JEE Main · 2021 · 22 Jul 2021 · Shift 2 · Solid State

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A copper complex crystallizing in a CCP lattice with a cell edge of 0.4518 nm has been revealed by employing X-ray diffraction studies. The density of a copper complex is found to be

7.26 g cm^{- 3}

. The molar mass of copper complex is ______

g mol^{- 1}

.
(Nearest integer)
[Given:

N_{A} = 6.022 \times 1 0^{23} mol^{- 1}

]

Answer: 106

Solution

For a CCP (cubic close-packed) lattice, the number of atoms per unit cell

Z = 4

.

The density formula is:

ρ = \frac{Z \times M}{N _{A} \times a ^{3}}

where

a

is the cell edge in cm. Converting:

a = 0.4518 nm = 0.4518 \times 1 0^{- 7} cm = 4.518 \times 1 0^{- 8} cm

.

Rearranging for molar mass

M

M = \frac{ρ \times N _{A} \times a ^{3}}{Z} = \frac{7.26 \times 6.022 \times 1 0 ^{23} \times ( 4.518 \times 1 0 ^{- 8} ) ^{3}}{4}

a^{3} = (4.518)^{3} \times 1 0^{- 24} = 92.13 \times 1 0^{- 24} cm^{3}

M = \frac{7.26 \times 6.022 \times 1 0 ^{23} \times 92.13 \times 1 0 ^{- 24}}{4} = \frac{7.26 \times 6.022 \times 92.13}{4 \times 10} \approx 159 g mol^{- 1}

JEE Main · 2021 · 22 Jul 2021 · Shift 2 · Integer answer

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JEE Main · 2021 · 22 Jul 2021 · Shift 2 · Solid State

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