Lesson 16. 1 Entropy
Suggested Reading
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Zumdahl Chapter 16 Sections 16.1 - 16.3 & 16.5
Essential Question
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What is the relationship between spontaneity and entropy?
Learning Objectives:.
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Define entropy.
State the second law of thermodynamics.
State the criteria for spontaneity according to the second law of
thermodynamics.
Predict the spontaneity of a reaction using the concept of entropy.
Calculate the change in entropy for a chemical reaction.
Introduction
Recall from Chapter 6 that thermodynamics is the study of the relationship
between heat and other forms of energy involved in a chemical or physical
process. With only heat measurements you can predict the natural direction of
a chemical reaction, and you can also determine the composition of a reaction
mixture at equilibrium. Why does a chemical reaction go naturally in a
particular direction? To answer this question, we need to look at spontaneous
processes. A spontaneous process is a physical or chemical change that
occurs all by itself. A rock at the top of a hill rolls down, heat flows from a hot
object to a cold one. An iron object rusts in moist air. These processes occur
spontaneous, or naturally. They continue until equilibrium is reached. If these
processes were to go in the opposite direction, they would be
nonspontaneous. The rolling of a rock uphill by itself is nonspontaneous, or
not natural. The rock could be moved uphill, but work would have to be
expended. Heat can be made to flow from a cold to a hot object, but a heat
pump or refrigerator is needed. Rust can be converted to iron, but chemical
processes are required. In this chapter we will investigate spontaneous
processes by defining enthalpy more precisely in terms of the energy of the
system and by introducing the concept of enthalpy.
Chapter 6 Vocabulary Review
Internal energy (U), is the sum of the kinetic and potential energies making
up a system.
State function, is a property of a system that depends only on its present
state, which is completely determined by variables such as temperature and
pressure.
Work (w) is the energy exchange that results when a force F moves an object
through a distance d; w = F x d
Heat is the energy that flows into or out of a system because of a temperature
difference between a system and its surroundings.
First Law of Thermodynamics states that the change in internal energy of a
system, ∆U, equals q + w; ∆U = q + w. This is essentially the law of
conservation of energy applied to chemical systems.
"Pressure-Volume Work" is the work done by chemical reactions, which
is equal to the pressure times the change in volume, w = -P∆V, where the
negative signs is given because work is done by the system and represents
energy lost by it.
Enthalpy is a quantity obtained from the first law of thermodynamics that is
equal to the heat of reaction at constant pressure (qp). Since most chemical
reactions take place under the constant pressure of the atmosphere, we use
enthalpy to describe the heat exchanges that occur between a chemical
system and its environment during a chemical reaction under constantpressure conditions. Enthalpy is obtained from the first law as follows.
1. The heat at constant pressure, qp, and pressure-volume work -P∆V
are substituted into the first law, ∆U = q + w, giving ∆U = qp -P∆V.
2. This equation is solved for qp giving qp = U + P∆V.
3. Enthalpy was defined by scientist as the quantity U + P∆V.
Thus, qp = H.
For chemical reactions where no work is done the the environment, as is
often the case, qp = U + P∆V, becomes qp = U. Thus, enthalpy is usually
equal to the internal energy of the system, H = U.
Entropy
When you want to know if a chemical reaction is spontaneous in the
direction written, the first law of thermodynamics can't help you. It does
help you keep track of the energy changes that occur in a chemical
reaction (conservation of energy). At one time it was thought that
spontaneous reactions must be exothermic (∆H < 0), however, many
spontaneous reaction are now known to be endothermic (∆H > 0). The
second law of thermodynamics provides a way to to answer questions
about spontaneity. The second law is expressed in terms of a quantity
called entropy. Entropy (S) is a thermodynamic quantity that is a measure
of the randomness or disorder in a system. Entropy, like enthalpy, is a state
function. Thus, the quantity of entropy depends only on variables such as
temperature and pressure. If these variables are fixed, then the quantity of
entropy is also fixed.
For example, 1 mol of ice at 0 deg C and 1 atm has an entropy that has
been determined experimentally to be 41 J/K. One mole of liquid water
under these same conditions has an entropy of 63 J/K.
The picture on the right helps to illustrate this. Recall from Chapter 10 that
ice is a molecular solid with a high degree of order in its structure.
Therefore, it has less entropy than a puddle of water which is must more
disordered.
The physical state(s) of the system contributes to its entropy.
You calculate the entropy change, ∆S, in the same way you
calculate ∆H; ∆S = Sf - Si.
Thus, for the melting of water ∆S = (63 - 43)J/K = 22 J/K. Entropy is a
positive value because it increases as ice melts.
Positional Entropy
The order or disorder of a system is related to the number of arrangements of
the system. Entropy increases with the number of configurations that result in
a particular state. You can think of this in terms of the way a library is
arranged using the Dewey decimal system. There is only one way to arrange
the books in a library according to this system. Thus, a library organized
according to this system is in a highly ordered state, and entropy is therefore
low. But how many ways are there for the books to be out of order? When we
pull the books off the shelves and begin mixing them up, we see that there are
many many ways for the books to be out of order. When the books are mixed,
the library is in a highly disordered state, and entropy is high.
Apply this to the states of matter. Solids often have atoms or molecules at
fixed points in a lattice. There is only one way to achieve the solid structure, it
is highly ordered, and therefore low in entropy. Gases, on the other hand, are
in constant random motion. There are numerous places each particle in the
gas can reside. This represents a highly disordered state, and the entropy of
gases is therefore high.
Second Law of Thermodynamics
The second law of thermodynamics describes the relationship between
entropy and spontaneity for natural processes. A process occurs naturally if
there is an overall increase in disorder because there is a natural tendency for
things to mix and to break down. Thus, the second law of thermodynamics
states that the total entropy of a system and its surroundings always increases
for a spontaneous process. Unlike energy, which is conserved, entropy is
created in a spontaneous process.
In chemistry, we are interested in whether a not a reaction will occur
spontaneously, so we usually use the following statement of the second law,
because it gives us a means of predicting spontaneity. For a spontaneous
process at a given temperature, the change in entropy of the system is greater
than the heat divided by the temperature of the system.
if q = qp then it can be inferred that
and at equilibrium
Since phase changes occur at equilibrium this equation is used to calculate
the entropy change associated with a phase change. Lets look at an example.
Example: Calculating the Entropy Change for a Phase Change.
The heat of vaporization, ∆Hvap, of carbon tetrachloride, CCl4, at 25 deg C
is 43.0 kJ/mol.
If 1 mol of liquid carbon tetrachloride at 25 deg C has an entropy of 214 J/K,
what is the entropy of 1 mol of vapor in equilibrium with the liquid at this
temperature?
Solution:
The entropy of the vapor equals the entropy of the liquid plus the entropy
change. Thus,
Predicting Spontaneity
The second law of thermodynamics gives us a tool for predicting whether or
not a chemical equation is spontaneous. Consider the following reaction for
the production of urea, an important industrial chemical with many
applications.
Is this reaction spontaneous? That is, does it go left to right as written? You
can use the second law in the form ∆S > q/T if you know both ∆S and ∆H.
Recall from above, that for a spontaneous reaction at constant T and P, ∆S
> ∆H/T. Since, ∆S is greater than ∆H/T if you subtract ∆S from ∆H/T, you get a
negative number giving
This inequality is important! We can use it to calculate enthalpy given T & S,
or entropy given T & H. Furthermore, it gives us a criterion for spontaneity. If
∆H - T∆S < 0, a reaction is spontaneous as written.
∆H - T∆S > 0, a reaction is non-spontaneous as written.
∆H - T∆S = 0, a reaction is at equilibrium.
Standard Entropies and the Third Law of
Thermodynamics
Recall from Chapter 6 that the standard enthalpy of formation is the enthalpy
change for the formation of one mole of a substance in its standard state from
its elements in their reference forms and standard states. Standard entropy is
analogous to standard enthalpy, but it is quantified by applying the third law of
thermodynamics.
The third law of thermodynamics states that a substance that is perfectly
crystalline at 0 K has an entropy of 0. This seems reasonable. A perfect
crystal substance at 0K should have perfect order. When the temperature is
raised, however, the substance becomes more disordered as it absorbs heat.
To calculate standard entropies, we start off with a perfect crystal at 0K and
then gradually add heat until 298 K is reached. We can then calculate the
change in entropy by dividing the heat added by temperature.
You will not have to calculate standard entropies, but when you use values for
standard entropy you should have an understanding of how they are obtained.
The standard entropy (aka absolute entropy) S∘,is the entropy value for the
standard state of the species. For a substance, the standard state is the pure
substance at 1 atm and 298K. For a species in solution, the standard state is
the 1 M solution at 298 K. The symbol S∘ is used instead of ∆S∘ to
emphasize that they originate from the third law. Also note that, unlike
standard enthalpy, elements have nonzero standard entropies. Values for
standard entropy can be found alongside values for standard enthalpies in
tables of thermodynamic data.
Entropy Change for a Reaction
You can calculate the change in entropy for a reaction from standard
entropies in the same way that you calculate standard enthalpies of
reaction. However, even without knowing the values for the entropies of
substances, you can sometimes predict the sign of ∆S∘ for a
reaction. Entropy usually increases in the following situations.
1. A reaction in which a molecule is broken into two or more smaller
molecules.
2. A reaction in which there is an increases in moles of gas.
3. A process in which he solid changes to a liquid or gas or a liquid
changes to a gas.
Example: Predicting the Sign of the Entropy Change in a Reaction
The following equation represents the essential change that takes place
during the fermentation of glucose to ethanol.
C6H12O6(s) → 2C2H5OH(l) + 2CO2(g)
Is S∘ positive or negative? Explain.
Solution:
All of the guidelines above are evident in this reaction. A larger molecule is
broken down, there is an increase in moles of gas (0 to 2), and a solid
changes to a liquid and a gas. Therefore, we would expect entropy to be
positive.
The change in entropy can be determined quantitatively using the equation
Example: Calculating ∆S∘ for a reaction.
Calculate the change in entropy at 25 deg C for the reaction in which urea
is formed.
The standard entropy for urea is 174 J/(mol K), ammonia is 193 J/(mol K),
carbon dioxide is 214 J/(mol K), and liquid water is 70 J/(mol K).
It is convenient to put the entropy values multiplied by stoichiometric
coefficients below the formulas in the equation.
2 x 193
214
174
70
Plugging in gives
=[(174 + 70) - (2 x 193 + 214)]J/K = -356 J/K
Homework: Book questions pg. 783 questions 19, 24,
25, 27, 35, 37, 39