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Chemical Equilibirum -Weak Acids and Bases

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Weak Acids and Bases

Weak acids and weak bases do not dissociate completely. An equilibrium exists between the weak acid, water, H₃O⁺, and the anion of the weak acid. The equilibrium lies to the left hand side of the equation, indicating that not much H₃O⁺ is being produced. The fact that very little H₃O⁺ is being produced is the definition of a weak acid. The K_a for a weak acid is small, usually a number less than 1.

There are three types of problems encountered with weak acids or bases: dissociation, buffers or hydrolysis. We'll look at each type in detail.

Dissociation of a Weak Acid

In this type of problem, you will be asked to find the hydronium ion concentration and/or the pH of a weak acid whose initial concentration is known. A typical problem may be:

What is the hydronium ion concentration and pH of a 0.10 M solution of hypochlorous acid, K_a = 3.5 x 10^-8?

In tackling this problem, first note that the K_a is a small number, meaning hypochlorous acid is a weak acid. To begin the problem, write down the equilibrium involved:

HOCl + H₂O = H₃O⁺ + OCl^-

The equilibrium may be expressed mathematically by setting the K_a equal to the mass action expression:

Next, use the equilibrium to establish a table of initial conditions, change in equilibrium and final equilibrium conditions. Initially, the HOCl concentration is 0.10 M, the concentrations of H₃O⁺ and OCl^- are zero:

Note that water will not be included in the calculation since is the solvent.

In order for equilibrium to be established, some of HOCl must dissociate and form H₃O⁺ and OCl^-. Since it is not known how much will dissociate, we'll call the amount of HOCl lost -x and the amount of H₃O⁺ and OCl^- formed +x:

The above operation is justified by LeChatlier's Principle, which states: if a stress is places on an equilibrium, the equilibrium will shift in the direction which will relieve the stress. In this case, the stress is the lack of H₃O⁺ and OCl^- so the equilibrium will shift to the right to relieve the stress by forming some H₃O⁺ and OCl^-.

By summing the initial concentrations and the change in concentrations, you can obtain the amount of each species at equilibrium:

These quantities will be used in the mass action expression for the equilibrium of the acid, as shown below. The K_a for HOCl is 3.5 x 10^-8.

The solution for x becomes simplified because the x shown in bold can be neglected. This x can be neglected because it will be negligibly small compared to the concentration, 0.10 M. To determine whether x is negligible, compare the magnitude of the last decimal place of the concentration of the acid to the magnitude of the equilibrium constant. If the difference in magnitude is greater than 100, the x may be neglected.

In this case, the concentration is known to the 10^-2 place and the equilibrium constant is the magnitude of 10^-8. The difference in magnitude is 10⁶, therefore, x may easily be neglected. This simplifies the equation to:

Multiplying both sides by 0.10 yields:

x² = 3.5 x 10^-9

Taking the square root of both sides yields:

x = [H₃O⁺] = 5.9 x 10^-5 = [OCl^-] (also)

To find the pH, take the negative log of the hydronium ion concentration:

pH = -log[H₃O⁺] = -log(5.9 x 10^-5) = 4.23

Incidently, the concentration of HOCl at equilibrium would be:

[HOCl] = 0.10 - 5.9 x 10^-5 = 0.10 M (2 significant figures)

This shows our assumption that x was negligible was valid.

A typical weak base problem may read: What is the hydroxide ion concentration and pH of a 0.10 M solution of NH₃, K_b = 1.8 x 10^-5?

Again, note that K_b is small. We will follow the same format as we used for weak acid solutions :

We are assuming that before equilibrium is established, no NH₄⁺ or OH^- have formed.

To establish equilibrium, a shift to the right has to occur. Since the amount of NH₃ lost, and the amounts of NH₄⁺ and OH^- formed are not known, we assign the value of -x and +x, respectively:

By summing the initial concentrations and change in concentrations, we have the algebraic amount of each species in solution at equilibrium:

These quantities will be used in the mass action expression:

Let's see if we can neglect the x in the denominator. The last decimal place in 0.10 is to the magnitude of10^-2. The magnitude of the constant is 10^-5. The difference in magnitude is 10³. Since this difference is greater than 100, the x may be neglected. This simplifies the mathematical expression to: