Acid–Base Equilibria | CHEMISTRY BY BURHAN ISHAQUE

 In any proton-transfer reaction:

we are concerned with the question of whether the position of equilibrium lies to the side of products or reactants. There is an easy way to determine this. The reaction proceeds in the direction that converts the stronger acid and the stronger base to the weaker acid and the weaker base.

This generalization can be stated even more simply. The reaction will be favorable when the stronger acid is on the left and the weaker acid is on the right. The equilibrium favors dissociation of the stronger acid.

Consider first the case of adding a strong acid such as HBr to water. The equation for the Brønsted acid–base reaction that occurs between them is:

For acid–base reactions in which water is the solvent, the pK_a of H₃O⁺ = 0

We identify the acid on the left and the acid on the right and compare their pK_a’s to decide which is stronger. (Remember, the more negative the pK_a, the stronger the acid). The acid on the left is HBr, which has a pK_a of −5.8. The acid on the right is H₃O⁺, which has a pK_a of 0. The stronger acid (HBr) is on the left and the weaker acid (H₃O⁺) is on the right, so the position of equilibrium lies to the right. The equilibrium constant K_eq for an acid–base reaction is given by the ratio of the K_a of the reactant acid to the K_a of the product acid.

Since 10^−pKa = K_a, we rewrite the expression as:

and substitute the pK_a values of HBr and H₃O⁺ to calculate K_eq.

This equilibrium constant is so large that we consider HBr to be completely ionized in water.

Compare the reaction of HBr with water to that of acetic acid with water

Here, the weaker acid (acetic acid) is on the left and the stronger acid (hydronium ion) is on the right. The equilibrium constant K_eq = 10^−4.7, and the position of equilibrium lies far to the left.

Two important points come from using relative pK_a’s to analyze acid–base equilibria:

1. They permit clear-cut distinctions between strong and weak acids and bases. A strong acid is one that is stronger than H₃O⁺. Conversely, a weak acid is one that is weaker than H₃O⁺.

   Example: The pK_a’s for the first and second ionizations of sulfuric acid are −4.8 and 2.0, respectively. Sulfuric acid (HOSO₂OH) is a strong acid; hydrogen sulfate ion (HOSO₂O⁻) is a weak acid.

   A strong base is one that is stronger than HO⁻.

   Example: A common misconception is that the conjugate base of a weak acid is strong. This is sometimes, but not always, true. It is true, for example, for ammonia, which is a very weak acid (pK_a 36). Its conjugate base amide ion (H₂N⁻) is a much stronger base than HO⁻. It is not true, however, for acetic acid; both acetic acid and its conjugate base acetate ion are weak. The conjugate base of a weak acid will be strong only when the acid is a weaker acid than water.

2. The strongest acid present in significant amounts at equilibrium after a strong acid is dissolved in water is H₃O⁺. The strongest acid present in significant amounts when a weak acid is dissolved in water is the weak acid itself.

   Example: [H₃O⁺] = 1.0 M in a 1.0 M aqueous solution of HBr. The concentration of undissociated HBr molecules is near zero. [H₃O⁺] = 0.004 M in a 1.0 M aqueous solution of acetic acid. The concentration of undissociated acetic acid molecules is near 1.0 M. Likewise, HO⁻ is the strongest base that can be present in significant quantities in aqueous solution.

Analyzing acid–base reactions according to the Brønsted–Lowry picture provides yet another benefit. Some values which lists acids according to their strength in descending order along with their conjugate bases, can be used to predict the direction of proton transfer. Acid–base reactions in which a proton is transferred from an acid to a base that lies below it in the table have favorable equilibrium constants. Proton transfers from an acid to a base that lies above it in the table are unfavorable. Thus, the equilibrium constant for proton transfer from phenol to hydroxide ion is greater than 1, but that for proton transfer from phenol to hydrogen carbonate ion is less than 1.

Hydroxide ion lies below phenol; hydrogen carbonate ion lies above phenol. The practical consequence of the reactions shown is that NaOH is a strong enough base to convert phenol to phenoxide ion, but NaHCO₃ is not