1) Consider barium sulfate crystals in saturated aqueous solution with interfacial energy of 120 mJ/m? and Gibbs free energy barrier of 5.02x1019 J a. Show with calculations whether a nucleus with a radius of 0.8 nm would grow or dissolve back into the solution. b. Determine whether the energy barrier to the nucleation process is greater for a cube or a sphere? c. What is the condition for spontaneous nucleation? For no nucleation? d. Which of these plots below correlate the supersaturation to: i) the crystal size, ii) nucleation rate, and i) growth rate, respectively. Justify your selection (one plot for each). Supersaturation Supersaturation Supersaturation Supersaturation Supersaturation Supersaturation