Consider a glass of 277 mL of water at 25°C. Calculate the mass of ice at -15°C that must be added to cool the water to 10°C after thermal equilibrium is achieved. To find the mass of water use the density of water = 1.0 g/mL.

Question

I have no idea how to start this. I guess i hae to first find the grams of water there are. I have the values of the Cs of ice and DeltaH of fusion.

Answer 1

q to move ice from -15 to zero C.
q1 = mass ice x specific heat ice x (Tfinal-Tinitial) [Note: Be careful that you keep the signs ok here. Tfinal = 0 and Tinitial = -15; therefore, Tf-Ti = +15.

q2 = heat to melt ice
q2 = mass ice x heat fusion

q3 = heat to move melting ice from zero C to 10 C.
q3 = mass x specific heat water x (Tfinal-Tinitial)

q4 = heat lost in moving 277 mL water from 25 to 10
q4 = mass x specific heat x (Tfinal-Tinitial)
Now add q1 + q2 + q3 + q4 = 0.
mass ice = x and mass melted ice = x. Solve for x. I get something close to 40 grams.