A copper complex crystallising 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 7.62 g cm⁻³. The molar mass of copper complex is ____________ g mol⁻¹. (Nearest integer)
[Given : N A = 6.022 × 10²³ mol⁻¹]

Solution

Chemistry ma’am · 4 steps

CCP means fcc, so put Z = 4 into the density formula and solve it for M.

1. Count the formula units. A CCP lattice is the same as face-centred cubic. Each unit cell holds 8 × 1/8 + 6 × 1/2 = 4 formula units, so Z = 4.

   d = (Z M)/(a³ N_A) ⇒ M = (d a³ N_A)/Z

2. Edge in cm. Density is in g cm⁻³, so convert the edge to cm: a = 0.4518 nm = 4.518 × 10⁻⁸ cm. Then a³ = 92.22 × 10⁻²⁴ cm³ = 9.222 × 10⁻²³ cm³.
3. Put in numbers. M = (7.62 × 9.222 × 10⁻²³ × 6.022 × 10²³)/4 = 423.2/4 = 105.8 g mol⁻¹.
4. So. The molar mass of the copper complex is 105.8 g mol⁻¹, which rounds to 106.

The common slip: 423. Leaving out Z = 4, as if the cell held one formula unit, gives 423 instead of 106.

The idea to keep. For any density question on a cubic cell, first fix Z from the lattice type (sc 1, bcc 2, fcc or CCP 4). Then work in cm so the units match density in g cm⁻³.

Answer from the NTA final answer key. Solution by PrepWiser.