Chapter 1: Chemical Equilibrium Part 12 SABIS Grade 11 (Level M) Chemistry

1.9 Factors which Determine Equilibrium

Factors which Determine Equilibrium

What determines the equilibrium constant? Why does one reaction favor reactants and another reaction favor products? What factors cause sodium chloride to have a large solubility in water and silver chloride to have a low solubility? Why does equilibrium favor the reaction of oxygen with iron to form Fe2O3 (rust) but not the reaction of oxygen with gold? As scientists, we cannot resist wondering what factors determine the conditions at equilibrium.

This is the activity of science we called “Wondering Why”—we are searching for an explanation. An explanation is a likeness, which connects the system under study with a model system which is well understood.

1.9.1 Tendency Towards Lower Potential Energy

Consider a bottle standing on its base. When it is pushed, it tends to fall over to the side so its centre of gravity is closer to the centre of the earth, so the bottle-earth system has a lower potential energy. The lost potential energy is converted to heat. Consider two magnets, placed with the north pole of one magnet close to the south pole of another. The poles tend to move together, collide, and the lost potential energy is converted to heat.

Similarly, if a flame ignites a piece of paper, chemical potential energy is released in the exothermic reaction that follows and the lost chemical potential energy is converted to heat.

We can generalize by saying that whenever possible, a system tends to “move” in the direction of minimum potential energy.

However, there is another complication that comes into the picture.

We might begin by considering Figure 1.16 Here we see golf balls spilled onto the floor of a station wagon. Because the floor has a step in it, the golf balls on the upper level possess more potential energy than at the lower level. The golf balls tend to roll to the lower level spontaneously. As a golf ball does this, its potential energy becomes kinetic energy (energy of motion). Finally, the golf balls lie at rest at the lower floor level. 

This situation has some similarities to the chemical change in a spontaneous, exothermic reaction (e.g. a burning piece of paper). The reactants of high heat content react spontaneously to form products of lower heat content. As each molecular reaction occurs, the excess heat content becomes kinetic energy. The product molecules separate from each other with high kinetic energy. As they collide with other molecules, this energy is dissipated into heat. Figure 1.16 shows this through a heat content diagram for the chemical reaction.

(1) There are two states of each system:

                        Initial State                Final State

Golf balls:       on upper level    →    on lower  level

Reaction:        reactants            →    products

(2) The potential energy of the initial state is higher than the potential energy of the final state:

                       Initial State                      Final State

Golf balls:       potential energy    →      kinetic energy and then heat

Reaction:        heat content          →      molecular kinetic energy, and then heat

(3) The changes from initial to final state proceed spontaneously toward lowest potential energy, the direction corresponding to ''rolling downhill'':

                      Initial State             →        Final State

Golf balls:                           spontaneous

Reaction:                            spontaneous

Having established these similarities, we might offer a possible generalization:

Since: golf balls always roll downhill spontaneously

Perhaps: reactions always proceed spontaneously in the direction toward minimum energy.

This proposal leads us to expect that a reaction will tend to proceed spontaneously if the products have lower energy than the reactants. This expectation is in accord with experience with many reactions, especially for those which release a large amount of heat.

There are two basic and serious difficulties with our proposed explanation.

(1) Some endothermic reactions proceed spontaneously. One example is the evaporation of a liquid. Water evaporates spontaneously but it absorbs heat as it does so. It is not “rolling downhill” energetically. When ammonium chloride dissolves in water, the solution becomes cooler. Again heat is absorbed — yet the ammonium chloride goes ahead and dissolves.

(2) Spontaneous chemical reactions do not go to completion. Even if a spontaneous reaction is exothermic, it proceeds only till it reaches equilibrium. But in our golf ball analogy, “equilibrium” is reached when all of the golf balls are on the lower level. Our analogy would lead us to expect that an exothermic reaction would proceed until all of the reactants are converted to products, not to a dynamic equilibrium.

Because of these failures, we need to alter our proposed explanation. We must seek a new analogy that gives a better correspondence with the behavior of chemical reactions. How should we alter our golf ball analogy to bring it into better accord with experimental facts? Here is a possible view.

1.9.2 Tendency Towards Maximum Randomness

Consider two cards, an ace (1), and the 2. There are only two ways of arranging the cards, both ways “ordered” 1,2 or 2,1.

Consider three cards, an ace (1), a 2 and a 3. There are six ways of arranging the cards, 1, 2, 3;  1, 3, 2;  2, 3, 1;  2, 1, 3;  3, 2, 1  and  3, 1, 2. Two of the six are ordered and they are shown in bold print.

Consider five cards, an ace (1), and the cards 2, 3, 4 and 5.

They can be arranged in 120 different ways, here are a few:

Each order has the same probability as any of the others. However, only two (in bold print) we consider as “special” or “ordered” and the rest are considered as “disordered”. As the number of cards increases, the ratio of ordered arrangements to disordered arrangements decreases rapidly.

We see that as the number of cards increases, the ordered arrangements rapidly become a very small fraction of the total number of possible arrangements.

If we are to shuffle the cards then look at the arrangement we get, most probably we will end up with one of the arrangements that are called disordered. We can say that there is a high tendency for the cards to be disordered, or “random”.

We can say that shuffling favors randomness.

In a chemical reaction, the molecular motions due to their temperature is equivalent to shuffling. Molecules tend to favor random arrangements. Since molecules have the greatest freedom of movement in the gaseous state and the least freedom of motion in a crystal, we say that the gaseous state is more random than the liquid state, which in turn is more random than the solid state.

Consider how the golf ball situation shown in Figure 1.17 will change when the station wagon is driven over a bumpy road. Now the golf balls are shaken and jostled about; they roll around and collide with each other. Every now and then one of the golf balls even accumulates enough energy (through collisions) to return to the upper level of the station wagon floor. Of course, any golf ball that is bounced up tends to roll back down to the lower level a little later. As this bumpy ride continues, a state is reached in which golf balls are being jostled up to the higher level at the same rate they are rolling back down to the lower level. Then “equilibrium” exists. Some of the golf balls are on the lower level and some on the upper level. Since the rate of rolling up equals the rate of rolling down, a dynamic balance exists.

This analogy solves the problems of the simpler “golf balls roll downhill” picture. The bumpy road model contains a new feature that gives a basis for expecting “reaction” in the endothermic direction. Some golf balls roll uphill if they are shaken hard enough.

The tendency to roll back down will always keep them coming back to the lower level and, finally, equilibrium will be reached when the rate of rolling down equals the rate of jostling up.

What happens if the road becomes smoother? The “jostling up” reaction is less favored—the equilibrium conditions change in favor of the golf balls at the lower level. Now turn to the chemical reaction. What feature in a reacting chemical system corresponds to the jostling of the bumpy road in our analogy? It is the temperature. At any temperature except absolute zero there is a constant random jostling of the molecules. Some molecules have low kinetic energies, some have high kinetic energies. Some of the molecules will occasionally accumulate enough energy to “roll uphill” to less stable molecular forms.

On one hand, molecular changes will take place in the direction of minimum energy. On the other hand, molecular changes will finally reach a dynamic equilibrium when the random jostling or energy transfers at the temperature of the system are restoring molecules to the molecular forms of higher energy at the same rate as they are “rolling downhill” to the lower energy forms.

Now we have an analogy that aids us in understanding chemical reactions and equilibrium. We can see the following features of chemical reactions:

(1) Chemical reactions proceed spontaneously to approach the equilibrium state.

(2) One factor that fixes the equilibrium state is the energy. Equilibrium tends to favor the state of the lowest energy.

(3) The other factor that fixes the equilibrium state is the randomness implied by the temperature. Equilibrium tends to favor the state of greatest randomness.

(4) The equilibrium state is a compromise between these two factors, minimum energy and maximum randomness. At very low temperatures, energy tends to be the more important factor. Equilibrium then favors the molecular substances with the lowest heat content. At very high temperatures, randomness becomes more important. Equilibrium then favors a random distribution among reactants and products without regard for energy differences.

Our analogy can be stretched one point further. We might ask whether the relative area of the upper floor level compared with that of the lower floor level has any bearing on the distribution of golf balls. After all, if the upper level area is small, as in Figure 1.16, few golf balls are likely to remain there. Contrast Figure 1.18, in which the upper floor level has much more area. Golf balls which reach the upper level will now have a great deal of space. They can roll around longer before returning to the lower level. The effect of extending the upper level will be to increase the fraction of the golf balls that occupy the upper level at “equilibrium.”

This extension of the analogy increases its value in considering chemical reactions. The simplest example is probably the vaporization of a liquid. It is true that the molecules have lower energy when they cluster together tightly in the liquid state. On the other hand, the gaseous state provides a broad upper level. Every molecule, which vaporizes has an amount of space available to it much larger than it had in the crowded liquid.

This “available space” factor, accompanied by the random jostling of temperature to overcome the potential energy difference, aids vaporization.

Now let us review what happens as we warm a solid substance from a very low temperature to a very high temperature. As the temperature is raised, small energy differences become unimportant. Thus, if the temperature of the solid is raised too much, the lower energy of the regular solid becomes unimportant compared with the random thermal energies. The solid melts, surrendering this energy stability in return for the randomness of the liquid state. If the temperature is raised still further, the energies of attraction among the molecules become unimportant compared with the random thermal energies. Then the liquid vaporizes, surrendering the lower potential energy afforded by the molecules remaining close together in favor of the still higher randomness of the gaseous state. If we raise the temperature still further, the energies that hold molecules together begin to become unimportant compared with random thermal energies. Finally, at extremely high energies, molecules no longer exist—all is chaos. This is the chemical situation within the Sun. Since at such high energies chemical reactions become unimportant, all chemists on the Sun are out of work. We’d better return to room temperature to apply our knowledge of equilibrium to chemical systems within our interest.

Example 1

The decomposition of calcium carbonate is endothermic:

Heat energy + CaCO3(s) ⇌ CaO(s) + CO2(g)

Therefore the products contain more chemical potential energy than the reactants.

The tendency towards minimum energy favors the reactants.

The tendency towards maximum randomness favors the products (the gaseous state is more random).

The two trends are opposing, so at equilibrium, both reactants and products will be found.

It is important to note that heating increases molecular motion, hence it tends to favor the more random state. Hence the higher the temperature (an increase in applied heat) the more the above reaction shifts towards the products.

Example 2

The dissolution of ethanol in water is exothermic:

C2H5OH(l) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mo»§#8594;«/mo»«mi»water«/mi»«/mover»«/math» C2H5OH(aq) + heat

Heat is released when ethanol dissolves in water. Therefore C2H5OH(l) has more potential energy. Therefore the tendency towards minimum energy favors the formation of C2H5OH(aq).

The tendency towards maximum randomness also favors the formation of C2H5OH(aq) (as opposed to two separate layers of water and ethanol).

Since both factors favor the formation of C2H5OH(aq), ethanol and water mix in all proportions, and there will be no equilibrium between separate phases of alcohol and solution.

Example 3

2NaOH(aq) + H2(g) → 2Na(s) + 2H2O(l)       ΔH >0

Tendency towards minimum energy favors the reactants.

Tendency towards maximum randomness also favors the reactants.

(A gas occupies more space than a liquid, so the molecules tend to have a more random arrangement in a gas)

No reaction takes place.

For of the following reaction, state:

- whether tendency toward minimum energy favors reactants or products,
- whether tendency toward maximum randomness favors reactants or products.

H2O(l)   ⇌   H2O(s)                             ΔH = –5.9 kJ

Tendency towards minimum energy favors

             Choose...             the reactants.             the products.         

Tendency towards maximum randomness favors

             Choose...             the reactants.             the products.         

For of the following reaction, state:

- whether tendency toward minimum energy favors reactants or products,
- whether tendency toward maximum randomness favors reactants or products.

H2O(l)  ⇌   H2O(g)                             ΔH = +42 kJ

Tendency towards minimum energy favors

             Choose...             the reactants.             the products.         

Tendency towards maximum randomness favors

             Choose...             the reactants.             the products.         

For of the following reaction, state:

- whether tendency toward minimum energy favors reactants or products,
- whether tendency toward maximum randomness favors reactants or products.

CaCO3(s) + 190kJ   ⇌  CaO(s) + CO2(g)

Tendency towards minimum energy favors

             Choose...             the products.             the reactants.         

Tendency towards maximum randomness favors

             Choose...             the products.             the reactants.         

End Of Chapter 1

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