How much energy is required to evaporate all of the liquid water in 1 m3 of the fog?

first thing is to calculate how much liquid water is there in 1m3 of fog. Fog has 0.05 g/m3 liquid water density => in 1m3 of fog there is 0.05 g of water.

and q = m Hv,
Heat of Vaporization of Water Hv = 2260 J /g.

q = 0.05 g * 2260 J/g = 113 joules.

==> Answer = 113 joules (energy required to evaporate all liquid water in 1m3 of fog)