Energy and Calorimetry

Thermochemistry

Energy changes during reactions are described by thermochemistry. An exothermic process releases heat and raises the temperature of the surroundings. An endothermic process absorbs heat and lowers the temperature of the surroundings.

In chemical systems, potential energy is often associated with bonds. It takes energy to break any type of molecular interaction, including chemical bonds and intermolecular interactions. This means that when a substance is heated, some of the energy goes into breaking these interactions. Energy that breaks the interactions do not actually affect the kinetic energy of the particles. This situation is often described with the phrase "energy is stored in chemical bonds," which is factually incorrect. Chemical bonds absorb energy to break and release energy to form.

During a chemical reaction, substances rearrange themselves into new substances. The products of a chemical reaction may have less energy than the reactants. In some reactions, the products have a net energy less than that of the reactants. An exothermic reaction is a reaction in which energy is released in the form of heat or light. The heat released is represented by q. Energy released during a chemical reaction is chemical energy, which is sometimes called chemical potential energy.
A+BC+D+energyA+BC+D+q\begin{aligned}A+B&\rightarrow C+D+{\rm{energy}}\\A+B&\rightarrow C+D+q\end{aligned}
In other reactions, the products have more energy than the reactants. An endothermic reaction is a reaction in which energy is absorbed in the form of heat or light.
A+B+energyC+DA+B+qC+D\begin{aligned}A+B+{\rm{energy}}&\rightarrow C+D\\A+B+\;q&\rightarrow C+D\end{aligned}
The science of energy changes associated with chemical reactions is called thermochemistry. Thermochemistry is often studied as systems and their surroundings. A system is the part of the universe that is being studied. When a gas expands in a piston, for example, the gas can be selected as the system. Alternatively, the entire piston can be selected as the system, depending on what the study aims to accomplish. The surroundings are the part of the universe that is in immediate contact with a system. Thermochemistry often studies the flow of heat and mass between a system and its surroundings. If a group of substances undergoing a chemical reaction is considered to be the system, the heat released or absorbed by the chemical reaction can change the temperature of the surroundings.

When a substance is heated, its temperature increases. The amount of the temperature change depends on two things: the mass of the substance and the nature of the substance. The amount of heat needed to raise the temperature of a system by 1°C is its heat capacity (C). This definition does not apply to a defined mass of the substance —the heat capacity of a pool of water is obviously greater than the heat capacity of a glass of water. Specific heat (c) is the amount of heat needed to raise one gram of a substance by 1°C. The specific heat capacity of water in a pool and water in a glass are the same. Different substances have different specific heat capacities. For example, water has a high specific heat capacity compared to many common liquids, such as oil.

Specific heat is an intrinsic material property, which means it does not depend on the amount of material. Heat, mass, specific heat capacity, and change in temperature relate to each other with the following equations:
q=mcΔTq=mc(TfTi)\begin{aligned}{q}&=mc\Delta {T}\\{q}&=mc(T_{f}-T_{i})\end{aligned}
In the equations, q is the heat, m is mass, c is the specific heat capacity, ΔT\Delta T is the change in temperature, Tf is the final temperature, and Ti is the initial temperature.
A 100.0-g aluminum pan filled with 100.0 g of water, both at 25.0°C, are placed into an oven. The oven is turned on and adds 10.0 kJ of heat to the pan and 10.0 kJ of heat to the water. Because the heat capacity of water is more than four times that of aluminum, ΔT\Delta T of the water is four times less than that of the aluminum pan.
The specific heat of a substance provides information for how much energy is needed to change its temperature.
Step-By-Step Example
Using Specific Heat to Calculate Change in Temperature
Consider a 100.0-g aluminum pan containing 100.0 g of water. Both the water and the pan are at an initial temperature of 25.0°C. Given that the specific heat of aluminum is 0.904 J/(g°C) and the specific heat of water is 4.184 J/(g°C), calculate the temperature changes of the pan and the water after the addition of 10.00 kJ of heat to each.
Step 1
First, rewrite the heat equation to isolate the final temperature variable.
q=mc(TfTi)Tf=qmc+Ti\begin{aligned}q&=mc{\rm}(T_{f}-T_{i})\\T_{f}&=\frac{q}{mc}+T_{i}\end{aligned}
Step 2
Then, use the specific heats for aluminum and water to calculate the final temperature. Be sure to convert kilojoules into joules, as the value for specific heat is given in J/(g°C).
Tf,water=1.00×104J(100.0g)(4.184g)(4.184J/g°C)+25.0°C=48.9°CTf,pan=1.00×104J(100.0g)(0.904g)(4.184J/g°C)+25.0°C=136°C\begin{aligned}T_{f,{\rm{water}}}&=\frac{1.00\times10^4\rm{ J}}{(100.0\;{\rm{g}})(4.184\;{\rm{g})}(4.184\;{\rm{J/g}{\cdot}\degree}\!{\rm{C}})}+25.0\degree\!{\rm{C}}\\&=48.9\degree\!{\rm{C}}\\\\T_{f,{\rm{pan}}}&=\frac{1.00\times10^{4}\;{\rm{J}}}{(100.0\;{\rm{g}})(0.904\;{\rm{g}})(4.184\;{\rm{J/g}{\cdot}\degree}\!{\rm{C)}}}+25.0\degree\!{\rm{C}}\\&=136\degree\!{\rm{C}}\end{aligned}
Solution
Next, calculate the change in temperature.
ΔTwater=Tf,waterTi=23.9°CΔTpan=Tf,panTi=111°C\begin{aligned}{\Delta T_{\rm{water}}}&=T_{f,{\rm{water}}}-T_{i}\\&=23.9\degree{\rm{C}}\\\\{\Delta T_{\rm{pan}}}&=T_{f,{\rm{pan}}}-T_{i}\\&=111\degree{\rm{C}}\end{aligned}
The temperature change of the aluminum is more than four times the temperature change of the water, even though the same amount of heat was applied to equal masses of aluminum and water. This is not surprising considering that cwater is more than four times greater than caluminum. In other words, it is more than four times easier to raise the temperature of the aluminum than of the water.
The specific heats of water and aluminum explain why it could still be safe to touch the water inside an aluminum pan in a hot oven, when touching the pan itself could cause a burn. Eventually, the water and the pan will both reach the temperature of the oven. At a constant rate of heating, it takes longer to raise the temperature of the water than it takes to raise the temperature of the pan.