Question

Write the equilibrium constant expression for each of the following weak acids: (a) \(\mathrm{HCHO}_{2}(a q) \rightleftarrows \mathrm{H}^{+}(a q)+\mathrm{CHO}_{2}^{-}(a q)\) (b) \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(a q) \rightleftarrows \mathrm{H}^{+}(a q)+\mathrm{HC}_{2} \mathrm{O}_{4}^{-}(a q)\) (c) \(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) \rightleftarrows \mathrm{H}^{+}(a q)+\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}^{-}(a q)\)

Short answer

For formic acid: \( K_a = \frac{[\text{H}^+][\text{CHO}_2^-]}{[\text{HCHO}_2]} \); for oxalic acid: \( K_a = \frac{[\text{H}^+][\text{HC}_2\text{O}_4^-]}{[\text{H}_2\text{C}_2\text{O}_4]} \); for citric acid: \( K_a = \frac{[\text{H}^+][\text{H}_2\text{C}_6\text{H}_5\text{O}_7^-]}{[\text{H}_3\text{C}_6\text{H}_5\text{O}_7]} \).

Step-by-step solution

Understanding Equilibrium Expression

For an acid dissociation equilibrium like \[ \text{HA} \rightleftharpoons \text{H}^+(aq) + \text{A}^-(aq) \]the equilibrium constant expression \( K_a \) is given by the formula: \[ K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]} \]where \([\text{HA}]\), \([\text{H}^+]\), and \([\text{A}^-]\) are the concentrations of the weak acid, hydrogen ion, and conjugate base, respectively.

Writing the Expression for Formic Acid

For the weak acid \(\text{HCHO}_2(aq) \rightleftharpoons \text{H}^+(aq) + \text{CHO}_2^-(aq)\), the equilibrium constant expression \( K_a \) is:\[ K_a = \frac{[\text{H}^+][\text{CHO}_2^-]}{[\text{HCHO}_2]} \]

Writing the Expression for Oxalic Acid

For the weak acid \(\text{H}_2\text{C}_2\text{O}_4(aq) \rightleftharpoons \text{H}^+(aq) + \text{HC}_2\text{O}_4^-(aq)\), the equilibrium constant expression \( K_a \) is:\[ K_a = \frac{[\text{H}^+][\text{HC}_2\text{O}_4^-]}{[\text{H}_2\text{C}_2\text{O}_4]} \]

Writing the Expression for Citric Acid

For the weak acid \(\text{H}_3\text{C}_6\text{H}_5\text{O}_7(aq) \rightleftharpoons \text{H}^+(aq) + \text{H}_2\text{C}_6\text{H}_5\text{O}_7^-(aq)\), the equilibrium constant expression \( K_a \) is:\[ K_a = \frac{[\text{H}^+][\text{H}_2\text{C}_6\text{H}_5\text{O}_7^-]}{[\text{H}_3\text{C}_6\text{H}_5\text{O}_7]} \]

Key concepts

Weak Acids

Weak acids are a fascinating yet essential topic in chemistry. These acids only partially dissociate in water, which means they do not fully release their hydrogen ions (H⁺) when dissolved.
This partial dissociation is what makes them weak, as they do not completely break apart. Instead, they reach a certain balanced state with their conjugate base counterparts.
Examples of weak acids include:

• Formic Acid (\(\mathrm{HCHO}_{2}(a q)\))
• Oxalic Acid (\(\mathrm{H}_2 \mathrm{C}_2 \mathrm{O}_4(a q)\))
• Citric Acid (\(\mathrm{H}_3 \mathrm{C}_6 \mathrm{H}_5 \mathrm{O}_7(a q)\))

Despite being weak, these acids play significant roles in biological and chemical processes. Understanding their behavior is pivotal in both academic and practical contexts. Therefore, studying weak acids helps in predicting how they will act in various environments, which is crucial in fields such as pharmacology, food chemistry, and biochemistry.

Acid Dissociation

The process of acid dissociation is central to understanding how weak acids interact with water. When a weak acid is added to water, it doesn't fully dissolve.
Instead, it splits up partially into hydrogen ions (H⁺) and a conjugate base. This is known as acid dissociation.
Let's look at this process for some common weak acids. For formic acid, the dissociation can be represented as: \[\text{HCHO}_{2}(aq) \rightleftharpoons \text{H}^+(aq) + \text{CHO}_{2}^-(aq)\]Similarly, this happens with oxalic acid: \[\text{H}_2\text{C}_2\text{O}_4(aq) \rightleftharpoons \text{H}^+(aq) + \text{HC}_2\text{O}_4^-(aq)\]And, citric acid dissociates as follows: \[\text{H}_3\text{C}_6\text{H}_5\text{O}_7(aq) \rightleftharpoons \text{H}^+(aq) + \text{H}_2\text{C}_6\text{H}_5\text{O}_7^-(aq)\]Note that equilibrium arrows (\rightleftharpoons) indicate partial dissociation, where the forward and backward reactions occur simultaneously. Hence, acid dissociation is not complete for weak acids, which is why calculating their equilibrium constants (K_a) is essential for understanding their behavior in solution.

Chemical Equilibrium

Chemical equilibrium is a fundamental concept that describes a state where the rates of the forward and reverse reactions are equal.
In the context of weak acids, it's vital to understand because it affects how the acid and its dissociated parts behave in a solution.
When a weak acid like the ones we discussed reaches equilibrium, it does not mean that reaction has stopped.

• Instead, the formation of hydrogen ions and conjugate bases from the acid occurs at the same rate as their recombination back into the acid.
• This balance is dynamic, meaning that molecules are constantly reacting, although the overall concentrations remain steady.
• At equilibrium, we can use the equilibrium constant (K_a) to express the extent of dissociation.

For example, the equilibrium constant expression for formic acid is determined by: \[K_a = \frac{[\text{H}^+][\text{CHO}_2^-]}{[\text{HCHO}_2]}\] This formula shows the ratio of the concentrations of the products to the undissociated reactants at equilibrium. Understanding these principles helps in predicting reactions and creating solutions with specific properties, essential in many scientific and industrial applications.