You add 50 g of ice cubes to 125 g of water that is initially at 20°C in a calorimeter of negligible heat capacity. When the system has reached equilibrium, how much of the ice remains?

Question

Quizplus · Accepted Answer

First, we need to calculate the amount of heat required to melt the ice and raise the temperature of resulting water to 20 degrees Celsius.
Heat required to melt the ice = (50 g) x (334 J/g) = 16700 J
Heat required to raise the temperature of resulting water to 20 degrees Celsius = (125 g) x (4.18 J/g°C) x (20°C) = 10450 J
Total heat required = 16700 J + 10450 J = 27150 J
This is the amount of heat released by the water as it cools from the initial temperature to 0 degrees Celsius and then freezes.
Heat released by water = (125 g) x (4.18 J/g°C) x (20°C) = 10450 J
Heat released by formation of ice = (50 g) x (334 J/g) = 16700 J
Total heat released = 27150 J
We know that the heat released by the water is equal to the heat required to melt the ice and cool the water, so we can set up an equation:
27150 J = (50 g) x (334 J/g) + (125 g) x (4.18 J/g°C) x (20°C) + (125 g) x (4.18 J/g°C) x (Tf - 0°C)
Solving for Tf, we get:
Tf = -3.4°C
Since this temperature is below the freezing point of water, we know that all of the remaining ice (19 g) must have remained in the calorimeter. Therefore, the answer is C.

You Add 50 G of Ice Cubes to 125 G