Question

Consider a solution formed by mixing \(100.0 \mathrm{~mL}\) of \(0.10 M\) HA \(\left(K_{\mathrm{a}}=1.0 \times 10^{-6}\right), 100.00 \mathrm{~mL}\) of \(0.10 M \mathrm{NaA}\), and \(100.0 \mathrm{~mL}\) of \(0.10 M \mathrm{HCl}\). In calculating the \(\mathrm{pH}\) for the final solution, you would make some assumptions about the order in which various reactions occur to simplify the calculations. State these assumptions. Does it matter whether the reactions actually occur in the assumed order? Explain.

Short answer

In this problem, we assume the following order of reactions: (1) HCl reacts completely with A- (from NaA) before reacting with HA. (2) Remaining HCl reacts with HA if any is left, causing dissociation of HA into H+ and A- ions. (3) The change in the solution's volume is negligible. The exact order of reactions is not crucial; these assumptions are made to simplify calculations. The final pH will depend on the equilibrium between H+, A-, and HA ions, regardless of the reaction order, since the strong acid-weak base reaction will dominate.

Step-by-step solution

Identify the components and their concentrations

We are given a solution that is formed by mixing 100.0 mL of 0.10 M HA (weak acid), 100.00 mL of 0.10 M NaA (conjugate base), and 100.0 mL of 0.10 M HCl (strong acid).

List the assumptions

To simplify the pH calculations, we make the following assumptions about the order of reactions: 1. The strong acid (HCl) reacts completely with the weak base (A-, which comes from NaA) before it reacts with the weak acid (HA). This is because strong acids react much faster with weak bases or strong bases than with weak acids. 2. After the strong acid reacts with the weak base, the remaining HCl can react with the weak acid (HA) if any is left, causing dissociation of HA to form H+ ions and A- ions. 3. The change in the volume of the solution is negligible, which means the concentrations of the components would remain the same.

Discuss the importance of the order of reactions

It is not crucial that the reactions occur precisely in the assumed order. The assumptions are made to simplify the calculations and to understand how the reactions will have an effect on the pH. The final result (pH) would be equivalent no matter the order of reactions because, in the end, we will still have a mixture of H+, A-, and HA ions, and the pH will be dependent on the equilibrium between these ions. The dominant reaction would be the one involving the strong acid and the weak base, so the remaining reactions would have a minimal effect on the pH.

Key concepts

Acid-Base Reactions

Understanding acid-base reactions is crucial for predicting the behavior of mixed solutions and calculating their pH. In such reactions, an acid donates a proton (H+) while a base accepts it.

An important principle to remember is the difference between strong and weak acids. Strong acids, like hydrochloric acid (HCl), dissociate completely in water, releasing all their hydrogen ions into the solution, making the solution highly acidic. On the other hand, weak acids, such as HA in our exercise, only partially dissociate, and at equilibrium, there's a mixture of undissociated acid (HA) and its conjugate base (A-), along with the liberated H+ ions.

In a solution that combines a weak acid with its conjugate base (like HA and A-), we have what is known as a buffer system. This system resists changes in pH when small amounts of an acid or a base are added. However, the addition of a strong acid (HCl) will disrupt this buffer system by reacting with the conjugate base (A-), reducing its ability to neutralize added H+ ions.

Equilibrium Concentrations

The concept of equilibrium concentrations is fundamental to pH calculations in acid-base chemistry. Equilibrium refers to the state in a reaction where the rate of the forward reaction equals the rate of the reverse reaction, so the concentrations of reactants and products remain constant over time.

In the context of the exercise, the weak acid HA partially dissociates into H+ and A- ions establishing an equilibrium. Meanwhile, the strong acid HCl reacts completely, not achieving an equilibrium. When mixed, the initial reactions proceed until the strongest acid is neutralized. At that point, if we have HA and A- left, we need to consider the dissociation equilibrium of HA to find the final concentrations of H+ and A- ions in solution.

To calculate pH, the use of the acid dissociation constant (Ka) becomes significant. This constant represents the equilibrium concentrations of the products and reactants for a weak acid. Using the Henderson-Hasselbalch equation, a form of the equilibrium expression specific for buffer solutions, allows us to calculate the pH when H+ and A- are both present after the neutralization reactions have occurred.

Weak Acid-Strong Base Reaction

The reaction between a weak acid and a strong base is a classic example of an acid-base neutralization reaction. However, these reactions do not go to completion as they would with strong acid-strong base pairs.

In our exercise, the weak acid (HA) would usually react with a strong base to form water and its conjugate base (A-). But since we have mixed HCl, a strong acid, our primary focus shifts to the neutralization between HCl and the conjugate base (A-) derived from the weak acid. Here, the strong acid completely neutralizes the A-, forming water and the corresponding salt (NaCl).

Once all of the A- is consumed, the pH of the solution is ultimately determined by the remaining concentration of unreacted weak acid (HA) and the additional H+ ions from any excess HCl. This forms an acidic solution, and the extent of HA dissociation into H+ and A- determines the final pH. Particularly in buffer solutions, this weak acid dissociation is essential in establishing the final equilibrium pH after the primary strong acid-strong base reaction has taken place.