Question

Ice at 0.0°C is placed in a Styrofoam cup containing 352 g of a soft drink at 20.0°C. The specific heat of the drink is about the same as that of water. Some ice remains after the ice and soft drink reach an equilibrium temperature of 0.0°C. Determine the mass of ice that has melted. Ignore the heat capacity of the cup. (Hint: It takes 334 J to melt 1 g of ice at 0.0°C.)

Answer 1

88.23 g of ice

Step-by-step explanation:

Given;

Mass of the soft drink = 352 g

Initial temperature of soft drink = 0°C

Initial temperature of ice = 0°C

Final temperature of the mixture = 0°C

We are required to determine the mass of ice that melted;

Step 1: Quantity of heat lost by the soft drink

Quantity of heat = Mass × specific heat × change in temperature

Q = m × c ×Δt

The specific heat capacity of soft drink = 4.186 J/g°C

Δt = 20 °C

Therefore;

Heat = 352 g × 4.186 J/g°C × 20°C

= 29,469.44 joules

Step 2: Heat used to melt ice

Heat used to melt ice will be calculated by multiplying the mass of ice by the latent heat of fusion.

Latent heat of fusion = 334 J/g

Assuming the mass of ice is m

Then;

Heat = 334 m Joules

Step 3: Calculating the mass of ice

Since heat released by the soft drink is used to melt the ice

Then;

334 m Joules = 29,469.44 joules

m = 29,469.44 joules ÷ 334

= 88.232 g

= 88.23 g

Therefore, the mass of ice that melted is 88.23 g