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Chapter 5: Problem 55

We want to determine the acetylsalicyclic acid content of a series of aspirin tablets by titration with \(\mathrm{NaOH}(\mathrm{aq})\) Each of the tablets is expected to contain about \(0.32\) \(\mathrm{g}\) of \(\mathrm{HC}_{9} \mathrm{H}_{7} \mathrm{O}_{4} \cdot\) What molarity of \(\mathrm{NaOH}(\mathrm{aq})\) should we use for titration volumes of about \(23\) \(\mathrm{mL}\) ? (This procedure ensures good precision and allows the titration of two samples with the contents of a 50 mL buret.) \(\mathrm{HC}_{9} \mathrm{H}_{7} \mathrm{O}_{4}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq}) \longrightarrow_{\mathrm{C}_{9} \mathrm{H}_{7} \mathrm{O}_{4}^{-}}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(1)\)

Short Answer

Expert verified
The molarity of the NaOH solution should be approximately 0.077 M

Step by step solution

01

Find the molar quantity of acetylsalicylic acid

The molar quantity is given by the weight of substance divided by its molar mass. The molar mass of acetylsalicylic acid (HC9H7O4) is approximately \(180.16 g \cdot mol^{−1}\). Thus, the number of moles of acetylsalicylic acid in one aspirin tablet will be \(\frac{0.32\ g}{180.16\ g \cdot mol^{−1}} = 0.00177\ mol\)
02

Use stoichiometry of the reaction

The given reaction involves one mole of acetylsalicylic acid reacting with one mole of hydroxide ions (OH-) from NaOH. Thus, the number of moles of NaOH needed will be the same as the number of moles of acetylsalicylic acid, which is 0.00177 moles.
03

Find molarity of NaOH

Molarity (M) is defined as the number of moles of a substance per litre of solution. The problem states that the titration volume should be about 23 mL, or 0.023 L. Using the formula M = \(\frac{moles}{volume}\), the molarity of the NaOH solution is \(\frac{0.00177\ mol}{0.023 L} = 0.077 M\)

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Most popular questions from this chapter

The number of moles of hydroxide ion in 0.300 L of \(0.0050 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) is (a) \(0.0015 ;(\mathrm{b}) 0.0030 ;(\mathrm{c}) 0.0050\) (d) 0.010.

Phosphorus is essential for plant growth, but an excess of phosphorus can be catastrophic in aqueous ecosystems. Too much phosphorus can cause algae to grow at an explosive rate and this robs the rest of the ecosystem of oxygen. Effluent from sewage treatment plants must be treated before it can be released into lakes or streams because the effluent contains significant amounts of \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) and \(\mathrm{HPO}_{4}^{2-}\). (Detergents are a major contributor to phosphorus levels in domestic sewage because many detergents contain \(\mathrm{Na}_{2} \mathrm{HPO}_{4}\) ) A simple way to remove \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) and \(\mathrm{HPO}_{4}^{2-}\) from the effluent is to treat it with lime, \(\mathrm{CaO}\) which produces \(\mathrm{Ca}^{2+}\) and \(\mathrm{OH}^{-}\) ions in water. The \(\mathrm{OH}^{-}\) ions convert \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) and \(\mathrm{HPO}_{4}^{2-}\) ions into \(\mathrm{PO}_{4}^{3-}\) ions and, finally, \(\mathrm{Ca}^{2+}, \mathrm{OH}^{-}\), and \(\mathrm{PO}_{4}^{3-}\) ions combine to form a precipitate of \(\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH}(\mathrm{s})\) (a) Write balanced chemical equations for the four reactions described above. [Hint: The reactants are \(\mathrm{CaO}\) and \(\mathrm{H}_{2} \mathrm{O} ; \mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) and \(\left.\mathrm{OH}^{-} ; \mathrm{HPO}_{4}^{2-} \text { and } \mathrm{OH}^{-} ; \mathrm{Ca}^{2+}, \mathrm{PO}_{4}^{3-}, \text { and } \mathrm{OH}^{-} .\right]\) (b) How many kilograms of lime are required to remove the phosphorus from a \(1.00 \times 10^{4}\) L holding tank filled with contaminated water, if the water contains \(10.0 \mathrm{mg}\) of phosphorus per liter?

Balance these equations for redox reactions occurring in basic solution. (a) \(\mathrm{CrO}_{4}^{2-}+\mathrm{S}_{2} \mathrm{O}_{4}^{2-} \longrightarrow \mathrm{Cr}(\mathrm{OH})_{3}(\mathrm{s})+\mathrm{SO}_{3}^{2-}\) (b) \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}+\mathrm{N}_{2} \mathrm{H}_{4} \longrightarrow\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}+\mathrm{N}_{2}(\mathrm{g})\) (c) \(\operatorname{Fe}(\mathrm{OH})_{2}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{Fe}(\mathrm{OH})_{3}(\mathrm{s})\) (d) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}+\mathrm{MnO}_{4}^{-} \longrightarrow\) \(\mathrm{CH}_{3} \mathrm{COO}^{-}+\mathrm{MnO}_{2}(\mathrm{s})\)

What are the oxidizing and reducing agents in the following redox reactions? (a) \(5 \mathrm{SO}_{3}^{2-}+2 \mathrm{MnO}_{4}^{-}+6 \mathrm{H}^{+} \longrightarrow\) \(5 \mathrm{SO}_{4}^{2-}+2 \mathrm{Mn}^{2+}+3 \mathrm{H}_{2} \mathrm{O}\) (b) \(2 \mathrm{NO}_{2}(\mathrm{g})+7 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{g})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (c) \(2\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}+\mathrm{H}_{2} \mathrm{O}_{2}+2 \mathrm{H}^{+} \longrightarrow\) \(2\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}+2 \mathrm{H}_{2} \mathrm{O}\)

What volume of \(0.248 \mathrm{M} \mathrm{CaCl}_{2}\) must be added to \(335 \mathrm{mL}\) of \(0.186 \mathrm{M} \mathrm{KCl}\) to produce a solution with a concentration of \(0.250 \mathrm{M} \mathrm{Cl}^{-2}\) Assume that the solution volumes are additive.
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