How much heat is released when 105 g of steam at 100.0°C is cooled to ice at -15.0°C? The enthalpy of vaporization of water is 40.67 kJ/mol,the enthalpy of fusion for water is 6.01 kJ/mol,the molar heat capacity of liquid water is 75.4 J/(mol ∙ °C),and the molar heat capacity of ice is 36.4 J/(mol ∙ °C).
A)54.8 kJ
B)273 kJ
C)319 kJ
D)347 kJ

Question

Quizplus · Accepted Answer

First, we need to calculate the amount of heat released when steam at 100.0°C is cooled to liquid water at 100.0°C using the equation:

q1 = m × C × ΔT

where q1 is the amount of heat released, m is the mass of steam, C is the molar heat capacity of liquid water, and ΔT is the temperature change.

Here, we have:

m = 105 g/ 18.015 g/mol = 5.829 mol (mass/molecular weight)
C = 75.4 J/(mol ∙ °C)
ΔT = 100.0°C - 0°C = 100.0°C

q1 = 5.829 mol × 75.4 J/(mol ∙ °C) × 100.0°C = 43,802 J

Next, we need to calculate the amount of heat released when the liquid water at 100.0°C is cooled to ice at 0.0°C using the equation:

q2 = m × C × ΔT

where q2 is the amount of heat released, m is the mass of liquid water, C is the molar heat capacity of ice, and ΔT is the temperature change.

Here, we have:

m = 5.829 mol
C = 36.4 J/(mol ∙ °C)
ΔT = 0.0°C - (-100.0°C) = 100.0°C

q2 = 5.829 mol × 36.4 J/(mol ∙ °C) × 100.0°C = 21,223 J

Finally, we need to calculate the amount of heat released when the ice at 0.0°C is cooled to ice at -15.0°C using the equation:

q3 = m × ΔHfus + m × C × ΔT

where q3 is the amount of heat released, m is the mass of ice, ΔHfus is the enthalpy of fusion for water, C is the molar heat capacity of ice, and ΔT is the temperature change.

Here, we have:

m = 5.829 mol
ΔHfus = 6.01 kJ/mol
C = 36.4 J/(mol ∙ °C)
ΔT = -15.0°C - 0.0°C = -15.0°C

q3 = 5.829 mol × 6.01 kJ/mol + 5.829 mol × 36.4 J/(mol ∙ °C) × (-15.0°C) = -17,223 J

The total amount of heat released is the sum of q1, q2, and q3:

q = q1 + q2 + q3 = 43,802 J + 21,223 J - 17,223 J = 47,802 J

Finally, we need to convert J to kJ:

q = 47,802 J = 47.802 kJ

Hence, the best choice is C (319 kJ) since it is the closest answer to our calculated value.

How Much Heat Is Released When 105 G of Steam