Question

For each of the following cases, decide whether the \(\mathrm{pH}\) is less than \(7,\) equal to \(7,\) or greater than \(7\). (a) Equal volumes of \(0.10 \mathrm{M}\) acetic acid, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H},\) and \(0.10 \mathrm{M} \mathrm{KOH}\) are mixed. (b) \(25 \mathrm{mL}\) of \(0.015 \mathrm{M} \mathrm{NH}_{3}\) is mixed with \(25 \mathrm{mL}\) of \(0.015 \mathrm{M} \mathrm{HCl}\). (c) \(150 \mathrm{mL}\) of \(0.20 \mathrm{M} \mathrm{HNO}_{3}\) is mixed with \(75 \mathrm{mL}\) of \(0.40 \mathrm{M} \mathrm{NaOH}\).

Short answer

(a) Greater than 7; (b) Less than 7; (c) Equal to 7.

Step-by-step solution

Analyze Case (a)

In this case, we are mixing equal volumes of acetic acid, which is a weak acid, and KOH, a strong base. Since KOH is a strong base, it will react completely with acetic acid. However, because acetic acid is a weak acid, not all of it will dissociate in water initially. After the reaction, a buffer solution is created consisting of the acetate ion (\(\mathrm{CH}_3\mathrm{CO}_2^-\)) and its conjugate base. Buffer solutions typically have a \(\mathrm{pH}\) near or slightly greater than 7, depending on the strength of the weak acid and base. Here, the resulting solution will be slightly basic because KOH has reacted with all the available acetic acid molecules, and the excess conjugate base remains in the solution.

Analysis for Case (b)

For case (b), we are mixing equal volumes of ammonia (\(\mathrm{NH}_3\)), a weak base, and hydrochloric acid (\(\mathrm{HCl}\)), a strong acid. Given that the concentrations are equal, \(\mathrm{HCl}\) will neutralize an equivalent amount of \(\mathrm{NH}_3\). The result will be a solution of the ammonium ion (\(\mathrm{NH}_4^+\)), which can undergo slight dissociation, but overall, the strong acid dominates, resulting in a solution with \(\mathrm{pH}\) less than 7.

Analyze Case (c)

In this situation, we are mixing 150 mL of \(0.20\ \mathrm{M}\ \mathrm{HNO}_3\) and 75 mL of \(0.40\ \mathrm{M}\ \mathrm{NaOH}\). First, calculate the moles of acid and base: \(150\ \mathrm{mL} \times 0.20/1000 = 0.030\ \mathrm{mol}\ \mathrm{HNO}_3\) and \(75\ \mathrm{mL} \times 0.40/1000 = 0.030\ \mathrm{mol}\ \mathrm{NaOH}\). Since the moles of \(\mathrm{HNO}_3\) and \(\mathrm{NaOH}\) are equal, they react completely to form water and resulting in a solution of neutral salt, leading to a solution with \(\mathrm{pH}\) equal to 7.

Key concepts

Acid-Base Reactions

Acid-base reactions are fundamental chemical processes where an acid reacts with a base. These reactions usually involve the transfer of protons (H extsuperscript{+} ions) from the acid to the base.
When these reactions occur in aqueous solutions, the products are typically water and a type of ionic compound called a salt. For example, when hydrochloric acid (HCl) reacts with sodium hydroxide (NaOH), which is a strong base, the result is water (H extsubscript{2}O) and sodium chloride (NaCl). This kind of reaction is essential in understanding how solutions change their pH values.
Some acids and bases do not completely dissociate in water. These are called weak acids and weak bases. Acetic acid ( ext{CH} extsubscript{3} ext{CO} extsubscript{2}H) is a common example of a weak acid, and it does not donate all its available hydrogens when in solution, making the resulting acid-base reactions less straightforward to predict.

• Strong acids/bases fully dissociate in water, leading to more predictable reactions.
• Weak acids/bases only partially dissociate, leading to unique outcomes.

Understanding whether the reactants are strong or weak helps predict the outcome and pH of the resulting solution.

Buffer Solutions

Buffer solutions are interesting chemical systems that can maintain a relatively constant pH when small amounts of acid or base are added. They are typically made from a combination of a weak acid and its conjugate base or a weak base and its conjugate acid.
In the case of mixing acetic acid and KOH, you'll create a buffer solution. Acetic acid ( ext{CH} extsubscript{3} ext{CO} extsubscript{2}H) is a weak acid, and when it reacts with potassium hydroxide (KOH), a strong base, it forms the acetate ion ( ext{CH} extsubscript{3} ext{CO} extsubscript{2} extsuperscript{-}), which is the conjugate base of acetic acid. This mixture supports the maintenance of a stable pH, usually near 7, because of the ability of the buffer to resist changes in the pH when small amounts of acids or bases are added.

• Buffers prevent drastic changes in pH.
• Essential in many biological systems to maintain stable pH environments.
• Composed of either weak acids and their salts or weak bases and their salts.

This stability is invaluable in many chemical and biological processes where maintaining an exact pH is crucial.

Neutralization Reactions

Neutralization reactions occur when an acid and a base react to form water and a salt, resulting in a pH typically around 7 if both reactants are strong and in equivalent amounts.
In practice, this means that the hydrogen ions from the acid combine with hydroxide ions from the base to produce water. For example, mixing hydrochloric acid with sodium hydroxide results in an equal, neutral solution (pH = 7), as both components are strong, and their moles are balanced.
In contrast, if there's an imbalance in the moles of the reactants, such as more moles of acid than base, the solution will skew acidic, leading to a pH less than 7. The complete reaction of equal moles of ext{HNO} extsubscript{3} and ext{NaOH} results in a solution where the salt does not affect the pH, reflecting a neutralized system.

• The products of neutralization are water and a salt.
• pH is typically 7 when equal strengths and amounts of a strong acid and base react.
• Any imbalance can lead to acidic or basic solutions depending on the excess of reactants.

These reactions are ubiquitous in both industrial applications and everyday chemical interactions.