Question

Detemine the \(\mathrm{pOH}\) of each solution and classify it as acidic, basic, or neutral. (a) \(\left[\mathrm{OH}^{-}\right]=4.5 \times 10^{-2} \mathrm{M}\) (b) \(\left[\mathrm{OH}^{-}\right]=3.1 \times 10^{-12} \mathrm{M}\) (c) \(\left[\mathrm{OH}^{-}\right]=5.4 \times 10^{-5} \mathrm{M}\) (d) \(\left[\mathrm{OH}^{-}\right]=1.2 \times 10^{-2} \mathrm{M}\)

Short answer

(a) pOH approximately 1.35, basic; (b) pOH approximately 11.51, acidic; (c) pOH approximately 4.27, basic; (d) pOH approximately 1.92, basic.

Step-by-step solution

- Calculate the pOH

Use the formula \(\mathrm{pOH} = -\log \left[\mathrm{OH}^-\right]\) to find the pOH of each solution.

Solution for (a)

For \(\left[\mathrm{OH}^-\right] = 4.5 \times 10^{-2} \mathrm{M}\), calculate the pOH using the formula: \(\mathrm{pOH} = -\log \left(4.5 \times 10^{-2}\right) = -\log (4.5) - \log (10^{-2})\).

Solution for (b)

For \(\left[\mathrm{OH}^-\right] = 3.1 \times 10^{-12} \mathrm{M}\), calculate the pOH using the formula: \(\mathrm{pOH} = -\log \left(3.1 \times 10^{-12}\right) = -\log (3.1) - \log (10^{-12})\).

Solution for (c)

For \(\left[\mathrm{OH}^-\right] = 5.4 \times 10^{-5} \mathrm{M}\), calculate the pOH using the formula: \(\mathrm{pOH} = -\log \left(5.4 \times 10^{-5}\right) = -\log (5.4) - \log (10^{-5})\).

Solution for (d)

For \(\left[\mathrm{OH}^-\right] = 1.2 \times 10^{-2} \mathrm{M}\), calculate the pOH using the formula: \(\mathrm{pOH} = -\log \left(1.2 \times 10^{-2}\right) = -\log (1.2) - \log (10^{-2})\).

- Classify each solution

A solution is neutral if \(\mathrm{pOH} = 7\), acidic if \(\mathrm{pOH} > 7\), and basic if \(\mathrm{pOH} < 7\). Use the pOH values calculated in Step 1 to classify each solution.

Key concepts

pOH and pH

Understanding the relationship between pOH and pH is crucial when studying the nature of solutions in chemistry. Both pOH and pH are measures of the concentrations of hydroxide ions (OH^-) and hydrogen ions (H⁺) in a solution, respectively. The pH scale ranges from 0 to 14 with lower values indicating high acidity and higher values indicating high alkalinity, or basicity. Similarly, the pOH scale also ranges from 0 to 14 but in the opposite direction; a lower pOH indicates a more basic solution, while a higher value indicates more acidity.

To convert between pH and pOH, you can use the formula pH + pOH = 14. This relationship comes from the ion product of water: \[K_w = [H^+][OH^-] = 1.0 \times 10^{-14}\text{ at 25°C }\] When you take the negative logarithm of both sides, because \[ -\log(K_w) = -\log([H^+][OH^-]) \text{ yields }\ pH + pOH = 14, \text{you get the above-mentioned relationship.}\] Understanding this concept is crucial as it allows one to determine the acidic or basic nature of a solution just by knowing either the pH or the pOH value.

Hydroxide Ion Concentration

Hydroxide ion concentration is a measure of the number of hydroxide ions present in a solution. It is often represented by [OH^-]. These ions play a pivotal role in determining the basicity of a solution. The more hydroxide ions that are present, the more basic the solution is. Conversely, the fewer hydroxide ions, the more neutral or acidic the solution will be.

To calculate the pOH of a solution, you can use the formula \[pOH = -\log[OH^-]\] This calculation involves taking the negative logarithm of the hydroxide ion concentration. In our textbook examples, we were given various hydroxide ion concentrations and used this formula to calculate the pOH. In scenarios where you have been given the pH instead, you can deduce [OH^-] through the relationship between pH and pOH (as explained in the previous section). This calculation is vital when trying to determine the properties of a solution and it affects various areas of chemistry including titration and buffer solution preparation.

Acidic and Basic Solutions

A solution can be classified as acidic, basic (alkaline), or neutral based on its pH or pOH value. This classification is significant in many chemical and biological processes where maintaining a certain pH level is critical.

Acidic solutions have a pH lower than 7, which corresponds to a pOH higher than 7. These solutions contain a higher concentration of hydrogen ions than hydroxide ions. On the other hand, basic solutions have a pH above 7 and therefore a pOH below 7, indicating a higher concentration of hydroxide ions. Neutral solutions are those where the pH equals 7, which means that the concentrations of hydrogen and hydroxide ions are equal, representing a balanced state.

When analyzing the given exercises, we calculate the pOH to determine the nature of each solution. If the pOH results to be greater than 7, it is acidic; if less than 7, it is basic. This categorization helps in predicting the behavior of the solutions in reactions, their corrosivity, and their potential usage in industry and research.