The enthalpy of a thermodynamic system is the sum of the system’s internal energy and the product of its pressure and volume.
In the previous article, we showed that the change in internal energy of the system at constant volume can be experimentally determined by quantifying the transfer of heat to the system. However, many chemical reactions are carried out under constant pressure instead of constant volume.
It would be useful to identify another state function that has a relationship with analogous to eq27, i.e. one that analyses the energy change of a system at constant pressure by quantifying the transfer of heat. From eq25, the 1st law of thermodynamics of a closed system that does only pV work at constant pressure can be expressed as
Since the system is at constant pressure, where , and we can rewrite eq28 as:
Let’s define . Eq29 becomes
or
We have identified a new state function called enthalpy. Therefore, the change in enthalpy of a closed system at constant pressure is a change in energy of the system that equals to the transfer of heat to the system. We can now determine the change in energy of a chemical reaction in a closed system at constant pressure that does only pV work by experimentally measuring the amount of heat transferred to the system.
Question
Explain why is a state function.
Answer
As explained in an earlier article, the product of two state functions is a state function and the sum of two state functions is again a state function. Since ,
and
are all state functions,
is a state function.
A process that, as a whole, absorbs heat from the surroundings, resulting in a positive change in the enthalpy of the system, is called an endothermic process. Conversely, a process that, as a whole, releases heat to its surroundings resulting in a negative change in the enthalpy of the system is called an exothermic process.
Consider the neutralisation reaction of hydrochloric acid and sodium hydroxide in a styrofoam cup calorimeter at (see diagram above).
Let’s regard the system as the reacting acid and alkali, and the surroundings as water, with both system and surroundings maintained at constant atmospheric pressure. We assume that heat and material are neither transferred from the solution to the styrofoam cup nor to the atmosphere. This means that the system is considered a closed one, as the reactants and products are confined within the cup throughout the reaction. Since any heat evolved by the reaction (system) is released to the water (surroundings),
where and
.
The enthalpy change of neutralisation is:
where
is the number of moles of water
is molar heat capacity of water at constant pressure
is the change in temperature of the solution
If ,
for the reaction, i.e. an exothermic reaction. The volume of the system may change, but for reactions in solutions, the change is usually very small. Therefore, we can also regard the above experiment as measuring the energy change in a constant volume system with negligible pressure changes. With reference to eq27 and eq30,
for such a reaction.
Let’s look at another common chemical reaction, combustion.
The change in enthalpy of a combustion reaction is often measured using a bomb calorimeter (see diagram above). However, the system in the device is not subject to constant pressure but constant volume. Therefore, we need to compute the change in internal energy of the process and convert the value to the change in enthalpy. The sample is placed in a crucible, which is enclosed in a chamber that is made of a thermally conductive material. Oxygen is pumped into the chamber and the reaction is initiated by a current flowing through a wire that is embedded in the sample. The energy released by the combustion reaction flows across the chamber walls to heat up the water in the reservoir, which is the surroundings.
For a process at constant volume, the first law of thermodynamics becomes:
can be estimated to be
where
is the specific heat capacity of water at constant volume and
is the mass of water.
is therefore negative for combustion reactions. Consider the combustion of naphthalene:
The general change in enthalpy is:
At constant volume,
The change in pressure of the system is mainly due to the change in gaseous content in the system as solids and liquids in most experiments do not occupy significant volume in the calorimeter. Substituting the ideal gas law in eq32,
If the change in temperature is small,
with its integrated form as
where for the combustion of naphthalene.
Substituting the value of obtained via eq31 in eq33, we have the change in enthalpy for the reaction. Since both
and
are negative,
is negative, validating that combustion reactions are exothermic. The change in enthalpy of a reaction can also be determined by other methods, e.g. via the van’t Hoff equation.