Question

44.0 g of ice at -20.0 °C is mixed with 325 g of water at 32.1 °C. Calculate the final temperature of the mixture. Assume that no energy in the form of heat is transferred to the environment. (Heat of fusion = 333 J/g; specific heat capacities: ice = 2.06 J/g⋅K, liquid water = 4.184 J/g⋅K)

Select one:

a. 38.9 °C
b. 12.1 °C
c. 5.5 °C
d. -0.6 °C
e. 17.6 °C

Answer 1

The final temperature is approximately (a) 38.9 °C.

Step-by-step explanation:

To find the final temperature of the mixture, we can use the principle of conservation of energy.

First, we need to calculate the heat required to melt the ice at -20.0 °C. The formula for calculating heat is Q = m * Hf, where Q is the heat, m is the mass, and Hf is the heat of fusion. Plugging in the values, we have Q = 44.0 g * 333 J/g = 14,652 J.

Next, we calculate the heat required to raise the temperature of the water from 32.1 °C to the final temperature. The formula for calculating heat is Q = m * c * ΔT, where Q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. Plugging in the values, we have Q = 325 g * 4.184 J/g⋅K * (final temperature - 32.1 °C).

Since no heat is lost or gained by the surroundings, the heat gained by the water is equal to the heat lost by the ice.

14,652 J = (325 g * 4.184 J/g⋅K * (final temperature - 32.1 °C). Solving for the final temperature, we find that the final temperature of the mixture is approximately 38.9 °C.