Question

To which of the following would the addition of an equal volume of \(0.60 \mathrm{M} \mathrm{NaOH}\) lead to a solution having a lower \(\mathrm{pH} ?\) (a) water, (b) \(0.30 \mathrm{M} \mathrm{HCl}\), (c) \(0.70 \mathrm{M} \mathrm{KOH}\) (d) \(0.40 \mathrm{M} \mathrm{NaNO}_{3}\).

Short answer

The solution with the lowest pH after the addition of an equal volume of 0.60 M NaOH is (b) 0.30 M HCl.

Step-by-step solution

Recognize the type of each solution

We must first understand the nature of each of the four solutions before any reactions occur. (a) Water is neutral with a pH of 7. (b) 0.30 M HCl is a strong acid which fully dissociates in water, lowering the pH. (c) 0.70 M KOH is a strong base, which dissociates in water to form OH- ions, increasing the pH. (d) 0.40 M NaNO3 is a salt that disassociates into ions but does not affect the pH.

Predict the pH adjustment effect of NaOH

Adding an equal volume of 0.60 M NaOH to any of the solutions presented will increase their pH (decrease their acidity), as NaOH is a strong base that increases the concentration of OH- ions in solution.

Identify which solution pH lowers after the addition of NaOH

While all solution pHs will technically increase (lower acidity), the question is asking which will result in the 'lowest' pH after the addition of the NaOH. In other words, even after the addition of NaOH, which solution will remain the most acidic? This would be solution (b) 0.30 M HCl, as it is the only acidic solution out of the four provided, thus having the lowest starting pH and remaining the lowest even after an increase due to the addition of NaOH.

Key concepts

Acid-Base Neutralization

Acid-base neutralization refers to the chemical reaction where an acid and a base combine to form water and a salt. This reaction is central to the process of adjusting pH levels in various solutions. For instance, when a strong acid like hydrochloric acid (HCl) reacts with a strong base such as sodium hydroxide (NaOH), they neutralize each other, yielding water (H₂O) and sodium chloride (NaCl) as products. The equation for this reaction is given by:
\[ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} \].
In the context of the exercise question, the addition of a strong base, NaOH, to solution (b) which is an HCl solution, will lead to such a neutralization process. The extent of the pH change depends on the initial concentrations of the acid and base, and the volume of NaOH added.

Strong Acid

A strong acid is characterized by its ability to completely dissociate into ions in water. Common examples of strong acids include hydrochloric acid (HCl), sulfuric acid (H₂SO₄), and nitric acid (HNO₃). These acids readily donate their protons (H⁺ ions) to water, creating a high concentration of H⁺ ions which results in a low pH value. In the exercise, solution (b) represents such a strong acid as it contains HCl, which will completely dissociate to produce a low pH environment.
This dissociation can be represented as: \[ \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \].
The complete dissociation of strong acids is a key factor in acid-base reactions and must be taken into account when predicting the outcome of pH adjustments.

Strong Base

Similarly, a strong base is a substance that completely dissociates in water to produce a high concentration of hydroxide ions (OH⁻). An excellent representation of a strong base in chemical reactions is sodium hydroxide (NaOH), used in the exercise. Once NaOH is dissolved, it dissociates into Na⁺ and OH⁻ ions:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \].
This complete ionization of strong bases like NaOH significantly raises the pH of a solution by decreasing the H⁺ ion concentration, resulting in a more basic (less acidic) environment. When NaOH is added to the solutions in the exercise, its strong basic nature comes into play, particularly affecting the pH of the acidic solution (b).

pH Scale

The pH scale is a measure of the acidity or basicity of an aqueous solution. It ranges from 0 to 14, with 7 being neutral, values less than 7 indicating acidity, and values greater than 7 indicating basicity. The pH of a solution is logarithmically based on the concentration of H⁺ ions:
\[ \text{pH} = -\text{log}(\text{H}^+) \].
In the exercise, adjusting the pH of different solutions by adding NaOH involves understanding this pH scale. Pure water, as mentioned in the exercise (a), naturally has a pH of around 7. The addition of a strong base such as NaOH will shift the pH above 7, making it more basic. By contrast, the addition of NaOH to HCl solution (b) will raise the pH but won't exceed that of other solutions like water or those containing other bases or salts, due to the original low pH caused by the strong acid.