HWK3/21
(a) What is the molar heat capacity of liquid water?
__ J/mol oC
(b) What is the heat capacity of 8.33 mol of liquid water?
 ________J/ oC
(c) How many kJ of heat are needed to raise the temperature of 4.17 kg of water from 42.6 oC to 68.4 oC?
__ kJ
The Correct Answer and Explanation is:
Correct Answers:
(a) The molar heat capacity of liquid water is approximately:
75.3 J/mol·°C
(b) Heat capacity of 8.33 mol of liquid water:
Heat capacity=8.33 mol×75.3 J/mol\cdotp°C=627.999 J/°C≈628 J/°C\text{Heat capacity} = 8.33 \, \text{mol} \times 75.3 \, \text{J/mol·°C} = 627.999 \, \text{J/°C} \approx \textbf{628 J/°C}
(c) First, convert mass to moles:
Molar mass of water = 18.015 g/mol
4.17 kg = 4170 g
Number of moles = 4170 g18.015 g/mol≈231.5 mol\frac{4170 \, \text{g}}{18.015 \, \text{g/mol}} \approx 231.5 \, \text{mol}
Temperature change:
ΔT = 68.4°C − 42.6°C = 25.8°C
Now calculate heat required:
q = n × C × ΔT = 231.5 mol × 75.3 J/mol·°C × 25.8°C
q ≈ 449,438 J ≈ 449.4 kJ
Explanation
Understanding how substances absorb and store heat is fundamental in thermodynamics and chemistry. This problem involves calculating the molar heat capacity, total heat capacity, and heat energy needed to change the temperature of water — a common but essential substance in physical chemistry.
(a) The molar heat capacity of a substance is the amount of heat needed to raise the temperature of one mole of that substance by 1°C. For liquid water, this value is about 75.3 J/mol·°C. This is relatively high compared to other substances because of hydrogen bonding between water molecules, which requires more energy to break during heating.
(b) The total heat capacity of a substance sample is the product of the number of moles and the molar heat capacity. For 8.33 moles of water, the heat capacity is calculated by multiplying 8.33 mol × 75.3 J/mol·°C, giving approximately 628 J/°C. This tells us that 628 joules are needed to raise the temperature of this specific amount of water by 1°C.
(c) To find the amount of heat energy (q) required to heat a mass of water, we use the equation: q=n×C×ΔTq = n \times C \times \Delta T
Where nn is the number of moles, CC is molar heat capacity, and ΔT\Delta T is the temperature change. Given 4.17 kg of water and a temperature increase of 25.8°C, we convert the mass to moles and use the molar heat capacity to find that approximately 449.4 kJ of heat is needed. This application shows how thermodynamic principles are crucial in practical scenarios like heating systems, climate modeling, and biological processes.
