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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 脳 10鈦烩伒, (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鈦�) 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 脳 10鈦烩伌 is stronger than a solution with Ka = 4 脳 10鈦烩伒. Therefore, the solution with Ka = 4 脳 10鈦烩伒 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鈦� 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鈦� 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鈦� ions) to a solution. A higher Ka value means the acid dissociates more in water, making it stronger. This leads to more H鈦� 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鈦� 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鈦� ions are released, lowering the pH. Conversely, a higher pKa value indicates a weaker acid, which releases fewer H鈦� 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鈦� ions. This results in a lower pH.

Weak acids, like acetic acid (CH鈧僀OOH), only partially dissociate in water, producing fewer H鈦� 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鈦� ion concentration. In review:
  • Strong acid = Complete dissociation = Lower pH
  • Weak acid = Partial dissociation = Higher pH
Always remember, the nature of the acid鈥攚hether weak or strong鈥攕ignificantly 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鈦� ions are present.

For instance, a 0.1 M solution of a weak acid will have more H鈦� 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鈦� ions = Lower pH
  • Lower concentration = Fewer H鈦� 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

Which are Lewis acids and which are Lewis bases? (a) \(\mathrm{Cu}^{2+}\) (b) Cl" (c) \(\mathrm{SnCl}_{2}\) (d) \(\mathrm{OF}_{2}\)

Tris(hydroxymethyl)aminomethane, known as TRIS or THAM, is a water-soluble base used in synthesizing surfactants and pharmaceuticals, as an emulsifying agent in cosmetics, and in cleaning mixtures for textiles and leather. In biomedical research, solutions of TRIS are used to maintain nearly constant pH for the study of enzymes and other cellular components. Given that the \(\mathrm{pK}_{\mathrm{b}}\) is \(5.91,\) calculate the \(\mathrm{pH}\) of \(0.075 \mathrm{M}\) TRIS.

(a) Is a weak Bronsted-Lowry base necessarily a weak Lewis base? Explain with an example. (b) Identify the Lewis bases in the following reaction: $$ \mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}^{2+}(a q)+4 \mathrm{CN}^{-}(a q) \rightleftharpoons \mathrm{Cu}(\mathrm{CN})_{4}^{2-}(a q)+4 \mathrm{H}_{2} \mathrm{O}(l) $$ (c) Given that \(K_{c}>1\) for the reaction in part (b), which Lewis base is stronger?

A \(0.035 M\) solution of a weak acid (HA) has a pH of 4.88 . What is the \(K_{a}\) of the acid?

Write balanced equations and \(K_{b}\) expressions for these Bronsted-Lowry bases in water: (a) Pyridine, \(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}\) (b) \(\mathrm{CO}_{3}^{2-}\)
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