CHEM!! You put a 75 g ice cube at 0 C into a glass of water at 25 C. The final temp is 12.5 C. How much water was there initially? Explain?

Specific latent heat of fusion of ice = 334 J/g
Specific heat capacity of water = 4.184 J/(g°C)

For change of state, Energy change = m L
For temperature change, Energy change = m c ΔT

Let y g be the mass of water in the glass.

Heat absorbed for 75 g of 0°C ice → 12.5°C water
= (Heat absorbed for 75 g of 0°C ice → O°C water) + (Heat absorbed for 75 g of 0°C water → O°C water)
= (75 × 334) + [75 × 4.184 × (12.5 - 0)] J
= 28972.5 J

Heat released by the water in glass
= y × 4.184 × (25 - 12.5) J
= 52.3y J

(Heat released by the water in glass) = (Heat absorbed for 75 g of 0°C ice → 12.5°C water)
52.3y = 28972.5
y = 554

Mass of water in glass = 554 g