**Part I:**

**Direction of Spontaneous Change-Entropy and Disorder**

© Silvia Kolchens

Pima Community College

Part I: Direction of spontaneous change - Entropy and Disorder

Part II: How to determine entropy changes

Part III: First Law of Thermodynamics

Part IV: Free Energy

**Introduction:**

So far we discussed:

**Kinetics** = tells us **how fast** a reaction occurs

**Equilibrium** = tells us **how much** product is formed (whether
a reaction is product or reactant favored).

**Thermochemistry**= tells us whether a reaction is **exothermic
or endothermic**

In this and the following two modules we will discuss **"Thermodynamics"-
which will answer the question: Why does a a chemical reaction occur? **Thermochemistry
is a sub discipline of Thermodynamics.

**Spontaneous and non-spontaneous chemical and physical changes**:

A spontaneous change takes place by itself. Examples are:

Rusting of iron when oxygen and moisture are present

- Production of aluminum from bauxite (an aluminum oxide)
- Isolation of sugar dissolved in tea
- Formation of iron from iron oxide

The term "spontaneous" has nothing to do with the speed at which
the process occurs. The term "spontaneous" means only a reaction will occur
given enough time.

Examples:

Product favored chemical reaction (=spontaneous)

2 Na (s) + 2 H_{2}O(l) ó
2 NaOH(aq) + H_{2}(g) K>>1

Reactant favored reaction (=not spontaneous), but very fast reaction

O_{3}(g) ó O(g) + O_{2}(g)
K<<1

Product favored (=spontaneous), but ignition necessary to overcome activation barrier.

2 H_{2}(g) + O_{2}(g) ó
2 H_{2}O(l) K>>1

**Why does a chemical reaction occur?**

There are two driving forces -

- The energy change that is associated with a chemical reaction (endothermic, exothermic)
- The change in "Entropy" or the natural tendency for a system to become disordered

**Example:** Hot coffee gets cold: its energy is transferred onto
the molecules of the surroundings (cup, air, table etc). Never will be
observed that a cold coffee gets spontaneously hotter by absorbing heat
from surrounding cup, air molecules, and the table (you will have to provide
energy in the form of heat or microwaves to heat the coffee). More generally
we can say that energy is transferred from a system (the coffee) to its
surroundings (cup, air, and table)

**System è surroundings**

Responsible for the cooling of coffee is the dispersal of energy from relatively few molecules within the coffee cup to many molecules of its surroundings.

**Energy Dispersal:** Potential energy that has been stored in relatively
few atoms and molecules (=reactants) is released and spreads out over many
more atoms and molecules (=products and surroundings).

**Why does this dispersal of energy occur?** The answer lies with
probability. Let's consider a very simple system such as two atoms (A and
B) and two units of energy. The two units of energy can now be both on
atom A or both on atom B or one on A and one on B and we have the following
distribution:

A2 AB B2

There are three different combinations and the probability of finding the energy units is 1/3 for each of these possibilities. Now let us consider that our system (atoms A and B) get in contact with some surroundings (atoms C and D). Atoms C and D have no energy units (they are "cooler" than the system). Now we have the following situation:

A2 AB B2 AC AD BC BD C2 D2 DC

We have the three original arrangements plus seven new arrangements,
i.e. the probability of finding the both energy units in any one of these
states is only 1/10, and as a result the energy is more dispersed. This
tendency to disperse is also called an increase in disorder. The thermodynamic
term for an increase in disorder is **ENTROPY** .

- Highly concentratated energy è disperse
- Highly concentrated matter è disperse

Just as highly concentrated energy will disperse, so will highly concentrated matter. An example is the expansion of gas.

If we consider a simple system composed of 1 gas atom and two compartments A and B, then we can find the gas atom either in A or in B. Therefore the probability of finding the atom is 1/2.

In a situation of two gas atoms (x and o) and two compartments we have
4 different arrangements and the probability of finding the gas atoms in
either arrangement is 1/4: For two atoms and two compartment the probability
of finding the atoms in either arrangement is (1/2)^{2}=1/4

**Generally: for n molecules: probablity = (1/2) ^{n}**

For one mole of gas n=6.022x10^{23 }atoms and the probability
of finding all gas atom in just one compartment are very, very small. Thus,
the expansion of gas is a spontaneous process. In order to reverse the
process outside work is required, such as provide by a pump.

In summary, both examples showed that energy as well as matter will always dispserse. This dispersal is a spontaneous process. Energy is required to reverse the process.

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