Final answer:
The correct answer is E. 13.1 kJ. This is calculated by considering the energy change during cooling while diethyl ether is in the gaseous phase and then when it transitions to and cools in the liquid phase, resulting in a total energy release of approximately 13.51 kJ.
Step-by-step explanation:
To calculate the energy released when 100.0 g of diethyl ether is cooled from 53.0°C to 10.0°C, we must consider that part of the cooling process occurs while the ether is in the gas phase (from 53.0°C to the boiling point of 34.5°C) and the rest occurs in the liquid phase (from 34.5°C to 10.0°C).
For the gas phase:
- Specific heat of (CH₃CH₂)₂O(g) = 2.35 J/g • °C
- Temperature change in gas phase = 53.0°C - 34.5°C = 18.5°C
- Energy change in gas phase = mass × specific heat × temperature change
- Energy change in gas phase = 100.0 g × 2.35 J/g°C × 18.5°C = 4353.75 J
For the liquid phase:
- Specific heat of (CH₃CH₂)₂O(l) = 3.74 J/g • °C
- Temperature change in liquid phase = 34.5°C - 10.0°C = 24.5°C
- Energy change in liquid phase = mass × specific heat × temperature change
- Energy change in liquid phase = 100.0 g × 3.74 J/g°C × 24.5°C = 9155 J
Total energy change = energy change in gas phase + energy change in liquid phase = 4353.75 J + 9155 J = 13508.75 J, which is approximately 13.51 kJ. Therefore, the closest answer is E. 13.1 kJ.