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Chapter 15: Problem 56

The pH of a \(0.30 M\) solution of a weak base is 10.66 . What is the \(K_{\mathrm{b}}\) of the base?

Short Answer

Expert verified
The \(K_{\mathrm{b}}\) of the base is \(6.97 \times 10^{-8}\).

Step by step solution

01

Calculation of pOH

Since pH + pOH = 14 at 25°C, the pOH can be calculated as pOH = 14 - pH = 14 - 10.66 = 3.34.
02

Calculation of [OH^-] Concentration

Using the formula \([OH^-] = 10^{-\mathrm{pOH}}\), the concentration of OH^- can be obtained: \([OH^-] = 10^{-3.34} M = 4.57 \times 10^{-4} M\). This result implies that the concentration of the OH- is also the concentration of the weak base in its ionized form, \(B^-\).
03

Calculation of \(K_{\mathrm{b}}\)

We consider the auto-ionization of the weak base \(B\), \(B + H_2O \rightleftharpoons B^- + H_3O^+\). At equilibrium, the \([B^-]\) equals \([OH^-]\) and \([B]\) can be approximated to the initial concentration of the base, 0.30 M. Therefore, substituting these values into the \(K_{\mathrm{b}}\) expression \(K_{\mathrm{b}} = \frac{[B^-][OH^-]}{[B]}\) gives \(K_{\mathrm{b}} = \frac{(4.57 \times 10^{-4})^2}{0.30} = 6.97 \times 10^{-8}\).

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Most popular questions from this chapter

Classify the following oxides as acidic, basic, amphoteric, or neutral: (a) \(\mathrm{CO}_{2},\) (b) \(\mathrm{K}_{2} \mathrm{O},\) (c) \(\mathrm{CaO}\), (d) \(\mathrm{N}_{2} \mathrm{O}_{5}\) (e) CO, (f) \(\mathrm{NO}\) (g) \(\mathrm{SnO}_{2}\), (h) \(\mathrm{SO}_{3}\), (i) \(\mathrm{Al}_{2} \mathrm{O}_{3},(\mathrm{j}) \mathrm{BaO}\)

A \(0.400 M\) formic acid (HCOOH) solution freezes at \(-0.758^{\circ} \mathrm{C}\). Calculate the \(K_{\mathrm{a}}\) of the acid at that temperature. (Hint: Assume that molarity is equal to molality. Carry your calculations to three significant figures and round off to two for \(K_{\mathrm{a}}\).)

A typical reaction between an antacid and the hydrochloric acid in gastric juice is \(\mathrm{NaHCO}_{3}(s)+\mathrm{HCl}(a q) \rightleftharpoons\) $$ \mathrm{NaCl}(a q)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g) $$ Calculate the volume (in L) of \(\mathrm{CO}_{2}\) generated from \(0.350 \mathrm{~g}\) of \(\mathrm{NaHCO}_{3}\) and excess gastric juice at 1.00 atm and \(37.0^{\circ} \mathrm{C}\).

Both the amide ion \(\left(\mathrm{NH}_{2}^{-}\right)\) and the nitride ion \(\left(\mathrm{N}^{3-}\right)\) are stronger bases than the hydroxide ion and hence do not exist in aqueous solutions. (a) Write equations showing the reactions of these ions with water, and identify the Brønsted acid and base in each case. (b) Which of the two is the stronger base?

In terms of orbitals and electron arrangements, what must be present for a molecule or an ion to act as a Lewis acid (use \(\mathrm{H}^{+}\) and \(\mathrm{BF}_{3}\) as examples)? What must be present for a molecule or ion to act as a Lewis base (use \(\mathrm{OH}^{-}\) and \(\mathrm{NH}_{3}\) as examples)?
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