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Chapter 15: Problem 239

Determine the ammonia concentration of an aqueous solution that has a pH of \(11.50\). The equation for the dissociation of \(\mathrm{NH}_{3}\) \(\left(\mathrm{K}_{\mathrm{b}}=1.8 \times 10^{-5}\right)\) is \(\mathrm{NH}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftarrows\) \(\mathrm{NH}_{4}^{+}(a q)+\mathrm{OH}^{-}(a q)\)

Short Answer

Expert verified
The ammonia concentration in the aqueous solution with a pH of 11.50 is \(0.0558 \, M\).

Step by step solution

01

Calculate pOH#

To calculate the pOH, use the relationship between pH and pOH: \(pH + pOH = 14\) Now, substitute the given pH value of 11.50 and solve for the pOH: \(pOH = 14 - 11.50 = 2.50\)
02

Calculate the concentration of OH- ions#

Use the pOH value to calculate the concentration of OH- ions: \( [OH^-] = 10^{-pOH} \) Substitute the pOH value (2.50) and solve for [OH^-]: \( [OH^-] = 10^{-2.50} = 3.16 \times 10^{-3} \, M \)
03

Write the Kb expression#

Write the Kb expression for the dissociation of ammonia: \(K_{b} = \frac{[NH_4^+][OH^-]}{[NH_3]}\)
04

Calculate the concentration of NH3#

Notice that the change in concentration for NH4+ and OH- ions is equal. Let x be the concentration of NH3 that ionizes. Then: \(K_{b} = \frac{[(3.16 \times 10^{-3})^2]}{x}\) Substitute the given Kb value (1.8 × 10^(-5)): \(1.8 \times 10^{-5} = \frac{[(3.16 \times 10^{-3})^2]}{x}\) Now, solve for x (the ammonia concentration): \( x = \frac{[(3.16 \times 10^{-3})^2]}{1.8 \times 10^{-5}} \) \( x = 0.0558 \, M \) So, the ammonia concentration in the aqueous solution is 0.0558 M.

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Most popular questions from this chapter

Classify each substance as strong electrolyte, weak electrolyte, or nonelectrolyte: (a) \(\mathrm{CH}_{3} \mathrm{COOH}\) (b) \(\mathrm{KCH}_{3} \mathrm{COO}\) (c) \(\mathrm{H}_{2} \mathrm{SO}_{4}\) (d) \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) (e) \(\mathrm{NH}_{3}\) (f) \(\mathrm{H}_{3} \mathrm{PO}_{4}\) (g) \(\mathrm{ZnSO}_{4}\)

How would the Bronsted-Lowry theory explain that ammonia is a weak base?

Solid ammonium chloride, \(\mathrm{NH}_{4} \mathrm{Cl}\), reacts with solid sodium hydroxide to produce ammonia gas, water, and sodium chloride, \(\mathrm{NaCl}\). (a) Write a balanced equation for this reaction. (b) According to the Bronsted-Lowry definition, which species is the acid and which species is the base? Explain.

If pure water has both hydronium ions (acid) and hydroxide ions (base) in it, how can it be neutral?

A solution is prepared by dissolving \(0.250\) mole of \(\mathrm{Ba}(\mathrm{OH})_{2}\) in enough water to get \(4.00 \mathrm{I}\). of solution. What are the \(\mathrm{OH}^{-}\) and \(\mathrm{H}_{3} \mathrm{O}^{+}\) molar concentrations?
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