Download Thermodynamics states that `the change in internal energy (∆ ) of a

Thermodynamics
The law of conservation of energy states that energy can neither be created nor destroyed,
it can only be transformed from one form to another e.g. when a fuel is burned in an engine
to form mechanical energy. Thermodynamics is the study of these transformations of
energy, and it is of great significance in chemistry.
Chemical energy is stored in a molecule through its chemical bond(s), energy is required to
break a bond while energy is released when a bond is formed. It is inevitable that during a
chemical reaction, where bonds are formed and broken, that energy is changed from one
form to another. During an exothermic reaction, e.g. the combustion of propane
C3H8 + 5O2
3CO2 + 4H2O,
the energy required to break the bonds of the reactants is far less than the energy released
by the formation of the products, hence chemical energy is converted to heat which is
released into the surroundings. Conversely, an endothermic reaction absorbs energy from
its surroundings since the chemical energy of the products is greater than that of the
reactants e.g. dissolving ammonium nitrate in water.
Internal Energy and the 1st Law of thermodynamics
An essential concept in thermodynamics is that of a system and its surroundings. The
system is the part of the ‘universe’ in which we are interested in, which in chemistry
generally refers to where a chemical reaction takes place, such as a reaction vessel or an
electrochemical cell. The energy of a system is defined as its capacity to do work. During an
exothermic reaction energy is released to the surroundings and hence the energy of the
system is decreased i.e. following the combustion of propane the products have less
capacity to do work.
It is crucial to note that a change in energy of a chemical system isn’t restricted to the
changes in chemical energy, but also to the physical changes imposed on it. To introduce
some fundamental concepts of thermodynamics it may be useful to consider them in the
context of a simple system, such as that of a sample of gas which is not subject to chemical
change. The internal energy (i.e. total energy) of such a system is the sum of the kinetic and
potential energy of its molecules and it is denoted by the symbol ‘𝑈’.
When heat (𝑞) is added to the system, the kinetic energy of its molecules increases and
consequently so does its internal energy. The kinetic and potential energy of the molecules
may also be increased by applying mechanical work (𝑤) on the system i.e. by compressing
the gas with an external force/pressure. This leads to the 1st law of thermodynamics which
states that ‘the change in internal energy (∆𝑈) of a system is equal to the heat
(𝑞) added to the system plus the work (𝑤) done on the system’. Mathematically
the 1st law takes the form
∆𝑈 = 𝑞 + 𝑤
where the sign of each component designates whether the heat/work is done on the system
(+ve) or by the system (-ve).
A thermodynamic system is classified by the nature of the boundary it shares with its
surroundings:
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

An open system can exchange matter and energy with its surroundings.
A closed system can exchange energy with its surroundings but not matter.
An isolated system cannot exchange matter or energy with its surroundings.
Other constraints which can be imposed on a system include an adiabatic barrier which
prevents heat energy transfer and a constant volume container which prevents energy in
the form of work being exchanged (since 𝑤 = 𝑝∆𝑉 and ∆𝑉 = 0 at constant volume). The
heat of combustion of a substance is measured in a constant volume bomb calorimeter,
since the system can do no mechanical work no energy is lost to the environment during the
reaction and the heat generated can be measured accurately.
Enthalpy
Another thermodynamic property of a system is its enthalpy ‘𝐻’. The enthalpy of a system is
related to its internal energy by the equation
𝐻 = 𝑈 + 𝑝𝑉
where 𝑝 is the pressure of the system and 𝑉 its volume. Both 𝐻 and 𝑈 are a measure of the
energy of a system and the difference between them is the term 𝑝𝑉. As previously stated
the internal energy of the system is the total energy (kinetic and potential) of the system,
while the enthalpy of the system may be considered to be the total energy required to
‘create’ the system i.e. the internal energy plus the work done in displacing a volume 𝑉 of
the surroundings at pressure 𝑝.
The term enthalpy is encountered much more often in chemistry than internal energy, and
is often used interchangeably with the terms heat and energy. It is also not possible to
measure the total enthalpy of a system directly and hence the chemist is more interested in
the change in enthalpy (∆𝐻) of a system, as well as its relative enthalpy compared to other
systems.
The convention in chemistry is to assign the elements in their most stable states at standard
conditions (temperature = 298K and Pressure = 1atm) an enthalpy of zero. It is then possible
to define the standard molar enthalpy change of formation (∆𝐻𝑓𝜃 ) of a substance as the
enthalpy change when one mole of the substance (at 298K and 1atm) is formed from its
constituent elements (at 298K and 1atm).
Calculating the ∆𝑯 of a reaction from the ∆𝑯𝜽𝒇 of the reactants and products
Hess’s law states that ‘the total energy change that occurs when a system changes from one
state to another is independent of the route taken to bring about the change’. A result of
Hess’s law is that it may be possible to predict the enthalpy change of a chemical reaction by
a simple calculation if an indirect route from reactants to products can be contrived from
chemical steps of known ∆𝐻. Perhaps the most straightforward way of doing this is to
envisage a hypothetical route from reaction to products with an intermediate state where
all the atoms are separated into their constituent elemental form at standard conditions.
Such an energy cycle for the prior example of the combustion of propane may look like:
C3H8 (g) + 5O2 (g)
3CO2 (g) + 4H2O (l)
3 × (−394)
(−104)
4 × (−286)
3C (s) + 5O2 (g) +4H2 (g)
Where the bracketed values represent the ∆𝐻𝑓𝜃 of each compound with units of kJmol-1. It is
now possible to write a simple calculation for the total enthalpy change along the
hypothetical route (taking care with the sign of each value depending if we are going with or
against an arrow)
∆𝐻 = +104 + 3 × −394 + 4 × −286 = 2220 kJmol-1
Hess’s law holds true for any hypothetical route from reactant to product, however for the
above example using the constituent elements as intermediates it is possible to reduce the
calculation to:
∆𝐻reaction = ∆𝐻𝑓𝜃 products − ∆𝐻𝑓𝜃 reactants
Entropy and the 2nd law of thermodynamics
When a system undergoes an exothermic process energy is released and the system
changes to a lower energy state. Lower energy (enthalpy) compounds are more stable than
higher energy compounds; hence the question must be asked why do endothermic
processes take place at all? Of course the answer to this question lies in the 1 st law and the
principle of conservation of energy; if the energy of a system decreases then the energy of
the adjacent system (i.e. surroundings) must increase by the same amount. There must be
another thermodynamic property which determines the direction of a spontaneous process,
but what is it?
By observing real world processes it can be seen that there is a certain trend in the direction
of energy transfer. A moving car, after switching off its engine, will gradually slow down as
its kinetic energy is transformed into the thermal energy of its surroundings through
friction. Similarly, a bouncing ball will decrease in height as its energy dissipates into the
ground on each impact. The common trend in these examples is that ordered mechanical
energy is transformed into disordered (or less useful) energy, and further we would never
expect these processes to happen in the opposite direction, such as a car spontaneously
gaining speed without the work of an engine or gravity.
The thermodynamic property being alluded to here is entropy, and it is a measure of the
disorder of a system. For the examples given, the total entropy of the system and its
surroundings increases over time. In terms of entropy, the 2nd law of thermodynamics may
be expressed as: ‘The total entropy of the universe always increases in the course
of a spontaneous change.’
It is implied in the above statement that the entropy of a system can decrease if it is
accompanied by a greater increase in the entropy of its surroundings. For example a glass of
water placed in surroundings below 0oC will begin to freeze and the molecules will become
more ordered, however the release of thermal energy will increase the disorder of the
molecules in the surroundings by a greater amount. Generally speaking a liquid has greater
entropy than a solid, and a gas has greater entropy than both.
Gibbs free energy
We have seen that exothermic and endothermic reactions/processes can take place, while
the entropy of the system can also increase or decrease spontaneously depending on the
changes inflicted on the surroundings. But how do we determine the feasibility of a
chemical reaction in terms of the changes in the thermodynamic properties of the system
alone? While enthalpy, 𝐻, is a measure of the total energy of the system, the Gibbs free
energy, 𝐺, of a system is a measure of its ‘useful’ energy. The change in Gibbs free energy of
a system is related to the other thermodynamic variables by the expression:
∆𝐺 = ∆𝐻 − 𝑇∆𝑆
where ∆𝐺 is always negative for a spontaneous change. It can be deduced from the above
equation that an endothermic reaction can occur as long as the increase in entropy
multiplied by the system’s temperature is larger than the increase in enthalpy.
Many salts, such as ammonium nitrate and sodium chloride, dissolve endothermically in
water. These processes are spontaneous because the increase in entropy (disorder) of the
salt’s ions outweighs the increase in enthalpy. It is also important to note that at higher
temperature the impact of the entropy change becomes more significant, and hence why
substances become more soluble at higher temperature, which is particularly important in
the purifying technique of recrystallisation.