Problem 50 - Chemistry: The Central Science

Question

Write the chemical equation and the \(K_{a}\) expression for the acid dissociation of each of the following acids in aqueous solution. First show the reaction with \(\mathrm{H}^{+}(a q)\) as a product and then with the hydronium ion: (a) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\), (b) \(\mathrm{HCO}_{3}^{-}\)

Step-by-Step Solution

Answer

(a) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH} (aq) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}^{-}(aq) +\mathrm{H}^{+}(aq)\) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH} (aq) + H_{2}O (l) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}^{-}(aq) + \mathrm{H}_{3} \mathrm{O}^{+}(aq)\) \(K_{a} = \cfrac{[\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}^{-}][\mathrm{H}^{+}]}{[\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}]}\) (b) \(\mathrm{HCO}_{3}^{-}(aq) \rightleftharpoons \mathrm{CO}_{3}^{2-}(aq) + \mathrm{H}^{+}(aq)\) \(\mathrm{HCO}_{3}^{-}(aq) + H_{2}O (l) \rightleftharpoons \mathrm{CO}_{3}^{2-}(aq) + \mathrm{H}_{3} \mathrm{O}^{+}(aq)\) \(K_{a} = \cfrac{[\mathrm{CO}_{3}^{2-}][\mathrm{H}^{+}]}{[\mathrm{HCO}_{3}^{-}]}\)

Step 1: (a) Acid dissociation of \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\) with \(\mathrm{H}^{+}(a q)\) as a product

Write down the chemical equation for the acid dissociation of benzoic acid (\(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\)) in aqueous solution, showing \(\mathrm{H}^{+}(a q)\) as a product: \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH} (aq) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}^{-}(aq) +\mathrm{H}^{+}(aq)\)

Step 2: (a) Acid dissociation of \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\) with hydronium ion as a product

Similar to the previous step, but show hydronium ion (\(\mathrm{H}_{3} \mathrm{O}^{+}\)) as a product instead: \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH} (aq) + H_{2}O (l) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}^{-}(aq) + \mathrm{H}_{3} \mathrm{O}^{+}(aq)\)

Step 3: (a) \(K_{a}\) expression for the dissociation of \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\)

Now write the \(K_a\) expression for the dissociation of \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\): \(K_{a} = \cfrac{[\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}^{-}][\mathrm{H}^{+}]}{[\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}]}\)

Step 4: (b) Acid dissociation of \(\mathrm{HCO}_{3}^{-}\) with \(\mathrm{H}^{+}(a q)\) as a product

Write down the chemical equation for the acid dissociation of bicarbonate ion (\(\mathrm{HCO}_{3}^{-}\)) in aqueous solution, showing \(\mathrm{H}^{+}(a q)\) as a product: \(\mathrm{HCO}_{3}^{-}(aq) \rightleftharpoons \mathrm{CO}_{3}^{2-}(aq) + \mathrm{H}^{+}(aq)\)

Step 5: (b) Acid dissociation of \(\mathrm{HCO}_{3}^{-}\) with hydronium ion as a product

Now, show hydronium ion (\(\mathrm{H}_{3} \mathrm{O}^{+}\)) as a product instead: \(\mathrm{HCO}_{3}^{-}(aq) + H_{2}O (l) \rightleftharpoons \mathrm{CO}_{3}^{2-}(aq) + \mathrm{H}_{3} \mathrm{O}^{+}(aq)\)

Step 6: (b) \(K_{a}\) expression for the dissociation of \(\mathrm{HCO}_{3}^{-}\)

Write the \(K_a\) expression for the dissociation of \(\mathrm{HCO}_{3}^{-}\): \(K_{a} = \cfrac{[\mathrm{CO}_{3}^{2-}][\mathrm{H}^{+}]}{[\mathrm{HCO}_{3}^{-}]}\)

Key Concepts

Chemical Equilibrium

Chemical equilibrium is a fundamental principle in chemistry that occurs when a chemical reaction and its reverse reaction proceed at equal rates, resulting in no net change in the composition of the system. This state can be reached from either direction of the reaction and is crucial because it allows chemists and students to understand how concentrations of reactants and products relate to each other when a reaction is left undisturbed over time. In the context of acid dissociation, the equilibrium state is where the rate of the acid releasing its protons is equal to the rate of the conjugate base recombining with protons to form the undissociated acid.

Ka Expression

The acid dissociation constant, or Ka, is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction known as the dissociation in the context of acid-base reactions. The Ka expression is derived from the equilibrium constant formula, applied to the dissociation of an acid (HA) as follows:
\(K_{a} = \frac{[A^{-}][H^{+}]}{[HA]}\)
In this expression, \([HA]\) represents the concentration of the undissociated acid, \([H^{+}]\) is the concentration of hydrogen ions or protons, and \([A^{-}]\) is the concentration of the conjugate base. A higher Ka value indicates a stronger acid because it implies a greater concentration of hydrogen ions in solution, signifying more complete dissociation. Typically, a low Ka value signifies a weak acid, as the dissociation is less pronounced.

Acid-Base Reaction

Acid-base reactions are one of the most common types of chemical reactions, involving the transfer of protons (H+) from an acid to a base. In an aqueous solution, acids tend to donate protons, while bases accept them. The strength of an acid or base is often expressed by the pH scale, which is inversely related to the concentration of hydrogen ions in the solution. During the acid dissociation process, the acid (HA) loses a hydrogen ion to form its conjugate base (A-), which can then go on to react with water or other substances within the solution. Understanding how acid-base reactions occur and their equilibrium implications allows you to predict the behavior of acids and bases in different chemical environments.

Hydronium Ion

The hydronium ion (\(H_3O^{+}\)) is a positively charged ion formed when acids dissolve in water and donate a proton (H+) to a water molecule. It plays a crucial role in acid-base chemistry and the pH of solutions. Hydronium ions are often used in acid dissociation expressions as an alternative to simply using H+ because it more accurately reflects the behavior of protons in aqueous solutions; protons tend to associate with water rather than existing alone. This is particularly important in understanding the nature of acidic solutions and the concept of pH, which is the measure of the acidity or basicity of an aqueous solution, determined by the concentration of hydronium ions.