Question

Determine the \(\mathrm{pOH}\) of each solution. (a) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=8.3 \times 10^{-10} \mathrm{M}\) (b) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.6 \times 10^{-7} \mathrm{M}\) (c) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=7.3 \times 10^{-2} \mathrm{M}\) (d) \(\left[\mathrm{OH}^{-}\right]=4.32 \times 10^{-4} \mathrm{M}\)

Short answer

The pOH values are: (a) 9.08, (b) 6.80, (c) 1.14, (d) 3.36.

Step-by-step solution

- Calculate pH

First, calculate the pH of each of the solutions using the formula pH = -log[H3O+].

- Calculate pOH from pH

The relationship between pH and pOH in an aqueous solution at 25°C is pH + pOH = 14. Use this to find pOH.

- Calculate pOH directly

For solution d, since the concentration of OH- is given, use the formula pOH = -log[OH-] to calculate the pOH directly.

- Perform Calculations

Now, calculate the pH and pOH as follows:(a) pH = -log(8.3 x 10^-10) and pOH = 14 - pH(b) pH = -log(1.6 x 10^-7) and pOH = 14 - pH(c) pH = -log(7.3 x 10^-2) and pOH = 14 - pH(d) pOH = -log(4.32 x 10^-4); no need to calculate pH first.

- Report the pOH values

Finally, report the calculated pOH values for each solution after performing these calculations.

Key concepts

pH scale

The pH scale is a measure of the acidity or basicity of an aqueous solution. It ranges from 0 to 14, with lower values being acidic, a pH of 7 representing neutrality, and higher values being basic. This scale is logarithmic, meaning each whole pH value below 7 is ten times more acidic than the next higher value, and each whole pH value above 7 is ten times more basic.

Understanding the pH scale is crucial when studying chemistry, as it helps predict the behavior of substances in solutions, their reactivity, and how they interact with different compounds. For example, when evaluating corrosiveness, nutrient absorption in biology, or the conditions needed for a chemical reaction to occur, the pH provides essential information for these assessments.

Hydronium ion concentration

Hydronium ion concentration, represented by \( [H_3O^+] \) in chemical notation, is vital for determining the acidity of a solution. It refers to the concentration of hydronium ions present in a solution. Lower hydronium ion concentrations indicate a more basic solution, while higher concentrations signal more acidity.

In the step-by-step solution of determining pOH, the concentration of hydronium ions directly influences the pH value, which is obtained through the formula \( pH = -\log[H_3O^+] \). As such, it's critical to accurately measure the hydronium ion concentration to understand the solution's chemical properties comprehensively.

Hydroxide ion concentration

Hydroxide ion concentration \( [OH^-] \) plays an equally important role in gauging the basicity of a solution. It is the counterpart to the hydronium ion concentration in the context of acidity and basicity. For solutions where the hydroxide ion concentration is given, like in part (d) of the exercise, the pOH can be calculated directly using the formula \( pOH = -\log[OH^-] \).

A higher concentration of hydroxide ions typically indicates a more basic solution, while a lower concentration indicates a more acidic solution. This concept is central to understanding acid-base chemistry and is used to balance chemical equations and predict the outcomes of reactions.

pH and pOH relationship

The relationship between pH and pOH is pivotal in understanding the acid-base properties of a solution. At a temperature of 25°C, the sum of pH and pOH always equals 14. This implies that knowing one value allows you to easily determine the other. In aqueous solutions, where the pH is known, pOH can be calculated by subtracting the pH from 14. Similarly, if the pOH is known, the pH can be found using the same relationship.

This interdependence is derived from the ion product of water, which states that the product of the concentrations of hydronium ions and hydroxide ions at 25°C is always \( 1.0 \times 10^{-14} M^2 \). It's a foundational concept in the study of chemical equilibrium and acid-base titrations.