Question

= T100 g
Q. 2. The edge length of NaCl unit cell is 564 pm. What is the density of NaCl ? The
atomic mass of Na and Cl are 23 and 35.5 respectively. NaCl has fcc structure.​

Answer 1

Answer:

Density = 2166.67 kg/m³

Explanation:

Given:

• The edge length of NaCl unit cell = 546 pm
• Atomic mass of Na = 23
• Atomic mass of Cl = 35.5
• NaCl has fcc structure

To Find:

• The density of NaCl

Solution:

The density of a unit cell is given by the formula,

$\sf d=\dfrac{z\:M}{a^3\:N_A}$

where d is the density, z is the number of atoms in the unit cell, M is the molar mass, a is the edge length and $\sf N_A$ = Avogadro's number = 6.023 × 10²³ atoms/mol

Here by given NaCl has fcc structure.

Number of atoms in a unit cell in fcc structure = 4 atoms

Edge length = 564 pm = 564 × 10⁻¹² m

Molar mass = 23 + 35.5 = 58.5 g/mol = 58.5 × 10⁻³ kg/mol

Substitute the data,

$\sf d=\dfrac{4\times 58.5\times 10^{-3}\:kg\: mol^{-1}}{(564\times 10^{-12}\:m)^3\times 6.022\times 10^{23}\:mol^{-1}}$

$\sf \implies \dfrac{0.234}{1.080\times 10^{-4}}$

$\sf \implies 2166.67\: kg\:m^{-3}$

Hence the density of NaCl is 2166.67 kg/m³.