Question

Can the pH of a solution of \(\mathrm{NaOH}\) ever be less than 7 at \(25^{\circ} \mathrm{C}\) ? Explain.

Short answer

No, a solution of NaOH cannot have a pH of less than 7 at 25°C. This is because NaOH is a strong base that completely dissociates in water causing an increased concentration of hydroxide ions, which consequently causes the solution's pH to rise above 7.

Step-by-step solution

Consider the Nature of Sodium Hydroxide (NaOH)

Sodium Hydroxide (NaOH) is a strong base. It is highly ionic, meaning that it's formed from the combination of a positively charged sodium ion (Na+) and a negatively charged hydroxide ion (OH-). When it is dissolved in water, it disassociates completely into these ions.

Understand pH and pOH

The pH of a solution is calculated as \(pH = -\log[H^+]\), where \(H^+\) is the concentration of hydrogen ions in the solution. On the other hand, pOH is calculated as \(pOH = -\log[OH^-]\), where \(OH^-\) is the concentration of hydroxide ions in the solution. At 25°C, for any aqueous solution, the sum of the pH and the pOH is 14.

Determine pH of NaOH solution

Since a solution of NaOH disassociates completely into hydroxide ions (OH-), it will definitely cause an increase in the concentration of OH- ions and will therefore decrease the pOH of the solution. According to the relation \(pH + pOH = 14\), a decrease in pOH leads to an increase in pH, pushing it over 7, which makes the solution basic. Therefore, it is not possible for NaOH solution to have a pH value less than 7 at 25° C.

Key concepts

strong base

A strong base, like sodium hydroxide (NaOH), has a unique property that sets it apart from weak bases. When dissolved in water, it dissociates completely. This means that all the NaOH molecules break apart into sodium ions (\(\text{Na}^+\)) and hydroxide ions (\(\text{OH}^-\)).

This complete dissociation is a defining characteristic of a strong base. Because of this behavior, a strong base contributes a high concentration of \(\text{OH}^-\) ions to the solution.

Importantly, this high concentration of hydroxide ions directly affects the pH of the solution. As a result, the solution becomes highly basic, with a pH typically greater than 7.

pH and pOH relationship

In the world of chemistry, pH and pOH are interconnected. They are linked by the simple equation:
\[\text{pH} + \text{pOH} = 14\] This relationship holds true at 25°C in aqueous solutions.

The pH scale measures the acidity of a solution through the concentration of hydrogen ions (\(\text{H}^+\)). Conversely, the pOH scale measures the basicity through hydroxide ions (\(\text{OH}^-\)).

As such, if the concentration of \(\text{OH}^-\) ions in the solution increases, the pOH decreases, while the pH increases. This seesaw-like dynamic ensures the total of pH and pOH is constant at 14.

So, when a strong base such as NaOH dissolves fully into \(\text{OH}^-\) ions, this decreases the pOH, reflecting a high pH, signaling a basic solution.

sodium hydroxide dissociation

The dissociation of sodium hydroxide (NaOH) in water is quite straightforward but crucial to understanding its effect on pH. Upon dissolving, each formula unit of NaOH splits into one sodium ion (\(\text{Na}^+\)) and one hydroxide ion (\(\text{OH}^-\)).

This reaction is represented by the following chemical equation:
\[\text{NaOH (aq)} \rightarrow \text{Na}^+ (aq) + \text{OH}^- (aq)\] Since NaOH is a strong base, this dissociation happens completely, leaving no undissociated NaOH in the solution.

The abundance of \(\text{OH}^-\) ions markedly raises the basicity of the solution, yielding a pH greater than 7. Such a clear-cut dissociation makes NaOH a common choice for laboratory and industrial applications where altering the pH to more basic levels is necessary.