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Chapter 17: Problem 22

(a) Calculate the \(\mathrm{pH}\) of a buffer that is 0.105 \(\mathrm{M}\) in \(\mathrm{NaHCO}_{3}\) and 0.125 \(\mathrm{M}\) in \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) . (b) Calculate the pH of a solution formed by mixing 65 \(\mathrm{mL}\) of 0.20 \(\mathrm{M} \mathrm{NaHCO}_{3}\) with 75 \(\mathrm{mL}\) of 0.15 \(\mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3} .\)

Short Answer

Expert verified
The pH of the buffer solution in Part (a) consisting of 0.105 M NaHCO3 and 0.125 M Na2CO3 is 6.15. The pH of the mixed solution in Part (b) with 65 mL of 0.20 M NaHCO3 and 75 mL of 0.15 M Na2CO3 is 6.56.

Step by step solution

01

Find the relevant pK_a

The buffer solution consists of the bicarbonate (\(\mathrm{HCO}_{3}^{-}\)) conjugate base and carbonic acid (\(\mathrm{H}_{2}\mathrm{CO}_{3}\)) weak acid pair. Find the dissociation constant, \(K_a\), for carbonic acid and then calculate its \(pK_a\), which will be used in the Henderson-Hasselbalch equation. For carbonic acid, \(K_a = 4.3 \times 10^{-7}\), so \(pK_a = -\log(K_a) = 6.37\).
02

Plug concentrations into the Henderson-Hasselbalch equation

We are given the following concentrations: \(\mathrm{[NaHCO}_{3}] = 0.105\, \mathrm{M}\) (acts as the conjugate base, \([\mathrm{A}^{-}]\), in the equation) \(\mathrm{[Na}_{2}\mathrm{CO}_{3}] = 0.125\, \mathrm{M}\) (acts as the weak acid, \([\mathrm{HA}]\), in the equation) Plug them into the Henderson-Hasselbalch equation: \[pH = 6.37 + \log \frac{0.105}{0.125}\]
03

Calculate pH

Perform the calculations: \[pH = 6.37 + \log \frac{0.105}{0.125} = 6.37 - 0.221 = 6.15\] So, the pH of the buffer solution in Part (a) is 6.15. Part (b):
04

Find new molar concentrations

Calculate the new molar concentrations of the two components after mixing the solutions: \[\mathrm{[NaHCO}_{3}] = \frac{65\, \mathrm{mL} \times 0.20\, \mathrm{M}}{65\, \mathrm{mL} + 75\, \mathrm{mL}} = \frac{13\, \mathrm{mmol}}{140\, \mathrm{mL}} = 0.093\, \mathrm{M}\] \[\mathrm{[Na}_{2}\mathrm{CO}_{3}] = \frac{75\, \mathrm{mL} \times 0.15\, \mathrm{M}}{65\, \mathrm{mL} + 75\, \mathrm{mL}} = \frac{11.25\, \mathrm{mmol}}{140\, \mathrm{mL}} = 0.080\, \mathrm{M}\]
05

Plug concentrations into the Henderson-Hasselbalch equation

Use the same \(pK_a\)-value from Part (a) and plug the new concentrations into the Henderson-Hasselbalch equation: \[pH = 6.37 + \log \frac{0.093}{0.080}\]
06

Calculate pH

Perform the calculations: \[pH = 6.37 + \log \frac{0.093}{0.080} = 6.37 + 0.189 = 6.56\] So, the pH of the solution in Part (b) is 6.56.

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Most popular questions from this chapter

For each of the following slightly soluble salts, write the net ionic equation, if any, for reaction with a strong acid: (a) MnS, \((\mathbf{b}) \mathrm{Pbl}_{2,}(\mathbf{c}) \mathrm{AuCl}_{3},(\mathbf{d}) \mathrm{Hg}_{2} \mathrm{C}_{2} \mathrm{O}_{4},\) (e) CuBr.

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

A biochemist needs 750 \(\mathrm{mL}\) of an acetic acid-sodium acetate buffer with \(\mathrm{pH} 4.50 .\) Solid sodium acetate \((\mathrm{CH}_{3}$$ \mathrm{COONa}\) and glacial acetic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) are \right. available. Glacial acetic acid is 99\(\% \mathrm{CH}_{3} \mathrm{COOH}\) by mass and has a density of 1.05 \(\mathrm{g} / \mathrm{mL}\) . If the buffer is to be 0.15 \(\mathrm{M}\) in \(\mathrm{CH}_{3} \mathrm{COOH}\) , how many grams of \(\mathrm{CH}_{3} \mathrm{COONa}\) and how many milliliters of glacial acetic acid must be used?

You are asked to prepare a \(\mathrm{pH}=3.00\) buffer solution starting from 1.25 \(\mathrm{L}\) of a 1.00 \(\mathrm{M}\) solution of hydrofluoric acid \((\mathrm{HF})\) and any amount you need of sodium fluoride \((\mathrm{NaF})\). (a) What is the \(\mathrm{pH}\) of the hydrofluoric acid solution prior to adding sodium fluoride? (b) How many grams of sodium fluoride should be added to prepare the buffer solution? Neglect the small volume change that occurs when the sodium fluoride is added.

A 1.00 -L. solution saturated at \(25^{\circ} \mathrm{C}\) with lead(lI) iodide contains 0.54 \(\mathrm{g}\) of \(\mathrm{Pbl}_{2}\) . Calculate the solubility- product constant for this salt at \(25^{\circ} \mathrm{C}\) .
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