Enthalpy
Enthalpy is an interesting concept: it is defined by its change rather than a single entity. A state property,
the word enthalpy comes from the Greek "heat inside". If you have a chemical system that undergoes
some kind of change but has a fixed volume, the heat output is equal to the change in internal energy (q =
ΔE). We will define the enthalpy change, ΔH, of a system as being equal to its heat output at constant
pressure:
dH = q at constant pressure
Where:
ΔH = change in enthalpy
We define enthalpy itself as:
H = E + PV
Where:
H = enthalpy
E = energy of the system
PV = pressure in atm times volume in liters
You will not need to be able to calculate the enthalpy directly; in chemistry, we are only interested in the
change in enthalpy, or ΔH.
ΔH = Hfinal - Hinitial or ΔH = H(products) - H(reactants)
Tables of enthalpies are generally given as ΔH values.
Example Problem: Calculate the ΔH value of the reaction:
HCl + NH3 → NH4Cl
(ΔH values for HCl is -92.30; NH3 is -80.29; NH4Cl is -314.4)
Answer:
ΔH = ΔHproducts - ΔHreactants
ΔHproducts = -314.4
ΔHreactants = -92.30 + (-80.29) = -172.59
ΔH = -314.4 - 172.59 = 141.8
We can also represent enthalpy change with the equation:
ΔH = ΔE + P ΔV
Where:
ΔV is the change in volume, in liters
P is the constant pressure
If you recall, work is defined as P ΔV, so enthalpy changes are simply a reflection of the amount of
energy change (energy going in or out, endothermic or exothermic), and the amount of work being done
by the reaction. For example, if ΔE = -100 kJ in a certain combustion reaction, but 10 kJ of work needs to
be done to make room for the products, the change in enthalpy is:
ΔH = -100 kJ + 10 kJ = -90 kJ
This is an exothermic reaction (which is expected with combustion), and 90 kJ of energy is released to the
environment. Basically, you get warmer. Notice the convention used here -- a negative value represents
energy coming out of the system.
You can also determine ΔH for a reaction based on bond dissociation energies. Breaking bonds requires
energy while forming bonds releases energy. In a given equation, you must determine what kinds of
bonds are broken and what kind of bonds are formed. Use this information to calculate the amount of
energy used to break bonds and the amount used to form bonds. If you subtract the amount to break bonds
from the amount to form bonds, you will have the ΔH for the reaction.
Example Problem: Calculate ΔH for the reaction:
N2 + 3H2 → 2NH3
(The bond dissociation energy for N-N is 163 kJ/mol; H-H is 436 kJ/mol; N-H is 391 kJ/mol)
Answer:
ΔH = ΔHproducts - ΔHreactants
To use the bond dissociation energies, we must determine how many bonds
are in the products and the reactants. In NH3 there are 3 N-H bonds so in 2 NH3
there are 6 N-H bonds. In N2 there is 1 N-N bond and in 3H2 there are 3 H-H bonds.
ΔHproducts = 6(391) = 2346
ΔHreactants = 163 + 3(436) = 1471
ΔH = 2346 - 1471 = 875
Entropy
Entropy is a measure of the disorder of a system. Take your room as an example. Left to itself, your room
will increase in entropy (i.e., get messier) if no work (cleaning up) is done to contain the disorder. Work
must be done to keep the entropy of the system low. Entropy comes from the second law of
thermodynamics, which states that all systems tend to reach a state of equilibrium. The significance of
entropy is that when a spontaneous change occurs in a system, it will always be found that if the total
entropy change for everything involved is calculated, a positive value will be obtained. Simply, all
spontaneous changes in an isolated chemical system occur with an increase in entropy. Entropy, like
temperature, pressure, and enthalpy, is also a state property and is represented in the literature by the
symbol "S". Like enthalpy, you can calculate the change of S (ΔS).
Δ S = Sfinal - S initial or Δ S = S (products) - S (reactants)
Where:
ΔS is change in entropy
Sfinal and Sinitial are the final and initial entropies, respectively
The following table shows the relationship between the state of a substance and its entropy:
State of substance Relative Entropy (S)
gas
highest S
aqueous
high S
liquid
medium S
solid
lowest S
Gibbs Free Energy
The free energy of a system, represented by the letter "G", is defined as the energy of a system that is free
to do work at constant temperature and pressure. Mathematically, it is defined as:
G = H - TS
Where:
G is the energy (sometimes called the free energy)
H is the enthalpy
T is the temperature
S is the entropy of the system.
You can also calculate the change in G the same way as you calculate the change in enthalpy or entropy:
ΔG = G(products) - G(reactants)
Where:
ΔG is change in free energy
A pop-up calculator is available to calculate the enthalpy and Gibbs free energy changes in reactions.
Given a constant temperature and pressure, the direction of any spontaneous change is toward a lower
Gibbs free energy. The graphic below shows that during a reaction, the amount of free energy decreases
until the reaction is at equilibrium. If the reaction goes towards completion, the free energy minimum
occurs very close to the pure products part of the curve. In other words, the curve moves depending on the
conditions of the reaction.
A table relating all of the state properties summarized on the previous page -- enthalpy change, entropy
change, and change in free energy -- is shown below. A spontaneous reaction is one that occurs without
any outside intervention. Processes that are spontaneous in one direction are non-spontaneous in the
reverse direction.
Enthalpy Change
Entropy Change
Spontaneous Reaction?
Exothermic (ΔH < 0)
Increase (ΔS > 0) Yes, ΔG < 0
Exothermic (ΔH < 0)
Decrease (ΔS < 0) Only at low temps, if |T ΔS| < |ΔH|
Endothermic (ΔH > 0) Increase (ΔS > 0) Only at high temps, if T ΔS > ΔH
Endothermic (ΔH > 0) Decrease (ΔS < 0) No, ΔG > 0
Enthalpy Practice Problem: Given the following bond dissociation energies (H-C is 413 kJ/mol; H-H is
436 kJ/mol; C=C is 614 kJ/mol; C-C is 348 kJ/mol), determine ΔH for the reaction:
H2C=CH2(g) + H2(g) --> H3C-CH3(g)
Enthalpy solution.
Entropy Practice Problem: Given the following entropy values Al2O3(s) is 51.00 kJ/mol; Al(s) is 28.32
kJ/mol; H2O(g) is 188.7 kJ/mol; H2(g) is 130.6 kJ/mol, determine ΔS for the reaction:
Al2O3(s) + 3H2(g) --> 2Al(s) + 3H2O(g)
Entropy solution.
Developed by
Shodor
in cooperation with the Department of Chemistry,
The University of North Carolina at Chapel Hill
Copyright © 1996-2008 Shodor
http://www.shodor.org/unchem/advanced/thermo/index.html
From Texas A & M
http://www.chem.tamu.edu/class/majors/tutorialnotefiles/enthalpy.htm
- Reaction in which a system
RELEASES
heat to its surroundings.
Exothermic
H is negative ( H < 0)
Ea is the activation energy which is discussed in more
detail in the kinetics unit. (See Activation Energy
notes)
- Reaction in which a system
ABSORBS
heat from its surroundings.
Endothermic
H is positive (
From Texas A & M