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Chapter 16: Problem 115

The \(\mathrm{p} K_{\mathrm{b}}\) of water is (a) 1 (b) 7 (c) 14 (d) not defined (e) none of the above

Short Answer

Expert verified
The pKb of water is 14. This is because water acts as both an acid and a base, and its pKa equals its pKb. Since the pKa of water is 14, the pKb is also 14.

Step by step solution

01

Review Definition of pKb

pKb is the negative logarithm of the base dissociation constant (Kb). pKb allows us to quantify the strength of a base. A low pKb value indicates a strong base, and a high pKb value denotes a weak base.
02

Relationship between pKa and pKb

For a given compound, the sum of its acidity constant (pKa) and its basicity constant (pKb) equals 14, which represents the ion product of water (Kw) at 25°C: \(pK_a + pK_b = 14\)
03

Calculate pKb of Water

As water acts as both an acid and a base, we know that its pKa equals its pKb. First, we will calculate the pKa value of water. The Ka value for water is 1 x 10^(-14) (at 25°C). To find the pKa, we will take the negative logarithm of the Ka value: \(pK_a = -\log_{10}(1 \times 10^{-14})\) \(pK_a = 14\) As pKa = pKb for water, the pKb value is also 14. Therefore, the correct answer is: (c) 14

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Most popular questions from this chapter

Saccharin, a sugar substitute, is a weak acid with \(\mathrm{p} K_{a}=2.32\) at \(25^{\circ} \mathrm{C}\). It ionizes in aqueous solution as follows: $$ \mathrm{HNC}_{7} \mathrm{H}_{4} \mathrm{SO}_{3}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{NC}_{7} \mathrm{H}_{4} \mathrm{SO}_{3}^{-}(a q) $$ What is the pH of a \(0.25 \mathrm{M}\) solution of this substance?

Write the chemical equation and the \(K_{a}\) expression for the acid dissociation of each of the following acids in aqueous solution. First show the reaction with \(\mathrm{H}^{+}(a q)\) as a product and then with the hydronium ion: (a) \(\mathrm{HSO}_{4}^{-}\), (b) $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}$.

Indicate whether each of the following statements is true or false. For each statement that is false, correct the statement to make it true. (a) In general, the acidity of binary acids increases from left to right in a given row of the periodic table. (b) In a series of acids that have the same central atom, acid strength increases with the number of hydrogen atoms bonded to the central atom. (c) Hydrotelluric acid \(\left(\mathrm{H}_{2} \mathrm{Te}\right)\) is a stronger acid than \(\mathrm{H}_{2} \mathrm{~S}\) because Te is more electronegative than \(\mathrm{S}\).

Label each of the following as being a strong base, a weak base, or a species with negligible basicity. In each case write the formula of its conjugate acid, and indicate whether the conjugate acid is a strong acid, a weak acid, or a species with negligible acidity: $(\mathbf{a}) \mathrm{F}^{-}(\mathbf{b}) \mathrm{Br}^{-}(\mathbf{c}) \mathrm{HS}^{-}(\mathbf{d}) \mathrm{ClO}_{4}^{-}(\mathbf{e}) \mathrm{HCOO}^{-}$

Identify the Lewis acid and Lewis base among the reactants in each of the following reactions: (a) $\mathrm{Fe}\left(\mathrm{ClO}_{4}\right)_{3}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons$ $$ \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}(a q)+3 \mathrm{ClO}_{4}^{-}(a q) $$ (b) $\mathrm{CN}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{HCN}(a q)+\mathrm{OH}^{-}(a q)$ (c) $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{~N}(g)+\mathrm{BF}_{3}(g) \rightleftharpoons\left(\mathrm{CH}_{3}\right)_{3} \mathrm{NBF}_{3}(s)$ (d) $\mathrm{HIO}(l q)+\mathrm{NH}_{2}^{-}(l q) \rightleftharpoons \mathrm{NH}_{3}(l q)+\mathrm{IO}^{-}(l q)$ (lg denotes liquid ammonia as solvent)
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