Question

What is the \(\mathrm{pH}\) of a solution that is \(2.5 \times 10^{-9} \mathrm{M}\) in \(\mathrm{NaOH}\) ? Does your answer make sense?

Short answer

The pH of a solution with \(2.5 \times 10^{-9} \mathrm{M}\) NaOH is found to be 5.40, indicating an acidic solution. This doesn't make sense, as NaOH is a strong base and the pH should be higher than 7. The acidic pH could be due to the presence of a stronger acid in the solution or the dissociation of water molecules.

Step-by-step solution

Calculate the concentration of \(\mathrm{OH}^{-}\) ions

Given the concentration of NaOH, which is \(2.5 \times 10^{-9} \mathrm{M}\). Since sodium hydroxide is a strong base, it will completely dissociate in water as follows: \(\mathrm{NaOH} \rightarrow \mathrm{Na^{+}} + \mathrm{OH}^{-}\) Thus, the concentration of \(\mathrm{OH}^{-}\) ions in the solution is equal to the concentration of NaOH: \([\mathrm{OH}^{-}]= 2.5 \times 10^{-9} \mathrm{M}\)

Calculate the pOH

Now that we know the concentration of \(\mathrm{OH}^{-}\) ions, we can calculate the \(\mathrm{pOH}\) using the following formula: \(\mathrm{pOH} = -\log [\mathrm{OH}^{-}]\) Plug in the given values: \(\mathrm{pOH} = -\log (2.5 \times 10^{-9})\)

Calculate the pH

We will use the relationship between \(\mathrm{pOH}\) and \(\mathrm{pH}\) to find the \(\mathrm{pH}\) of the solution: \(\mathrm{pH} + \mathrm{pOH} = 14\) Now, substitute the calculated pOH value: \(\mathrm{pH} = 14 - \mathrm{pOH}\)

Analyze the answer

After calculating the pH, evaluate whether the answer makes sense. Since NaOH is a strong base, the pH should be higher than 7, indicating a basic solution.

Complete the calculations

Calculate the pH and pOH values: \(\mathrm{pOH} = -\log (2.5 \times 10^{-9}) = 8.60\) \(\mathrm{pH} = 14 - \mathrm{pOH} = 14 - 8.60 = 5.40\) The calculated pH value of 5.40 is less than 7, indicating an acidic solution, which isn't consistent with the presence of a strong base like NaOH. The concentration of OH- ions is very low, so it is likely that the acidic pH is due to the presence of a stronger acid in the solution or the dissociation of water molecules. So, the answer doesn't make sense in the context of a pure NaOH solution.

Key concepts

Strong Base Dissociation

When a strong base like sodium hydroxide (NaOH) is introduced into water, it undergoes a process known as dissociation. This occurs when the base separates into its constituent ions, sodium (Na⁺) and hydroxide (OH^-). Since NaOH is a strong base, it dissociates completely, meaning all the NaOH molecules will break apart in solution.

Understanding this concept is crucial in determining the concentration of hydroxide ions, represented by \( \mathrm{OH}^{-} \) in a solution. For example, when a solution contains \( 2.5 \times 10^{-9} \mathrm{M} \) of NaOH, the concentration of hydroxide ions will also be \( 2.5 \times 10^{-9} \mathrm{M} \) because of the 1:1 mole ratio in which NaOH dissociates.

pOH Calculation

pOH is a measure that represents the acidity or basicity of a solution, specifically concerning the concentration of hydroxide ions. The calculation of pOH is relatively straightforward: take the negative logarithm of the hydroxide ion concentration. The mathematical expression for calculating pOH is given by \( \mathrm{pOH} = -\log [\mathrm{OH}^{-}] \).

For example, with our given hydroxide ion concentration of \( 2.5 \times 10^{-9} \mathrm{M} \), the pOH would be calculated as \( \mathrm{pOH} = -\log (2.5 \times 10^{-9}) \). The result of this calculation provides insight into the basicity of the solution.

pH and pOH Relationship

The pH and pOH of a solution are interconnected and are part of the pH scale that measures how acidic or basic a solution is. This relationship is defined by the equation \( \mathrm{pH} + \mathrm{pOH} = 14 \), at a temperature of 25°C which is the standard laboratory condition. This means that by knowing the pOH, you can easily calculate the pH, and vice versa.

As seen in the problem explanation, once pOH is calculated, the pH can be determined by subtracting pOH from 14. In practice, if there's an error or misconception in the calculation of pOH, it will directly affect the pH calculation, leading to an incorrect assessment of the solution's properties.

Acid-Base Chemistry

In the realm of acid-base chemistry, pH is a central concept that measures the hydrogen ion concentration in a solution. Bases have a pH above 7, while acids have a pH below 7. Strong acids and bases, like HCl or NaOH, will fully dissociate in water to produce hydrogen ions (H⁺) or hydroxide ions (OH^-), respectively.

It is essential to note that the pH value obtained from the calculation for a strong base solution should reflect its basic nature, meaning the pH should be greater than 7. If upon calculation, you find the pH of a strong base solution to be less than 7, there might be an error in the calculations or assumptions. In acid-base chemistry, such discrepancies must be thoroughly investigated to ensure a correct understanding of the solution's true acidic or basic character.