Answer
0.315 nm.
Work Step by Step
See problem 14. Use the hint. Every ion sits at the corner of a cube of side length s, which is the distance between ions.
See Figure 29–20. A cube of side length s is associated with four KCl pairs. However, only one-eighth of each K or Cl ion is part of that cube, because 8 cubes meet at that corner.
In summary, each cube of side length s has the equivalent of one-half of a KCl molecule.
Calculate the mass per unit volume, i.e., the density.
$$\rho=\frac{0.5m_{KCl}}{s^3}$$
$$s=\left( \frac{0.5m_{KCl}}{\rho}\right)^{1/3}$$
$$s=\left( \frac{0.5(74.55 g/mole)}{1.99g/cm^3}\frac{mole}{6.02\times10^{23}}\right)^{1/3}$$
$$s=3.15\times10^{-8}cm$$