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Chapter 17: Problem 10

Lactic acid, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH},\) is found in sour milk. A solution containing \(1.00 \mathrm{g} \mathrm{NaCH}_{3} \mathrm{CH}_{2} \mathrm{COO}\) in 100.0 \(\mathrm{mL}\) of \(0.0500 \mathrm{M} \mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}\) has a \(\mathrm{pH}=4.11 .\) What is \(K_{\mathrm{a}}\) of lactic acid?

Short Answer

Expert verified
The Ka of lactic acid is \(1.413x10^{-5}\).

Step by step solution

01

Find the concentration of sodium lactate

First, you need to find the concentration of sodium lactate in the solution. The molar mass of \(\mathrm{NaCH}_{3} \mathrm{CH}_{2} \mathrm{COO}\) is about 112 g/mol. Given that there is 1g of sodium lactate in the solution, the molarity, M, of \(\mathrm{NaCH}_{3} \mathrm{CH}_{2}\mathrm{COO}\) is \(1g/(112 g/mol) =0.00893 mol\). Since it's in 100 mL of solution, the concentration is \(0.00893 mol/0.1 L = 0.0893 M\).
02

Find the concentration of acid and hydronium ion

You are told that there is 0.050 M of lactic acid in the solution, so that is your \(\[HA\]\). The pH of the solution is given as 4.11, so to find the \([H_3O^+]\), use the formula \([H_3O^+] =10^{-pH} = 10^{-4.11}=7.94x10^{-5} M\).
03

Substitute into Ka expression

Finally, substitute these values into the Ka expression: \(Ka = [H_3O^+][A^-]/[HA] = ( 7.94x10^{-5} M)(0.0893 M)/(0.0500 M) = 1.413x10^{-5}\).

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Most popular questions from this chapter

This single equilibrium equation applies to different phenomena described in this or the preceding chapter. \(\mathrm{CH}_{3} \mathrm{COOH}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{CH}_{3} \mathrm{COO}^{-}\) Of these four phenomena, ionization of pure acid, common-ion effect, buffer solution, and hydrolysis, indicate which occurs if (a) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) and \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\) are high, but \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]\) is very low. (b) \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]\) is high, but \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\) and \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) are very low. (c) \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\) is high, but \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) and \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]\) are low. (d) \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\) and \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]\) are high, but \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) is low.

In the titration of \(20.00 \mathrm{mL}\) of \(0.175 \mathrm{M} \mathrm{NaOH},\) calculate the number of milliliters of \(0.200 \mathrm{M} \mathrm{HCl}\) that must be added to reach a pH of (a) \(12.55,\) (b) \(10.80,\) (c) 4.25

Explain whether the equivalence point of each of the following titrations should be below, above, or at pH 7: (a) \(\mathrm{NaHCO}_{3}(\text { aq) titrated with } \mathrm{NaOH}(\mathrm{aq}) ; \text { (b) } \mathrm{HCl}(\mathrm{aq})\) titrated with \(\mathrm{NH}_{3}(\mathrm{aq}) ;\) (c) KOH(aq) titrated with HI(aq).

Even though the carbonic acid-hydrogen carbonate buffer system is crucial to the maintenance of the \(\mathrm{pH}\) of blood, it has no practical use as a laboratory buffer solution. Can you think of a reason(s) for this?

Given \(125 \mathrm{mL}\) of a solution that is \(0.0500 \mathrm{M} \mathrm{CH}_{3} \mathrm{NH}_{2}\) and \(0.0500 \mathrm{M} \mathrm{CH}_{3} \mathrm{NH}_{3}^{+} \mathrm{Cl}^{-}\) (a) Over what pH range will this solution be an effective buffer? (b) What is the buffer capacity of the solution? That is, how many millimoles of strong acid or strong base can be added to the solution before any significant change in pH occurs?
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