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Chapter 18: Problem 51

Which solution has the higher pH? Explain. (a) A \(0.1 M\) solution of an acid with \(K_{a}=1 \times 10^{-4}\) or one with \(K_{\mathrm{a}}=4 \times 10^{-5}\) (b) \(A 0.1 M\) solution of an acid with \(p K_{a}=3.0\) or one with \(p K_{a}=3.5\) (c) A \(0.1 M\) solution or a \(0.01 M\) solution of a weak acid (d) A \(0.1 M\) solution of a weak acid or a \(0.1 M\) solution of a strong acid

Short Answer

Expert verified
(a) Ka = 4 × 10⁻⁵, (b) pKa = 3.5, (c) 0.01 M, (d) 0.1 M weak acid

Step by step solution

01

- Understanding the relationship between pH, pKa, and Ka

The pH of a solution depends on the concentration of hydrogen ions (H⁺) present, which is determined by the acid's dissociation constant (Ka). A higher Ka means a stronger acid, which dissociates more in water, resulting in a lower pH. Conversely, a lower Ka or higher pKa (where pKa = -log(Ka)) means a weaker acid, resulting in a higher pH.
02

- Comparing two acids with different Ka values

For part (a), compare the Ka values: A solution with Ka = 1 × 10⁻⁴ is stronger than a solution with Ka = 4 × 10⁻⁵. Therefore, the solution with Ka = 4 × 10⁻⁵ will have a higher pH.
03

- Comparing two acids with different pKa values

For part (b), compare the pKa values: pKa = 3.5 is higher than pKa = 3.0. The higher the pKa, the weaker the acid. Therefore, the solution with pKa = 3.5 will have a higher pH.
04

- Comparing two concentrations of a weak acid

For part (c), compare the concentrations: A 0.01 M solution will have a lower concentration of H⁺ ions compared to a 0.1 M solution. Therefore, the 0.01 M solution of a weak acid will have a higher pH.
05

- Comparing a weak acid to a strong acid at the same concentration

For part (d), compare the types of acids: A strong acid will fully dissociate, leading to more H⁺ ions compared to a weak acid with the same concentration. Therefore, a 0.1 M solution of a weak acid will have a higher pH than a 0.1 M solution of a strong acid.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

acid dissociation constant (Ka)
The acid dissociation constant, represented as Ka, is a crucial factor in understanding the strength of an acid. Ka measures how well an acid can donate its protons (H⁺ ions) to a solution. A higher Ka value means the acid dissociates more in water, making it stronger. This leads to more H⁺ ions in the solution, which in turn lowers the pH.

On the other hand, a lower Ka value indicates a weaker acid, as it dissociates less, resulting in fewer H⁺ ions and a higher pH. Essentially, knowing the Ka value helps you predict how acidic or basic your solution will be. In summary,
  • High Ka = Strong acid = Low pH
  • Low Ka = Weak acid = High pH
Comparing Ka values is essential when determining the relative pH of different solutions.
pKa and pH relationship
The pKa is another useful measure that helps us understand the strength of an acid. It is derived from Ka and is calculated as the negative logarithm of the Ka value, or pKa = -log(Ka).

A lower pKa value means a stronger acid, similar to a higher Ka value. This means more H⁺ ions are released, lowering the pH. Conversely, a higher pKa value indicates a weaker acid, which releases fewer H⁺ ions, resulting in a higher pH.

Understanding the relationship between pKa and pH is very straightforward:
  • Low pKa = Strong acid = Low pH
  • High pKa = Weak acid = High pH
This relationship helps us easily infer acid strength and solution pH from the pKa values given.
weak vs strong acids
Acids are classified based on their ability to dissociate in water. Strong acids, such as hydrochloric acid (HCl), dissociate almost completely, releasing a large number of H⁺ ions. This results in a lower pH.

Weak acids, like acetic acid (CH₃COOH), only partially dissociate in water, producing fewer H⁺ ions and thus a higher pH.

When comparing weak and strong acids of the same concentration, a strong acid will always produce a lower pH because of its higher H⁺ ion concentration. In review:
  • Strong acid = Complete dissociation = Lower pH
  • Weak acid = Partial dissociation = Higher pH
Always remember, the nature of the acid—whether weak or strong—significantly impacts the resulting pH of the solution.
acid concentration on pH
The concentration of an acid solutions plays a vital role in determining its pH. For two solutions of the same acid, the one with the higher concentration will have a lower pH. This is because a higher concentration means more H⁺ ions are present.

For instance, a 0.1 M solution of a weak acid will have more H⁺ ions compared to a 0.01 M solution of the same acid. Therefore, the 0.1 M solution will be more acidic, yielding a lower pH.

When discussing acid concentration and pH:
  • Higher concentration = More H⁺ ions = Lower pH
  • Lower concentration = Fewer H⁺ ions = Higher pH
Keeping track of these principles helps understand how varying concentrations affect the acidity of a solution.

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Most popular questions from this chapter

The \(\mathrm{NH}_{4}^{+}\) ion forms acidic solutions, and the \(\mathrm{CH}_{3} \mathrm{COO}^{-}\) ion forms basic solutions. However, a solution of ammonium acetate is almost neutral. Do all of the ammonium salts of weak acids form neutral solutions? Explain your answer.

In each of the following cases, is the concentration of acid before and after dissociation nearly the same or very different? Explain your reasoning: (a) a concentrated solution of a strong acid; (b) a concentrated solution of a weak acid; (c) a dilute solution of a weak acid; (d) a dilute solution of a strong acid.

What is a conjugate acid-base pair? What is the relationship between the two members of the pair?

Calcium propionate \(\left[\mathrm{Ca}\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COO}\right)_{2} ;\right.\) calcium pro- panoate \(]\) is a mold inhibitor used in food, tobacco, and pharmaceuticals. (a) Use balanced equations to show whether aqueous calcium propionate is acidic, basic, or neutral. (b) Use Appendix C to find the resulting \(\mathrm{pH}\) when \(8.75 \mathrm{~g}\) of \(\mathrm{Ca}\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COO}\right)_{2}\) dissolves in enough water to give \(0.500 \mathrm{~L}\) of solution.

Hypochlorous acid, HClO, has a p \(K_{a}\) of \(7.54 .\) What are \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right], \mathrm{pH},\left[\mathrm{ClO}^{-}\right],\) and \([\mathrm{HClO}]\) in \(0.115 \mathrm{M} \mathrm{HClO} ?\)
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