Chapter 20 Lecture Notes

In this Chapter we return to a discussion of thermodynamics, the study of heat and energy flow. Actually we have been doing thermodynamics most of this semester although it has been 'hidden'.

The thermodynamics that we have discussed openly were the concepts of edothermicity and exothermicity. This is a good place to start. To determine whether a particular reaction is endothermic or exothermic we need to calculate the H^o_rxn for the reaction of interest. (To review calculating H^o_rxn check out this lecture from CHEM 1314.)

When we discuss the first law of thermodynamics (heat is neither created or destroyed, or the conservation of energy) in CHEM 1314. One of the many ideas discussed was the concept of internal energy, the sum of the kinetic and potential energy of all the particles in a particular system. We can calculate the change in internal energy, E, by measuring the amount of work done by or on the system and the amount of heat that flows into or out of the system.

In this Chapter we are more interested in reactions that occur on their own, and reactions or changes that can not occur on their own. For example consider two reactions we have seen before;

2Al(s) + 3Br₂(l) ---> Al₂Br₆(s) H^o_rxn = -526.3 kJ

CH₄(g) + 3O₂(g) ----> CO₂(g) + 2H₂O(l) H^o_rxn = -890 kJ

Both of these reactions are very exothermic. Both of these reactions are spontaneous. The word spontaneous means something very specific when we discuss thermodynamics. Spontaneous means , a tendency to proceed in one particular direction unassisted. A reaction considered spontaneous is one which proceeds from reactants towards products without any assistance. This is the case for these two reactions. A nonspontaneous reaction would be the following;

CO₂(g) + 2H₂O(l) ----> CH₄(g) + 3O₂(g) H^o_rxn = +890 kJ

We would never expect to see carbon dioxide mixed with water producing methane gas spontaneously. One difference, thermodynamically, between these two reaction is that one is exothermic and the other is endothermic. Could we use this difference to predict whether a particular reaction is spontaneous or not (assuming we could not test the reaction ourselves). Reactions that are exothermic are reactions where the reactants are at higher energy compared to the products. Going from reactants to products releases the difference in energy to the surrounding, so why not?

It would be like allowing an object at high potential energy to fall/move downhill (in energy), by dropping the object. That is a spontaneous process and ther everse of that process is nonspontaneous.

At first glance it actually looks reasonable. However, there are reactions that are endothermic that do occur unassisted, and therefore are spontaneous. One example is the reaction;

So we can not use our knowledge of H^o_rxn to determine whether it is sppontaneous or not.

Some other examples are useful. Consider the following physical changes;

H₂O(l) ----> H₂O(s)

H₂O(s) ----> H₂O(l)

The first is exothermic and the second is endothermic. Below 0 degrees Celsius liquid water will spontaneous convert to the solid phase (freeze), and above 0 degrees Celsius water in the solid phase will spontaneous melt. Both reactions are spontaneous at slightly different temperatures, under different conditions.

The process of dissolution of solids in water is generally endothermic, and we know lots of ionic solids that dissolve in water.

NaCl(s) --H₂O(l)--> Na⁺(aq) + Cl^-(aq)

So whether a reaction is endothermic or not may not be the best predictor of whether a reaction is spontaneous or not.

But is there anything interesting about these systems that were endothermic, yet spontaneous? Lets look at those reactions more carefully;

Ba(OH)₂.8H₂O_(s) + 2NH₄SCN_(s) ---> Ba(SCN)_2(aq) + 2NH_3(g) + 10H₂O_(l)

H₂O(s) ----> H₂O(l)

NaCl(s) --H₂O(l)--> Na⁺(aq) + Cl^-(aq)

In the first case there are three moles of reactants going to 13 moles of products, and the reactants are both solids and the products are liquid, gas, or dissolved. In the second change water in the solid state changes to water in the liquid state, and finally the sodium chloride, in the solid state, dissolves forming ions in solution.

In each case the products are in states that are not as ordered as the reactants. Solids are very ordered, but liquids and gases are not. Perhaps this change in order is a key to our search to understand spontaneity?

The concept of order is not that strange to us. What happens when shuffle a deck of cards and deal out five cards, what do you think is the chance that I might deal a straight flush? Not very good? Beginning with a deck of cards in rank order from ace to king of each suit, and then shuffling them. How long would I need to shuffle to shuffle them back into order again?

If we shuffle the deck the cards become disordered. In fact the more we shuffle the more disorded it becomes. In fact there are 8.066 x 10⁶⁷ possible different ways to arrange the 52 cards in this deck. When we shuffle the probability that any particular order occurs is then 1 chance in 8.066 x 10⁶⁷. So there are lots of differnet possible arrangements of the cards. We can think of some ordered arrangements, but the number of disordered arrangements far out number the number of ordered arrangements. And in a deck of cards we are only concerned with 52 cards!

What about molecules and atoms? Here we are talking about really big numbers!! 6.023 x 10²³ in a mole of any substance.

Suppose we have a container separated into two compartments, one side with 20 particles on one side and none on the other side. If I open the door between the two compartments what would you expect the distribution of particles to be after a period of time?

Answer

Scientists use the concept of entropy to describe the number of different possible arrangements for a system. That is, entropy measures the amount of disorder in a system. High entropy values indicate a high degree of disorder.

In a chemical reaction if the products side of the equation has great dissorder compared to the reactants the reaction is described as increasing in entropy, increasing in disorder. Increasing disorder is the favored direction. The system with the 20 particles expanding into an evacuated container is an excellent example. There is no change in temperature in this system, before and after the removal of the barrier. The drive of the change is an increase in disorder. There is a greater volume for the particles so there are a greater number of arrangements of the positions of the particles.

It is in fact this natural tendency towards disorder that defines spontaneity in events, chemical or otherwise. We stated earlier the first law of thermodynamics, the second law is related to entropy.

the second law of thermodynamics states that spontaneous natural processes are accompanied by an increase in the entropy of the universe.

We can express this mathematically using the symbol for entropy, S, in the following terms,

S_universe = S_system + S_surrounding > 0

This relationship says that if we add the change in entropy for a system, like a chemical reaction, to the change in entropy of the surrounding, and that value is greater than zero the process is favored.

Spontaneous processes have a S_universe that is greater than zero. So a chemical reaction (the system) may have a negative S, but as long as the S of the surroundings is positive and greater in magnitude compared to the S of the reaction the reaction will still be spontaneous.

Since entropy is a measure of dissorder we would expect something that is ordered to have a very low entropy. This is the case. In fact this is the basis of the third law of thermodynamics,

the third law of thermodynamics says that the entropy of any pure substance a absolute zero is zero.

When we add heat to a pure substance the particles of that substance begin to vibrate and the solid begins to expand and the substance absorbs energy. When this occurs there is an increase in the disorder of the substance and the entropy increases. Since the entropy of a pure substances depends on its temperature the units on entropy are joules Kelvins^-1.

We are most interested in the entropy of substances at 25 degrees Celsius and 1 atmosphere (standard state conditions).

Some entropy values for pure substances are shown below;

You should have some intuition about entropy values in terms of physical states, temperature, solution process and molecular complexity.

physical states - looking at the table above in gneral the entropy values for gases are larger than entropy values for liquids and for solids. A gas is more disordered compared to a liquid and both liquid and gas are more disordered than a solid. So we would expect that chemical reactions producing more gases compared to the reactants will have a positive S.

temperature - As discussed earlier about the third law of thermodynamics, the higher the temperature the greater the disorder for the substance/system.

solution process - dissolving solids in water/solvent generally leads to greater disorder. So comparing NaCl(s) to NaCl(aq) the aqueous solution is more disordered compared to the solid. However, there are some exceptions to this rule. some ions have a very large charge and when added to water, order the water molecules resulting in a more order state. Al³⁺ is an example of an ion that when dissolved in water produces produces a more ordered system. When gases dissolve in water the S is always negative. For example, O₂(g) has a higher entropy than O₂(aq).

molecular complexity - this is a more complicated issue. From the table above we can see some trends, for example, HF, HCl, HBr and HI. The entropy value increases going down the group. The more electrons in the molecule of similar structure the greater the entropy. We can also see a similar trend for CH₄(g), C₂H₆(g), and C₃H₈(g). In this case the molecule is getting more complex as CH₂ groups are added.

So try your intuition on the following examples.

Predict whether S is positive, negative, or close to zero for the following changes.

a) 2H₂(g) + O₂(g) ----> 2H₂O(g) Answer

b) 2KClO₃(s) ----> 2KCl(s) + 3O₂(g) Answer

c) 2NO₂(g) ----> N₂O₄(g) Answer

d) CH₄(g) + 3O₂(g) ----> CO₂(g) + 2H₂O(l) Answer

It is important to have some intuition about whether the value of S is positive or negative for a chemical reaction, but we also have to be able to calculate the value for S^o for a reaction. The equation we use to calculate S^o for a reaction uses the fact that entropy is a state function. Since entropy is a state function we can use Hess' Law to determine the S^o for a reaction. So the mathematical equation we use to calculate S^o for a reaction is;

Lets consider some sample problems.

Calculate S^o for a each of the following reactions,

a) 2H₂(g) + O₂(g) ----> 2H₂O(g) Answer

So we can calculate S^o for a reaction, but how does that help us determine whether a reaction is spontaneous.?

The issue of spontaneity according to the 2nd law is related to the S_universe for a chemical or physical change. So the question is how do we calcualte the S_universe? According to the 2nd law,

S_universe = S_system + S_surrounding > 0

We know how to calculate the S_system , we did that in the example above where we calculated the S^o for the reaction, 2H₂(g) + O₂(g) ----> 2H₂O(g). But how do we calculate the S_surrounding? That is a little more difficult.

Let's begin by thinking about S_surrounding from a qualitative stand point. The way we'll approach the entropy of the surrounding is to consider what happens when an exothermic reaction occurs in a container. An exdothermic reaction is one in which the heat produced in the reaction is liberated/transferred to the surroundings. So the surrounding get hotter. We also know from our earlier discussion of entropy that as the temperature increases so does the entropy. So we can say mathematically that,

S_surrounding -q_surrounding

Additionally when heat is transferred to the surrounding and the surroundings are at a low temperature the effect on the change in entropy is much greater than when that same amount of heat is transferred to the surroundings when the surroundings are at a higher temperature. We can express this mathematically as,

S_surrounding

So combinning these two ideas we have,

If we are studying the reaction at constant pressure than q_surrounding = H_system.

So if we return to the orginal 2nd law equation,

S_universe = S_system > 0

this relationship can be re-arranged in the following way,

Now we will define a new function, called free energy (G) to represent -TS_universe and the relationship becomes,

G_system = H_system - TS_system > 0

The way we use this relationship to determine if a reaction is spontaneous is to calculate H and S for the reaction of interest, then use the equation above to calculate G for the reaction. If G is less than zero the reaction is spontaneous, if G is greater than zero the reaction is nonspontaneous.

We know how to calculate H and S for a reaction, so calculating G is not too difficult. Lets look at an example, by continuing with the reaction producing water for which we've already calculated S,

Sample Problem

Is the reaction below spontaneous at 298 K?

a) 2H₂(g) + O₂(g) ----> 2H₂O(g) Answer