Memo: Thermodynamics in Chemistry

All energy transferences are done in two ways: by heat or by work. In any given system and any given process, the total energy transferred is the sum of the heat transferred and the amount of work transferred. This says nothing about the ratio of work and heat in the total energy, or why energy can only be transferred one way and not the other, or why only a certain amount of energy can be transferred under certain conditions.

The study of heat and work transferrence, whose goal is to answer the above questions, is called “thermodynamics” (thermal and dynamic energy). Thermodynamics combines and explains the ideas and phenomena in chemistry, physics, statistics, etc. Hence, it is not uncommon for practicians of these related fields to stumble upon thermodynamic concepts in their studies.

This memo serves as a glossary and a link between thermodynamics and chemistry.

Thermodynamic states, variables, and functions

The thermodynamic state of a system is described by a set of its state variables (aka, state parameters, aka, state quantities) and its state functions at any given time.

Some common state variables and state functions (with their common notation) in thermodynamics are:

Pressure, P
Temperature, T
Volume, V
Entropy, S
Enthalpy, H
Gibbs’ free energy, G
Mass, m
Particle number, n
Density, p

Except for Entropy, Enthalpy, and Gibbs’ free energy, other properties should be self-explanatory.

Enthalpy and heat product of reactions

Enthalpy is the measurement of the system’s available energy (internal energy + the work required to displace it in the environment–the product of pressure and volume). Absolute enthalpy of any system is unknowable. Therefore, only the enthalpy delta is useful.

$\Delta H = \Delta U + P \Delta V$

where:

H: enthalpy (kJ)
U: internal energy (kJ)
P: pressure (cubic square)
V: volume (Pascal)

At constant pressure and under the assumption that the only work done in the system is to change the volume (pressure-volume work), the delta of enthalpy is equal to heat exchange of a reaction.

$\Delta H = q + w + P \Delta V$

$\Delta H = q - P \Delta V + P \Delta V$

$\Delta H = q$

where:

q: heat
w: work

A vast number of chemical substances have their $\Delta H$ value determined in standard states. These baseline values are called standard enthalpy of formation and they are available in reference tables.

Using the standard enthalpy of formation of reactants and products on a reaction, it is possible to determine the enthalpy delta of the reaction.

$\Delta H = H_f - H_i$

where:

$H_f$ : final enthalpy, the sum of products’ standard enthalpy of formation.
$H_i$ : initial enthalpy, the sum of reactants’ standard enthalpy of formation.

The sign of enthalpy delta indicates the direction of the heat transference. In particular:

$\Delta H > 0$ , the reaction is “endothermic“, heat is absorbed.

$\Delta H < 0$ , the reaction is “exothermic“, heat is released.

For example, the combustion of carbon monoxide:

$2 CO(g) + O_2(g) => 2 CO_2(g)$

$\Delta H = -393.5 * 2 -(-110.5 * 2 + 0) = - 566.6 kJ$

The reaction is exothermic and releases 566.6 kJ of heat.

Referring to the previous memo on Gas laws, we have:

$m^3 * Pa = J$ .

This particular conversion allows further calculation of pressure-volume work quantity $P \Delta V$ and then the internal energy $U$ from enthalpy.

Entropy and gas product of reactions

Entropy is the measurement of disorder. When the system is shifted to a higher entropy state, it is difficult (impossible in isolated systems) to reverse to a lower entropy state. This is in accordance with the second law of thermodynamics, which states the following:

The entropy in an isolated system will never decrease over time.

The second law leads to some processes are deemed “irreversible processes” in nature.

Entropy does not necessarily always increase. In some ideal scenarios, the entropy can remain constant (or increase in negligible amount), leading to the idea of “reversible processes“.

It should be noted that the reversibility here is thermodynamic reversibility and NOT chemical reversibility. Referring to the previous memo on chemical equilibrium:

These reactions are technically neverending although, in practice, the chemical reaction is considered completed when these two opposite processes reach an equilibrium, at which point the composition of the solution ceases to change.

As reversible reactions don’t have an end, their initial and final states cannot be determined. Thus, their entropies cannot be feasibly determined.

What is seen as “reversible” in a chemical sense is how easy it is to change the equilibrium in favor of products or reactants by introducing new elements to the system. By this very idea, the definition of “chemical reversibility” is incompatible with the second law of thermodynamics, which requires the system to be isolated.

All are not lost, however. Entropy can be used in chemistry to determine whether a reaction produces or consumes gases. Like enthalpy, many chemical substances have their $S$ value determined in standard states and are given in reference tables. These baseline values are called standard molar entropy and they are used in determining the entropy delta as follow:

$\Delta S = S_f - S_i$

where:

$S_f$ : final entropy, the sum of products’ standard molar entropy.
$S_i$ : initial entropy, the sum of reactants’ standard molar entropy.

As a rule of thumb, gases have higher entropy than liquids and liquids have higher entropy than solids.

$\Delta S > 0$ , the reaction produces gases.

$\Delta S < 0$ , the reaction consumes gases.

An example of how the math goes for carbon monoxide combustion is as follow:

$2 CO(g) + O_2(g) => 2 CO_2(g)$

$\Delta S = 239.9 - (197.7 + 130.7 * 2) = -219.2 \frac{J}{K}$

The entropy delta is negative, the reaction consumes gases.

In contrast, see below the hydrogen production from mixing methane and steam:

$CH_4(g) + H_2O(g) => CO(g) + 3 H_2$

$\Delta S = (239.9 + 130.7 * 3) - (186.3 + 188.8) = 256.9 \frac{J}{K}$

The entropy delta is positive, the reaction produces gases

This applies to reactions involving liquid products from solid reactants as well.

Gibbs’ free energy and spontaneity of reactions

Gibbs’ free energy is the measurement of non-pressure-volume work available in an isolated system. It is the difference between enthalpy delta and the product of entropy delta and absolute temperature. Similar to enthalpy, the absolute amount of free energy in any system is unknowable, only the free energy delta can be determined from the formula below.

$\Delta G = \Delta H - T\Delta S$

where:

$\Delta H$ : enthalpy delta (Joule)
$\Delta S$ : entropy delta (Joule per Kelvin)
$T$ : absolute temperature (Kelvin)

Reactions can only happen when there exists free energy to transfer. Reactions that can release free energy happen spontaneously.

$\Delta G > 0$ , the reaction requires energy, it is non-spontaneous.

$\Delta G < 0$ , the reaction releases energy, it is spontaneous.

This says nothing about the heat production or absorption of the reaction as energy flow can be in the form of heat or work. One spontaneous reaction can absorb heat and release work back into the environment, while other spontaneous reaction can release heat and absorb work from the environment.

For example, the combustion of carbon monoxide at room temperature (25 Centigrade or 298.15 Kelvin):

$2 CO(g) + O_2(g) => 2 CO_2(g)$

$\Delta H = -393.5 * 2 -(-110.5 * 2 + 0) = - 566.6 kJ$

$\Delta S = 239.9 - (197.7 + 130.7 * 2) = -0.2192 \frac{kJ}{K}$

$T\Delta S = -0.2192 \frac{kJ}{K} * 298.15 K = -65.354 kJ$

$\Delta G = -566.6 -(-65.354) = -501.246 kJ$

The reaction is spontaneous.

The free energy delta can also be determined from the baseline values–standard molar free energy, which can be found in reference tables–using the below formula:

$\Delta G = G_f - G_i$

where:

$G_f$ : final free energy, the sum of products’ standard molar free energy.
$G_i$ : initial free energy, the sum of reactants’ standard molar free energy.

Verify the above calculation using the standard molar free energy formula:

$2 CO(g) + O_2(g) => 2 CO_2(g)$

$\Delta G = (-394.4 * 2)-(-137.2 * 2 + 0) = -514.4 kJ$

The reaction is spontaneous.

Bonus: State function vs. Non-state function

The process of changing one or more state variables from one value to another is called a state function. State functions describe the relationship between the state variables. State functions are dependent only on the equilibrium state of the system. A few such state functions already covered by the previous memos are the gas laws and the chemical reaction quotient.

State functions are considered (variable) properties of a thermodynamic system. Non-state functions are processes that change the state function itself. For example, heat and work are non-state functions of energy transference from one system to another; unlike the state functions of the system’s temperature change in response to volume change.

There’s an overlap of various terms used in different sources, making it difficult to draw the line between these terms. But, for the most parts, “thermodynamic process” refers to both state and non-state functions while “thermodynamic variable” refers to only state function (and other quantitative variables).

https://en.wikipedia.org/wiki/Thermodynamic_state

https://en.wikipedia.org/wiki/State_function

https://en.wikipedia.org/wiki/Enthalpy

https://en.wikipedia.org/wiki/Standard_enthalpy_of_reaction

https://en.wikipedia.org/wiki/Standard_state

https://en.wikipedia.org/wiki/Introduction_to_entropy

https://en.wikipedia.org/wiki/Entropy

https://en.wikipedia.org/wiki/Second_law_of_thermodynamics

https://chemistry.stackexchange.com/questions/41414/when-is-a-reaction-reversible

https://en.wikipedia.org/wiki/Gibbs_free_energy

https://en.wikipedia.org/wiki/Spontaneous_process

2 thoughts on “Memo: Thermodynamics in Chemistry”

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[…] of any conjugate variable process is the same. The general formula for enthalpy was given in the previous memo on thermodynamics and is mentioned again as […]

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Memo: Atomic models – Fujihita March 3, 201810:44 pm Reply

[…] of matter and energy. When they look at the rules of chemistry through the lens of energy, it is thermodynamics. When they look through the lens of matter, it is atomic physics. Atomic theory belongs the field […]

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