Consider the specific heats h2o (s) = 2.09 j/g · ◦c, h2o (ℓ) = 4.18 j/g · ◦c, and h2o (g) = 2.03 j/g · ◦c. the heat of fusion for water is 334 j/g and its heat of vaporization is 2260 j/g. calculate the amount of heat required to convert 59 g of ice at - 35◦c completely to liquid water at 55◦c. answer in units of kj.

Refer to the diagrams shown below.

Goal:

We want to determine the amount of heat required to convert 59 g of ice at - 35 °C to liquid water at 55 °C.

Given:

c = 2.09 J / (g-°C), the specific heat of ice

= 4.18 J / (g-°C), the specific heat of water

= 2.03 J / (g-°C), the specific heat of steam

L = 334 J/g, the latent heat of fusion of water

= 2260 J/g, the latent heat of vaporization of water

Stage 1: Convert ice at - 35 °C to ice at 0 °C.

The heat required is

Q₁ = (59 g) * (2.09 J / (g-°C)) * (0 - (-35) °C) = 4,315.85 J

Stage 2: Convert ice at 0 °C to water at 0 °C.

The heat required is

Q₂ = (59 g) * (334 J/g) = 19,706 J

Stage 3: Raise the temperature of the water from 0 °C to 55 °C.

The heat required is

Q₃ = (59 g) * (4.18 J / (g-°C)) * (55 °C) = 13,564.10 J

The total heat required is

Q = Q₁ + Q₂ + Q₃ = 37,585.95 J = 37.586 kJ

Answer: 37.6 kJ