Problem 116 - Chemistry and Chemical Reactivity

Question

Two acids, each approximately 0.01 M in concentration, are titrated separately with a strong base. The acids show the following pH values at the equivalence point: \(\mathrm{HA}, \mathrm{pH}=9.5,\) and \(\mathrm{HB}\) \(\mathrm{pH}=8.5\) (a) Which is the stronger acid, HA or HB? (b) Which of the conjugate bases, \(A^{-}\) or \(B^{-},\) is the stronger base?

Step-by-Step Solution

Answer

(a) HB is the stronger acid; (b) \(A^{-}\) is the stronger base.

Step 1: Understanding the Problem

We need to determine which of the given acids, HA or HB, is stronger, and which of their conjugate bases is stronger, based on the pH values at their equivalence points.

Step 1: Interpret pH at Equivalence Point

At the equivalence point, the acid has been neutralized, and the solution contains only the conjugate base and water. The pH reflects the strength of the conjugate base. A higher pH at equivalence indicates a stronger conjugate base.

Step 2: Compare Given pH Values

For acid HA, the pH a the equivalence point is 9.5, whereas for acid HB it is 8.5. HA's higher pH suggests it has a stronger conjugate base than HB.

Step 3: Relate Conjugate Base Strength to Acid Strength

A stronger conjugate base means the original acid is weaker because it indicates a lesser degree of ionization. Therefore, the acid with a stronger conjugate base (HA, in this case) is the weaker acid.

Step 4: Determine the Stronger Acid

Since HA has a stronger conjugate base, HA is the weaker acid. Therefore, HB, with a lower pH at equivalence, is the stronger acid.

Step 5: Determine the Stronger Base

Since HA's pH at equivalence is higher, its conjugate base, \(A^{-}\), is the stronger base than \(B^{-}\).

Key Concepts

Acid Strength

The concept of acid strength is crucial when understanding acid-base titration. Acid strength refers to an acid's ability to donate a proton (H⁺) in a chemical reaction. Strong acids ionize completely in solution, while weak acids only partially ionize. This means that strong acids produce a higher concentration of H⁺ ions in water, resulting in a lower pH value.

In the given problem, we compare two acids, HA and HB, both at the same concentration. To determine which acid is stronger, we look at the pH values at their equivalence points. Acid HB has a lower pH of 8.5 at equivalence, suggesting that it retains stronger acidic properties, hence is the stronger acid compared to HA which has a pH of 9.5.

In essence, a lower pH at the equivalence point indicates a stronger original acid. This understanding is pivotal in predicting and controlling chemical reactions in various fields, from industrial to biological processes.

Conjugate Base

Conjugate bases are formed when an acid loses a proton. Every acid-base reaction involves the conversion of an acid into its conjugate base. The strength of a conjugate base is inversely related to its corresponding acid. A strong conjugate base comes from a weak acid, which doesn't completely ionize, leaving more of its base form in solution.

In the context of the problem, HA and HB form conjugate bases labeled as A⁻ and B⁻, respectively. The pH at the equivalence point reflects the strength of these conjugate bases. A higher pH at equivalence implies a stronger conjugate base because it can accept protons more readily. Thus, A⁻, with a pH of 9.5, is a stronger base when compared to B⁻, which has a pH of 8.5.

This relationship helps in understanding how acids and bases interact, affects the equilibrium of reactions, and guides the selection of substances in synthesis and formulation.

Equivalence Point

The equivalence point in a titration is when the number of moles of the titrant equals the number of moles of the substance being titrated. This is a crucial juncture where the acid is completely neutralized by the base, leaving only the conjugate base in the solution and no excess reactant.

For strong acids, the equivalence point often results in a pH close to neutral (around 7) because the conjugate base is weak. Conversely, weak acids have equivalence points with pH values greater than 7 because their conjugate bases are relatively stronger.

In our example, HA and HB reach their equivalence points at pH 9.5 and 8.5, respectively. HA, with a higher pH, is indicative of a stronger conjugate base meaning it started as a weaker acid. Understanding the equivalence point can greatly aid in the design of industrial titrations or laboratory experiments, enhancing the precision and success of your work.

pH Measurement

pH measurement is a method used to determine the acidity or basicity of a solution. The pH scale ranges from 0 to 14, with lower numbers representing more acidic solutions, higher numbers indicating more basic (alkaline) solutions, and a pH of 7 being neutral.

The pH of a solution is calculated as the negative logarithm (base 10) of the hydrogen ion concentration: \[ pH = -\log [H^+] \].
In the example, measuring pH at the equivalence point provides insight into the characteristics of the conjugate base. For instance, a measured pH of 9.5 implies a relatively strong basic solution, resulting from the weak acid HA. Conversely, a pH of 8.5 reflects a weaker base and thus a stronger original acid, HB.

Effective pH management is fundamental in numerous scientific and industrial processes, from pharmaceuticals to agriculture, ensuring the desired conditions and outcomes.