Basic Concepts

Consider the following gas-phase chemical reaction:

$$H_2 + I_2 \rightleftharpoons 2HI$$

The apparatus shown belows contains 0.02 mol/L I2 gas in the left syringe and 0.01 mol/L H2 gas in the right syringe. When the two syringes are depressed, the two gases are mixed and the above reaction occurs. The graph at the right shows the variations of the H2, I2, and HI concentrations as a function of time. Run the experiment and examine the concentration-time plots.



As the reaction progresses, the concentrations of iodine and hydrogen decrease as they are consumed while the concentration of hydrogen iodide increases as it is formed. Eventually, however, the concentrations of all three species reach constant values. This behavior is a result of the reverse in which hydrogen iodide reacts to form iodine and hydrogen. Initially there is no hydrogen iodide, so the reverse reaction cannot occur. As hydrogen iodide accumulates, the reverse reaction can progress and becomes significant.

Eventually the rate at which iodine is being consumed by the forward reaction is perfectly balanced by the rate at which it is being produced by the back reaction. The same is true for hydrogen and hydrogen iodide. When the rates of forward and reverse reactions are perfectly balanced in this way, the reaction is said to be at equilibrium.

The Law of Mass Action

When a chemical reaction reaches equilibrium, the concentrations of the reactants and products obey the Law of Mass Action.

For the generic chemical reaction

$$aA + bB \rightleftharpoons cC + dD$$

the Law of Mass Action is

$$K_C = \dfrac{[C]^c[D]^d}{[A]^a[B]^b}$$

The uppercase letters represent chemical species, whereas the lowercase letters represent the corresponding stoichiometric coefficients. The notation [A] represents the molar concentration of species A. In this expression, the numerator contains the concentration of each product raised to the power of its stoichiometric coefficient. The denominator contains the corresponding expression for the reactants.

If the species are gases, an entirely analogous expression may be written using partial pressures instead of molar concentrations.

$$K_P = \dfrac{P_C^cP_D^d}{P_A^aP_B^b}$$

The equilibrium constant KC applies to an equilibrium expression written in terms of molar concentrations, and the equilibrium constant KP applies to an equilibrium expression written in terms of partial pressures (with units of atm). One can convert between KC and KP using the ideal gas law:

$$P = RTC$$

The equilibrium constant characterizes the "position" of the equilibrium. The larger the equilibrium constant, the more the equilibrium favors products; the smaller the equilibrium constant, the more the equilibrium favors reactants. In an ideal system, the equilibrium constant depends only upon the temperature of the system.

Note: Only species that are gases or solutes appear in the equilibrium expression. Pure solids and pure liquids do not appear in the expression.

Contributors

• Dr. David Blauch (Davidson College)