A heating curve can be used to calculate the enthalpy when a substance is heated. If we were to heat 25.00 g of water from -15.0 °C to 115.0 °C, we can determine ΔH for the heating process. Below is a heating curve for water from -15.0 °C to 115.0 °C. Temperature is on the y axis and includes the temperature range of heating as well as the melting and boiling points of water. The x axis is the amount of heat added.

We see the heating curve can be divided into regions. The regions are: Region AB, Region BC, Region CD, Region DE, and Region EF. Region AB is water in the solid phase. The temperature continues to rise until it reaches the melting point of water, Region BC.

Region BC is solid and liquid water in equilibrium. The solid is melting, at the melting point, and once all of the solid melts we are in Region CD which is the liquid phase. The temperature does not rise until all of the solid is converted to liquid. This is because the heat is being used to distance the particles. Recall, a liquid is fluid and the particles are able to slide past one another.

In Region CD, the temperature continues to rise until we get to the boiling point of the water. Again, in Region DE, the liquid and gas phases are in equilibrium and the temperature remains constant because the thermal energy is being used to overcome the intermolecular attractions between water molecules. Once all of the liquid has been converted to gas, the temperature continues to rise in Region EF.

To calculate the energy required to heat water from -15.0 °C to 115.0 °C, we need to know how to calculate the energy for each region. For the solid, liquid, and gas phases we use the following equation:

q = m x c x ΔT where m is the mass, c is the specific heat capacity, and ΔT is the final temperature – the initial temperature. At the melting point we use ΔH_fus and at the boiling point we use ΔH_vap.

Here we will calculate ΔH for the process of heating 25.00 g of water from -15.0 °C to 115.0 °C. We need the following information to solve the problem.

 
\(\displaystyle q_{AB}=m\times c\times ΔT\)
 
\(\displaystyle q_{AB}=25.00\;g\times 2.02\frac{J}{mol⋅°C}\times (0.00°C-(-15.0°C)\;=\;757.5\;J\;=\;0.758\;kJ\)
 
\(\displaystyle q_{BC}=ΔH_{fus}\times moles H_2O\;=\;6.01\frac{kJ}{mol}\times 1.39\;mol\;=\;8.4\;kJ\)
 
\(\displaystyle q_{CD}=25.00\;g\times 4.184\frac{J}{mol⋅°C}\times (100.0°C-(0.0°C)\;=\;10350\;J\;=\;10.4\;kJ\)
 
\(\displaystyle q_{DE}=ΔH_{vap}\times moles H_2O\;=\;40.67\frac{kJ}{mol}\times 1.39\;mol\;=\;56.5\;kJ\)
 
\(\displaystyle q_{EF}=25.00\;g\times 1.84\frac{J}{mol⋅°C}\times (115.0°C-(1000.0°C)\;=\;690\;J\;=\;0.690\;kJ\)
 

Now we sum the heats for each region to find ΔH.

ΔH = q_AB + q_BC + q_CD + q_DE + q_EF
= 0.758 kJ + 8.4 kJ + 10.4 kJ + 56.5 kJ + 0.690 kJ = 834.0 kJ

Below is a cooling curve for water for the temperature range 115°C down to -15.0°C. For this temperature range ΔH is equal to -834.0 kJ. When a liquid is cooled it is an exothermic process.

Worksheet: Heating and Cooling Curves Part 1
Worksheet: Heating and Cooling Curves Part 2

Exercises

Exercise 1. Calculate the amount of heat required to convert 25.0 g of benzene (C₆H₆) from 22.0°C to 90.0°C.

Check Answer/Solution to Exercise 1

Exercise 2. What is ΔS for ethanol if the boiling point is 73.37°C and ΔH = 42.3 kJ/mol?

Check Answer/Solution to Exercise 2

Exercise 3. Answer the questions below about the following curve for a substance that is being heated.

Check Answer/Solution to Exercise 3

Exercise 4. What is ΔH if acetone cools from 75.5°C to 25.0°C?

Check Answer/Solution to Exercise 4

Back to Liquids
Back to Study Guides for General Chemistry 2