How much energy (in kilojoules) is released when 12.3 of steam at 121.5 is condensed to give liquid water at 64.5? The heat of vaporization of liquid water is 40.67 , and the molar heat capacity is 75.3 for the liquid and 33.6 for the vapor.
To calculate the energy released when steam is condensed, we need to consider the heat of vaporization and the temperature change.
First, we need to calculate the energy required to vaporize the steam:
Q1 = m × Hvap
Where:
Q1 = energy required to vaporize the steam in joules
m = mass of the steam in kilograms
Hvap = heat of vaporization of liquid water in joules per kilogram
To convert the mass from grams to kilograms, we divide by 1000:
m = 12.3 g / 1000 = 0.0123 kg
Now, we can calculate Q1:
Q1 = 0.0123 kg × 40,670 J/kg = 500.84 J
Next, we calculate the energy released during the temperature change from 121.5°C to 64.5°C. We need to consider both the energy needed to cool the steam to 100°C (latent heat) and the energy needed to cool the liquid water from 100°C to 64.5°C.
Q2 = (m × Cp_vapor × ΔT_vapor) + (m × Cp_liquid × ΔT_liquid)
Where:
Q2 = energy released during the temperature change in joules
Cp_vapor = molar heat capacity of the vapor (steam) in joules per kilogram per degree Celsius
Cp_liquid = molar heat capacity of the liquid water in joules per kilogram per degree Celsius
ΔT_vapor = temperature change of the vapor (121.5°C - 100°C)
ΔT_liquid = temperature change of the liquid water (100°C - 64.5°C)
Now, let's calculate Q2:
ΔT_vapor = 121.5°C - 100°C = 21.5°C
ΔT_liquid = 100°C - 64.5°C = 35.5°C
Q2 = (0.0123 kg × 33.6 J/(kg·°C) × 21.5°C) + (0.0123 kg × 75.3 J/(kg·°C) × 35.5°C)
= 8.3364 J + 32.3837 J
= 40.72 J
Finally, we can calculate the total energy released during the condensation process by adding Q1 and Q2:
Total energy released = Q1 + Q2
= 500.84 J + 40.72 J
= 541.56 J
To convert the energy from joules to kilojoules, we divide by 1000:
Total energy released in kilojoules = 541.56 J / 1000
= 0.54156 kJ
Therefore, approximately 0.5416 kilojoules of energy is released when 12.3 grams of steam at 121.5°C is condensed to liquid water at 64.5°C.