Chemical Equilibria

Calculations involving Reaction Stoichiometry

Concepts

The previous experiment involved reactions in which only one species existed in the gas phase; all other species were solids. The pressure of the system could thus be used to directly calculate the equilibrium constant, because the system pressure was the same as the partial pressure of the gas-phase species. For most reactions, however, the calculations are more complicated.

Consider the following reactions, which is an important atmospheric reaction.

O2 (g) + 2 SO2 (g) 2 SO3 (g)


Suppose the system initially contains only oxygen and sulfur dioxide. As the reaction progresses, sulfur trioxide is formed and oxygen and sulfur dioxide are consumed. The pressure of the system is the sum of the partial pressures of the components of the gas, and each of these partial pressures differs from the initial values.

P = PO2 + PSO2 + PSO3


How can one take these changes into account and determine each individual partial pressure from the system pressure?

A useful concept for this purpose is the extent of reaction, which will be given the symbol x for this experiment. In reality the reaction occurs on the molecular scale, with individual molecules of oxygen, sulfur dioxide, and sulfur trioxide being involved. Chemists prefer to think in terms of moles of material, however. Each unit of x (the extent of reaction) corresponds to the number of molecules of each reactant and product indicated by the respective stoichiometric coefficients. Thus when x = 1, one mole of oxygen and two moles of sulfur dioxide have been consumed and two moles of sulfur trioxide have been formed. The sense of the change can be reversed. When x = -1, one mole of oxygen and two moles of sulfur dioxide have been formed and two moles of sulfur trioxide have been consumed.

The extent of reaction allows the change in amount of one species to be related to the change in the amount of a different species. The most straightforward way to illustrate this relationship is through the use of a table such as that shown below.

  O2 SO2 SO3
Initial P1 P2 P3
Change - x - 2 x + 2 x
Equilibrium P1 - x P2 - 2 x P3 + 2 x

Strictly speaking, the table should be constructed in terms of moles of each species. The equilibrium expression, however, requires partial pressures or molar concentrations. So long as each species exists in the same phase (and thus the volume is the same for each species), the moles can be replaces by partial pressure or molar concentration. In this example the extent of reaction is expressed in terms of partial pressure.

The first row of the table contains the initial partial pressures of each species. These values are called "analytical partial pressures" and are the partial pressures of each species the experimenter put in the system. The second row simply reflects the stoichiometry of the reaction and employs the extent of reaction to show how the change in amount of one reactant or product is linked to the change in the amounts of the other reactants and products. The bottom row is simply the sum of the first two rows and contains the actual equilibrium partial pressures of each species. In this context, the extent of reaction, x, is the value necessary to reach equilibrium. At equilibrium, the values in the bottom row of the table may be substituted into the equilibrium expression to evaluate KP.

PO2 = P1 - x

PSO2 = P2 - 2 x

PSO3 = P3 + 2 x

KP = PSO32

PO2 PSO22
= (P3 + 2 x)2

(P1 - x) (P2 - 2 x)2

Can you calculate the value of x if you are given the pressure P and the three initial partial pressures P1, P2, and P3?

Can you calculate the individual partial pressures and the equilibrium constant, if you are given x and the three initial partial pressures P1, P2, and P3?

Will this strategy for determining KP from P work for the reaction shown below?

CO (g) + H2O (g) CO2 (g) + H2 (g)




Experiment

Objective:

Determine the equilibrium constant for a chemical reaction.

Part 1.

In this part of the experiment, the following reaction is studied.

O2 (g) + 2 SO2 (g) 2 SO3 (g)


The experimental apparatus consists of a pair of glass bulbs. The bulb on the left is first evacuated and then filled with a certain amount of oxygen. The pressure of the oxygen is measured with the manometer on the left. Similarly the bulb on the right is evacuated and then filled with a certain amount of sulfur dioxide, the pressure of which is measured with the manometer on the right.

The reaction occurs when the stopcock between the two bulbs is opened, allowing the gases to mix. Either manometer may be used to measure the equilibrium pressure of the system.

Perform this experiment several times using various initial pressures of oxygen and sulfur dioxide gas. You should obtain the same value for KP each time.

Each bulb has a volume of 1.000 liter. (Note that this reaction is performed at a high temperature.)

Note: The pressures you measure for oxygen and sulfur dioxide are NOT the quantities P1 and P2 in the table shown above. Why is this the case? How can you calculate P1 and P2?

How much variability from one experiment to another is there in the value for KP? Why is there so much variability? A discussion of experimental error in this experiment is available.

After performing the experiment a few times, you may check your answer to see if your calculations are correct.

O2
           
SO2


Part 2.

In this part of the experiment, the reaction used by industry to synthesize ammonia (the Haber process) is being studied.

N2 (g) + 3 H2 (g) 2 NH3 (g)


The experimental apparatus and the procedure are the same as those in Part 1. As before each bulb has a volume of 1.000 liter. You goal is to determine the equilibrium constant (KP) for this reaction at 400 K.

As before, repeat the experiment several times to determine the precision of your value of the equilibrium constant.

H2
     
N2


Equilibrium Constant           Uncertainty in Equilibrium Calculations           Le Châtelier's Principle

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