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Chapter 16: Problem 3

Define \(\mathrm{p} K_{\text {a }}\) for a weak acid. What is the relationship between the value of the \(\mathrm{p} K_{\mathrm{a}}\) and the strength of the acid? Do the same for a weak base.

Short Answer

Expert verified
The \(pK_a\) and \(pK_b\) are the negative logs of the acid and base dissociation constants, respectively. Lower \(pK_a\) and \(pK_b\) values correspond to stronger acids and bases, while higher values indicate weaker acids and bases, because they are measured as negative logarithms of the dissociation constants.

Step by step solution

01

Definition of \(pK_a\)

The \(pK_a\) is the negative logarithm (base 10) of the acid dissociation constant \(K_a\) of a solution. It can be expressed as: \(pK_a = -\log(K_a)\). This term characterizes the strength of an acid in solution.
02

Relationship between \(pK_a\) and Acid Strength

The relationship between the value of \(pK_a\) and the strength of the acid is inverse. Lower values of \(pK_a\) correspond to stronger acids. Similarly, higher \(pK_a\) values indicate weaker acids. This is because \(K_a\) values for strong acids are larger, and taking the negative log of a large number gives a smaller result.
03

Definition of \(pK_b\)

The \(pK_b\) is the negative logarithm (base 10) of the base dissociation constant \(K_b\) of a solution. This can be written as: \(pK_b = -\log(K_b)\). It is used to measure the strength of a base in solution.
04

Relationship between \(pK_b\) and Base Strength

The relationship between the value of \(pK_b\) and the strength of the base is also inverse. Lower \(pK_b\) values correspond to stronger bases while higher \(pK_b\) values indicate weaker bases. This is because \(K_b\) values for strong bases are larger, and taking the negative log of a large number gives a smaller result.

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