Question

The pyknometric density of sodium chloride crystal is 2.165×10³ kg m^–3 while its X-ray density is 2.178×10³ kg m^–3. The fraction of unoccupied sites in sodium chloride crystal is:

• A. 5.96
• B. 5.96×10^–2
• C. 5.96×10^–1
• D. 5.96×10^–3

Answer 1

The Correct Option is D

To determine the fraction of unoccupied sites in the sodium chloride crystal, we will compare the pyknometric density and X-ray density of the crystal.

The pyknometric density (\rho_p) is given as 2.165×10³ kg m^–3 and the X-ray density (\rho_x) is given as 2.178×10³ kg m^–3.

The fraction of unoccupied sites (often referred to as the fractional vacancy) can be found using the formula:

\text{Fraction of unoccupied sites} = \frac{\rho_x - \rho_p}{\rho_x}

Plugging in the given values:

\text{Fraction of unoccupied sites} = \frac{2.178 \times 10^3 \, \text{kg m}^{-3} - 2.165 \times 10^3 \, \text{kg m}^{-3}}{2.178 \times 10^3 \, \text{kg m}^{-3}}

Calculating the difference:

= \frac{0.013 \times 10^3 \, \text{kg m}^{-3}}{2.178 \times 10^3 \, \text{kg m}^{-3}}

Now, simplifying the fraction:

= \frac{0.013}{2.178}

Computing the division yields:

\approx 5.96 \times 10^{-3}

Thus, the fraction of unoccupied sites in the sodium chloride crystal is approximately 5.96×10^–3. This corresponds to option 5.96×10^–3.