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Chapter 16: Problem 102

Which, if any, of the following statements are true? (a) The stronger the base, the smaller the \(\mathrm{p} K_{b}\). (b) The stronger the base, the larger the \(\mathrm{p} K_{b}\). (c) The stronger the base, the smaller the \(K_{b}\). (d) The stronger the base, the larger the \(K_{b}\). (e) The stronger the base, the smaller the \(\mathrm{p} K_{a}\) of its conjugate acid. (f) The stronger the base, the larger the \(\mathrm{p} K_{a}\) of its conjugate acid.

Short Answer

Expert verified
Statements (a), (d), and (e) are true. Stronger bases have smaller \(\mathrm{p} K_{b}\) values, larger \(K_b\) values, and smaller \(\mathrm{p} K_{a}\) values of their conjugate acids.

Step by step solution

01

Statement (a)

The stronger the base, the smaller the \(\mathrm{p} K_{b}\). This statement is true. Strong bases have higher \(K_b\) values, meaning their \(\mathrm{p} K_{b}\) values will be smaller because \(\mathrm{p} K_{b} = -\log(K_b)\).
02

Statement (b)

The stronger the base, the larger the \(\mathrm{p} K_{b}\). This statement is false. As already stated in statement (a), stronger bases have smaller \(\mathrm{p} K_{b}\) values.
03

Statement (c)

The stronger the base, the smaller the \(K_{b}\). This statement is false. Strong bases have larger \(K_b\) values, implying more effective ionization.
04

Statement (d)

The stronger the base, the larger the \(K_{b}\). This statement is true. As already stated in statement (c), strong bases have larger \(K_b\) values.
05

Statement (e)

The stronger the base, the smaller the \(\mathrm{p} K_{a}\) of its conjugate acid. This statement is true. A strong base will have a weak conjugate acid. Weak acids have smaller \(K_a\) values, meaning their \(\mathrm{p} K_{a}\) values will be larger. Therefore, the stronger the base, the smaller the \(\mathrm{p} K_{a}\) of its conjugate acid.
06

Statement (f)

The stronger the base, the larger the \(\mathrm{p} K_{a}\) of its conjugate acid. This statement is false. As already stated in statement (e), a stronger base has a weaker conjugate acid. The weaker the acid, the smaller the \(K_a\) value, and the larger the \(\mathrm{p} K_{a}\). So, the stronger the base, the smaller the \(\mathrm{p} K_{a}\) of its conjugate acid, not larger as stated in this statement. In conclusion, statements (a), (d), and (e) are true, while the others are false.

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