Four ice cubes at exactly 0 ∘C with a total mass of 50.0 g are combined with 135 g of water at 90 ∘C in an insulated container. (ΔH∘fus=6.02 kJ/mol, cwater=4.18J/g⋅∘C).
Hey there. So for this question we first need to calculate the amount of heat the ice cubes must absorb in order to melt. Remember that during a phase change that q = m x delta H.
Heat to melt the ice cubes:
50.0 g x (1 mole / 18.016 g) x (6.02 kJ / mol) x (1000 J / 1 kJ) = 16707.4 kJ
The heat of the 135 g of water:
q = m x c x delta T = (135 g) (4.18 J / g x C) (90 - 0 C) = 50787 J
The amount of heat remaining:
50787 J - 16707.4 J = 34079.6 J
Now that we have the difference in heat absorbed versus released we can deal with the final temperature of the solution.
qsolution = m x c x delta T 34079.6 J = (50.0 g + 135.0 g) x (4.18 J / g x C) (Tfinal - 0) 34079.6 J = 773.3 (Tfinal - 0) 44.07 Celsius = Tfinal
Hope that helps.