How much heat energy is required to vaporize a 1.0-g ice cube at 0°C? The heat of fusion of ice is 80 cal/g.The heat of vaporization of water is 540 cal/g,and c_water = 1.00 cal/g⋅°C.

Question

Quizplus · Accepted Answer

To solve for the total heat energy required to vaporize the ice cube, we need to follow these steps:
1. First, we need to determine the amount of heat energy required to melt the ice cube. Using the heat of fusion of ice, we can calculate this as:
q1 = m ∙ ΔHfus = 1.0 g ∙ 80 cal/g = 80 cal
2. Next, we need to determine the amount of heat energy required to raise the temperature of the melted ice to its boiling point. Since the ice is at 0°C, we need to raise its temperature to 100°C (the boiling point of water). Using the specific heat capacity of water, we can calculate this as:
q2 = m ∙ c ∙ ΔT = 1.0 g ∙ 1.00 cal/g⋅°C ∙ (100°C - 0°C) = 100 cal
3. Finally, we need to determine the amount of heat energy required to vaporize the water. Using the heat of vaporization of water, we can calculate this as:
q3 = m ∙ ΔHvap = 1.0 g ∙ 540 cal/g = 540 cal
4. The total heat energy required is the sum of q1, q2, and q3:
qtotal = q1 + q2 + q3 = 80 cal + 100 cal + 540 cal = 720 cal
Therefore, the best choice is B.

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