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Chapter 17: Problem 20

A sample of \(0.1276 \mathrm{~g}\) of an unknown monoprotic acid was dissolved in \(25.0 \mathrm{~mL}\) of water and titrated with \(0.0633 \mathrm{M} \mathrm{NaOH}\) solution. The volume of base required to reach the equivalence point was \(18.4 \mathrm{~mL}\). (a) Calculate the molar mass of the acid. (b) After \(10.0 \mathrm{~mL}\) of base had been added to the titration, the \(\mathrm{pH}\) was determined to be 5.87 . What is the \(K_{\mathrm{a}}\) of the unknown acid?

Short Answer

Expert verified
a) The molar mass of the acid is \(110 \mathrm{g/mol}\), b) The acid dissociation constant of the unknown acid is approximately \( 1.07 \times 10^{-5}\).

Step by step solution

01

Calculate moles of the base

First we need to determine the moles of \(\mathrm{NaOH}\) base that's used in the reaction. We do this by multiplying the volume of the solution by its molarity \(0.0633 \mathrm{M}\). We also need to convert the volume from milliliters to liters by dividing by 1000:\[0.0633 \mathrm{M} \times \dfrac{18.4 \mathrm{ml}}{1000 \mathrm{ml/L}} = 0.00116 \mathrm{moles}\]
02

Determine molar mass of the acid

Next, we will use the molarity of the acid to determine the molar mass. We do this by dividing mass by number of moles. So the molar mass of the unknown acid would be: \[\frac{0.1276 \mathrm{g}}{0.00116 \mathrm{mol}}= 110 \mathrm{g/mol}\]
03

Calculate the acid dissociation constant (\(K_a\))

When the \(\mathrm{pH}\) was determined, it was non-equivalent because only \(10.0 \mathrm{mL}\) of the base was added. So at that point, the acid has not fully dissociated. This point in the reaction can be described by the formula: \[K_a=(x)(x)/(0.00516-x)\] Where x is the concentration of \(OH^-\) ions. We first calculate the \(OH^-\) concentration using the \(pH\) and \(pOH\) relationship: \[pOH= 14 - pH = 14 - 5.87 = 8.13\] Then, we calculate the concentration by using the formula: \[ [OH^-]= 10^{-pOH}= 10^{-8.13}= 7.4 \times 10^{-9}\] Therefore, x is \(7.4 \times 10^{-9}\). After substituting x into equation we can solve for \(K_a\) giving approximately \( 1.07 \times 10^{-5}\).

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Most popular questions from this chapter

Describe how you would prepare \(1 \mathrm{~L}\) of the buffer \(0.20 \mathrm{M} \mathrm{CH}_{3} \mathrm{COONa} / 0.20 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\) by (a) mix- ing a solution of \(\mathrm{CH}_{3} \mathrm{COOH}\) with a solution of \(\mathrm{CH}_{3} \mathrm{COONa},\) (b) reacting a solution of \(\mathrm{CH}_{3} \mathrm{COOH}\) with a solution of \(\mathrm{NaOH}\), and (c) reacting a solution of \(\mathrm{CH}_{3} \mathrm{COONa}\) with a solution of \(\mathrm{HCl}\).

Write balanced equations and solubility product expressions for the solubility equilibria of these compounds: (a) \(\mathrm{CuBr},\) (b) \(\mathrm{ZnC}_{2} \mathrm{O}_{4},\) (c) \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}\) (d) \(\mathrm{Hg}_{2} \mathrm{Cl}_{2}\) (e) \(\mathrm{AuCl}_{3}\) (f) \(\mathrm{Mn}_{3}\left(\mathrm{PO}_{4}\right)_{2}\).

Explain, with balanced ionic equations, why (a) \(\mathrm{CuI}_{2}\) dissolves in ammonia solution, (b) AgBr dissolves in NaCN solution, (c) \(\mathrm{Hg}_{2} \mathrm{Cl}_{2}\) dissolves in \(\mathrm{KCl}\) solution.

A student mixes \(50.0 \mathrm{~mL}\) of \(1.00 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) with \(86.4 \mathrm{~mL}\) of \(0.494 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4} .\) Calculate the mass of \(\mathrm{BaSO}_{4}\) formed and the \(\mathrm{pH}\) of the mixed solution.

Acid-base reactions usually go to completion. Confirm this statement by calculating the equilibrium constant for each of the following cases: (a) a strong acid reacting with a strong base, (b) a strong acid reacting with a weak base \(\left(\mathrm{NH}_{3}\right),\) (c) a weak acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) reacting with a strong base, \((\mathrm{d})\) a weak acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) reacting with a weak base \(\left(\mathrm{NH}_{3}\right)\) (Hint: Strong acids exist as \(\mathrm{H}^{+}\) ions and strong bases exist as \(\mathrm{OH}^{-}\) ions in solution. You need to look up the \(K_{\mathrm{a}}, K_{\mathrm{b}}\), and \(K_{\mathrm{w}}\) values.)
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