Question

Calculate the lattice enthalpy of sodium chloride. use a=1.748 and do= rna+ rcl- = 283 pm

Answer 1

Answer:

To estimate the lattice enthalpy of sodium chloride, we use $z(\mathrm{Na}^{+}) = +1$ , $z(\mathrm{Cl}^{-}) = -1$ , $A = 1.748$ and $d = r_{\mathrm{Na}^{+}} + r_{\mathrm{Cl}^{-}} = 283$ pm, hence (using fundamental constants from inside the back cover and ensuring that the units of $d$ are appropriate to each part of the equation)

$$\begin{array}{l} \Delta_ {\mathrm {L}} H ^ {O} = \frac {(6 . 0 2 2 \times 1 0 ^ {2 3} \mathrm {m o l} ^ {- 1}) \times | \{+ 1 \} \times (- 1) | \times (1 . 6 0 2 \times 1 0 ^ {- 1 9} \mathrm {C}) ^ {2}}{4 \pi \times (8 . 8 5 4 \times 1 0 ^ {- 1 2} \mathrm {J} ^ {- 1} \mathrm {C} ^ {2} \mathrm {m} ^ {- 1}) \times (2 . 8 3 \times 1 0 ^ {- 1 0} \mathrm {m})} \times \left(1 - \frac {3 4 . 5 \mathrm {p m}}{2 8 3 \mathrm {p m}}\right) \times 1. 7 4 8 \\ = 7. 5 6 \times 1 0 ^ {5} \mathrm {J m o l} ^ {- 1} \\ \end{array}$$

or $756\mathrm{kJ mol^{-1}}$

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