Question

Calculate the \(\mathrm{pH}\) of each of the following solutions from the information given. a. \(\left[\mathrm{H}^{+}\right]=3.42 \times 10^{-10} M\) b. \(\mathrm{pOH}=5.92\) c. \(\left[\mathrm{OH}^{-}\right]=2.86 \times 10^{-7} M\) d. \(\left[\mathrm{H}^{+}\right]=9.11 \times 10^{-2} M\)

Short answer

a. The pH of the solution is \( \approx 9.47 \). b. The pH of the solution is \( \approx 8.08 \). c. The pH of the solution is \( \approx 6.54 \). d. The pH of the solution is \( \approx 1.04 \).

Step-by-step solution

a. Calculate the pH using the given [H⁺] concentration

Given that the [H⁺] = 3.42 × 10⁻¹⁰ M, we can use the pH formula to determine the pH of the solution. pH = -log([H⁺]) pH = -log(3.42 × 10⁻¹⁰) The pH of the solution is \( \approx 9.47 \).

b. Calculate the pH using the given pOH

The problem gives us the pOH = 5.92. Using the third formula (pH + pOH = 14), we can calculate the pH: pH = 14 - pOH pH = 14 - 5.92 The pH of the solution is \( \approx 8.08 \).

c. Calculate the pH using the given [OH⁻] concentration

First, we need to find the pOH using the [OH⁻] concentration. The [OH⁻] is given as 2.86 × 10⁻⁷ M. pOH = -log([OH⁻]) pOH = -log(2.86 × 10⁻⁷) Now, we calculate the pH using the pOH value: pH = 14 - pOH The pH of the solution is \( \approx 6.54 \).

d. Calculate the pH using the given [H⁺] concentration

Given that the [H⁺] = 9.11 × 10⁻² M, we can use the pH formula to determine the pH of the solution. pH = -log([H⁺]) pH = -log(9.11 × 10⁻²) The pH of the solution is \( \approx 1.04 \).

Key concepts

Acid-Base Chemistry

In the world of acid-base chemistry, understanding the principles that govern the relationships between acids, bases, and their ions is fundamental. The pH scale is a pivotal concept here. It measures how acidic or basic a solution is, ranging from 0 to 14. Solutions with a pH less than 7 are acidic, while those with a pH higher than 7 are basic.This topic also involves concepts like equilibrium in water, reflected as the product of hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\) always equating to \[Kw = 1 \, \times \, 10^{-14} \, M^2\].When acids dissolve in water, they increase the concentration of \([H^+]\), and bases increase \([OH^-]\). This fundamental interplay is what determines the \([H^+]\) and \([OH^-]\) concentrations in a solution, dictating its pH and pOH values respectively.

pOH

The pOH scale is used alongside the pH scale to understand the basicity of a solution. While pH gives you a number stating the acidity, pOH does the same for basicity. They together give a full picture of a solution's nature.Understanding the pOH is straightforward:

• The lower the pOH, the more basic the solution.
• The higher the pOH, the more acidic it is.

To connect pH and pOH, use the formula: \[pH + pOH = 14\]. This shows they are inversely related—knowing one lets you determine the other. For example, a pOH of 5.92 leads to a pH of \[14 - 5.92 \, \approx \, 8.08\].

Hydrogen Ion Concentration

Hydrogen ion concentration, represented as \[\left[H^{+}\right]\], is a measure of the number of hydrogen ions present in a solution. This affects the pH value directly, with a higher concentration indicating a more acidic solution.To convert \[\left[H^{+}\right]\] to pH, the formula used is \[pH = -\log(\left[H^{+}\right])\]. As an example, given \[\left[H^{+}\right] = 3.42 \, \times 10^{-10} \, M\], the pH calculates to approximately 9.47. Remember:

• Lower \[\left[H^{+}\right]\] means higher pH, more basic.
• Higher \[\left[H^{+}\right]\] means lower pH, more acidic.

Understanding \[\left[H^{+}\right]\] is crucial for predicting how changes in a solution affect its overall acidity.

Hydroxide Ion Concentration

Hydroxide ion concentration, noted as \[\left[OH^{-}\right]\], plays a complementary role to \([H^+]\) in acid-base chemistry. This focuses on the basic aspect of solutions. To find pOH from \[\left[OH^{-}\right]\], use the formula: \[pOH = -\log(\left[OH^{-}\right])\]. For instance, a given concentration of \[\left[OH^{-}\right] = 2.86 \, \times 10^{-7} \, M\] results in a pOH of approximately 6.54.Key points to note:

• Lower \[\left[OH^{-}\right]\] indicates a lower pOH and a more acidic solution.
• Higher \[\left[OH^{-}\right]\] implies a higher pOH and a more basic solution.

By mastering \[\left[OH^{-}\right]\] and \[\left[H^{+}\right]\] relations, you can determine the pH and pOH of any aqueous solution.