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Chapter 17: Problem 24

A buffer is prepared by adding \(3.5 \mathrm{~g}\) of ammonium chloride \(\left(\mathrm{NH}_{4} \mathrm{Cl}\right)\) to \(100 \mathrm{~mL}\) of $1.00 \mathrm{M} \mathrm{NH}_{3}$ solution. (a) What is the \(\mathrm{pH}\) of this buffer? (b) Write the complete ionic equation for the reaction that occurs when a few drops of hydrochloric acid are added to the buffer. (c) Write the complete ionic equation for the reaction that occurs when a few drops of sodium hydroxide solution are added to the buffer.

Short Answer

Expert verified
a) The pH of the buffer is 9.43. b) The complete ionic equation for the reaction with hydrochloric acid added is: \(NH_3 + H^+ + Cl^- \rightarrow NH_4^+ + Cl^-\) c) The complete ionic equation for the reaction with sodium hydroxide added is: \(NH_4^+ + OH^- \rightarrow NH_3 + H_2O\)

Step by step solution

01

Calculate the concentration of NH4+ and NH3 in the buffer

First, we need to find the concentration of ammonium ions and ammonia in the buffer. We are given 3.5g of ammonium chloride (NH4Cl), which is added to 100 mL of 1.00 M NH3 solution. To find the concentration of ammonium ions, we need to convert grams of NH4Cl to moles: Moles of NH4Cl = (3.5 g) / (Molecular Weight of NH4Cl) Molecular Weight of NH4Cl = 14 (N) + (1 * 4) (H) + 35.5 (Cl) = 53.5 g/mol Moles of NH4Cl = (3.5 g) / (53.5 g/mol) = 0.0654 moles Concentration of NH4+ = moles / volume (in liters) = 0.0654 moles / 0.100 L = 0.654 M Since NH4Cl is added to the solution containing NH3, the concentration of NH3 remains 1.00 M.
02

Calculate the pH of the buffer

Now we can use the Henderson-Hasselbalch equation to find the pH of the buffer: pH = pKa + log([A-]/[HA]) For NH3/NH4+ buffer, pKa = 9.25 pH = 9.25 + log([NH3] / [NH4+]) pH = 9.25 + log(1.00 / 0.654) pH = 9.25 + 0.183 pH = 9.43 So, the pH of the buffer is 9.43.
03

Complete ionic equation with hydrochloric acid (HCl) added

Now we will write the complete ionic equation when hydrochloric acid (HCl) is added to the buffer. The balanced reaction is: NH3 + HCl → NH4+ + Cl- Now, we will represent the soluble compounds in their ionic form: NH3 + H+ + Cl- → NH4+ + Cl-
04

Complete ionic equation with sodium hydroxide (NaOH) added

Now we write the complete ionic equation when sodium hydroxide (NaOH) is added to the buffer. The balanced reaction is: NH4+ + OH- → NH3 + H2O Now, we will represent the soluble compounds in their ionic form: NH4+ + OH- → NH3 + H2O So, the final answers are: a) The pH of the buffer is 9.43. b) The complete ionic equation for the reaction with hydrochloric acid added is: NH3 + H+ + Cl- → NH4+ + Cl- c) The complete ionic equation for the reaction with sodium hydroxide added is: NH4+ + OH- → NH3 + H2O

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Most popular questions from this chapter

Which of these statements about the common-ion effect is most correct? (a) The solubility of a salt MA is decreased in a solution that already contains either \(\mathrm{M}^{+}\) or \(\mathrm{A}^{-} .\) (b) Common ions alter the equilibrium constant for the reaction of an ionic solid with water. \((\mathbf{c})\) The common-ion effect does not apply to unusual ions like \(\mathrm{SO}_{3}^{2-} .(\mathbf{d})\) The solubility of a salt MA is affected equally by the addition of either \(\mathrm{A}^{-}\) or a noncommon ion.

Suppose you want to do a physiological experiment that calls for a pH 6.50 buffer. You find that the organism with which you are working is not sensitive to the weak acid $\mathrm{H}_{2} \mathrm{~A}\left(K_{a 1}=2 \times 10^{-2} ; K_{a 2}=5.0 \times 10^{-7}\right)$ or its sodium salts. You have available a \(1.0 \mathrm{M}\) solution of this acid and a 1.0 \(M\) solution of \(\mathrm{NaOH}\). How much of the \(\mathrm{NaOH}\) solution should be added to \(1.0 \mathrm{~L}\) of the acid to give a buffer at \(\mathrm{pH}\) 6.50? (Ignore any volume change.)

(a) What is the ratio of \(\mathrm{HCO}_{3}^{-}\) to $\mathrm{H}_{2} \mathrm{CO}_{3}\( in blood of \)\mathrm{pH} 7.4$ ? (b) What is the ratio of \(\mathrm{HCO}_{3}^{-}\) to $\mathrm{H}_{2} \mathrm{CO}_{3}\( in an exhausted marathon runner whose blood \)\mathrm{pH}$ is \(7.1 ?\)

Suggest how the cations in each of the following solution mixtures can be separated: (a) \(\mathrm{Na}^{+}\) and $\mathrm{Cd}^{2+},(\mathbf{b}) \mathrm{Cu}^{2+}\( and \)\mathrm{Mg}^{2+},(\mathbf{c}) \mathrm{Pb}^{2+}$ and \(\mathrm{Al}^{3+},(\mathbf{d}) \mathrm{Ag}^{+}\) and \(\mathrm{Hg}^{2+} .\)

(a) Will \(\mathrm{Co}(\mathrm{OH})_{2}\) precipitate from solution if the \(\mathrm{pH}\) of a \(0.020 \mathrm{M}\) solution of \(\mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2}\) is adjusted to $8.5 ?(\mathbf{b})\( Will \)\mathrm{AgIO}_{3}\( precipitate when \)20 \mathrm{~mL}$ of \(0.010 \mathrm{M} \mathrm{AgIO}_{3}\) is mixed with \(10 \mathrm{~mL}\) of $0.015 \mathrm{M} \mathrm{NaIO}_{3} ?\left(K_{s p}\right.\( of \)\mathrm{AgIO}_{3}$ is \(3.1 \times 10^{-8} .\) )
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