 \times 1 0 ^{23} \times 2.26 \times 1 0 ^{- 29}}{4} \approx 0.0305 kg/mol

JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Single correct option