Lets first answer the first question:
a. Assuming no heat loss to the surroundings, will the ice melt?
We can determine if the ice will melt by calculating the kJ produced once we dropped the Na metal
A 0.250-g chunk of sodium metal is cautiously dropped into a mixture of 50.0 g water and 50.0 g ice, both at 0 ˚C. The reaction is
2 Na (s) + 2 H2O (l) → 2 NaOH (aq) + H2 (g) ΔH = -368 kJ
Assuming no heat loss to the surroundings, will the ice melt? Assuming the final mixture has a specific heat capacity of 4.18 J/g • ˚C, calculate the final temperature. The enthalpy of fusion for ice is 6.02 kJ/mol.