Question

A certain salt, MX (containing the \(\mathrm{M}^{+}\) and \(\mathrm{X}^{-}\) ions ), is dissolved in water, and the \(\mathrm{pH}\) of the resulting solution is \(7.0 .\) What can you say about the strengths of the acid and the base from which the salt is derived?

Short answer

The parent acid and base are of similar strength, leading to a neutral solution.

Step-by-step solution

Identify the Ions of the Salt

The salt MX is composed of the ions M⁺ and X⁻. These ions are the conjugates of a weak base and a weak acid, respectively.

Assess pH neutrality

Given that the pH of the solution is 7.0, it is neutral. This implies that neither ions of the salt contribute to the acidity or basicity of the solution.

Determine Relative Strengths of Parent Compounds

Since the solution remains neutral at pH 7.0, both the acid and the base from which the ions are derived are of similar strength. This means that neither the acid nor the base is significantly stronger or weaker than the other.

Key concepts

pH neutrality

Understanding pH neutrality is essential when discussing acid-base chemistry. The pH scale, which ranges from 0 to 14, measures how acidic or basic a solution is. A pH of 7.0 is considered neutral, meaning the solution is neither acidic nor basic. In a neutral solution, the concentrations of hydrogen ions (hydronium) ext{( ext{H}^+ ext{or} ext{H}_3 ext{O}^+ )} and hydroxide ions ( ext{OH}^-) are equal. Water is the classic example of a neutral liquid.

• A neutral solution has a pH of 7.0.
• Equal concentrations of ext{H}^+ and ext{OH}^- ions result in neutrality.

In the context of the given exercise, when the salt MX is dissolved in water, it maintains the neutral pH of 7.0. This suggests that the ions produced do not alter the solution's acidity or basicity. Therefore, the presence of M⁺ and X⁻ ions doesn't shift the ext{pH} away from neutrality, indicating a balance in their respective acidic and basic qualities.

conjugate acid-base pairs

In acid-base chemistry, conjugate acid-base pairs play a crucial role. A conjugate acid-base pair consists of two species in a chemical reaction that differ by one hydrogen ion ( ext{H}^+ ). An acid donates a hydrogen ion in a reaction to form its conjugate base, while a base accepts a hydrogen ion, forming its conjugate acid.

• A conjugate acid-base pair differs by one ext{H}^+ ion.
• An acid forms its conjugate base by losing ext{H}^+ .
• A base forms its conjugate acid by gaining ext{H}^+ .

In the provided exercise, the ions M⁺ and X⁻ are derived from their conjugate acid and base, respectively. This suggests that the ions originate from the dissociation of a weak acid and a weak base that are of equal strength. The neutrality of the solution hints that neither of these conjugate species significantly alters the pH, as their effects cancel each other out.

ion strength

Ion strength refers to the ability of ions in a solution to affect its pH and is closely related to the concept of strong and weak acids and bases. The stronger an acid or base, the more it can dissociate in water to form ions, resulting in a marked pH change. Strong acids or bases will significantly alter the ext{pH} , whereas weak ones will not.

• Strength of ions influences ext{pH} changes.
• Strong acids/bases dissociate more completely, influencing ext{pH} .
• Weak acids/bases have less impact on ext{pH} .

In the context of the exercise, the ions in solution are derived from a weak acid and a weak base. Their relative weakness means that they do not fully dissociate in water to form significant amounts of ext{H}^+ or ext{OH}^- ions, hence, maintaining a ext{pH} of 7.0. This balance indicates that both the acid and the base from which M⁺ and X⁻ arise have similar strengths, allowing them to equilibrate without bias in the pH level.