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Chapter 17: Problem 26

How many grams of sodium lactate \(\left[\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COONa}\right.\) or \(\left.\mathrm{NaC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}\right]\) should be added to \(1.00 \mathrm{~L}\) of \(0.150 \mathrm{M}\) lactic acid \(\left[\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COOH}\right.\) or \(\left.\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}\right]\) to form a buffer solution with \(\mathrm{pH} 4.00\) ? Assume that no volume change occurs when the sodium lactate is added.

Short Answer

Expert verified
To create a buffer solution with a pH of 4.00, approximately 23.2 grams of sodium lactate should be added to the 1.00 L of 0.150 M lactic acid solution.

Step by step solution

01

Write the Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is given by: \(pH = pK_a + \log\frac{[\textrm{base}]}{[\textrm{acid}]}\)
02

Find the pKa value of lactic acid

The acidic dissociation constant, Ka, of lactic acid is given as \(\textrm{Ka} = 1.38 \times 10^{-4}\). To find the pKa, we take the negative logarithm of Ka: \(pK_a = -\log(\textrm{Ka}) = -\log(1.38 \times 10^{-4})\) Calculating this value, we get: \(pK_a = 3.86\)
03

Calculate the ratio of base/acid concentrations

Using the Henderson-Hasselbalch equation, we can find the ratio of base/acid concentrations: \(pH = pK_a + \log\frac{[\textrm{base}]}{[\textrm{acid}]}\) \(4.00 = 3.86 + \log\frac{[\textrm{base}]}{[\textrm{acid}]}\) \(0.14 = \log\frac{[\textrm{base}]}{[\textrm{acid}]}\) Now, we can calculate the base/acid concentration ratio: \(\frac{[\textrm{base}]}{[\textrm{acid}]} = 10^{0.14} = 1.38\)
04

Calculate the concentration of the base

We are given that the concentration of the lactic acid solution is 0.150 M. To find the concentration of the base, we can use the calculated ratio: \([\textrm{base}] = [\textrm{acid}] \times \frac{[\textrm{base}]}{[\textrm{acid}]}\) \([\textrm{base}] = 0.150 \mathrm{M} \times 1.38\) \([\textrm{base}] = 0.207 \mathrm{M}\)
05

Calculate the moles of the base needed

We now know the required concentration of the base, and we are given the volume of the solution (1.00 L). To find the moles of sodium lactate needed, we can use the following formula: \(\textrm{moles} = \mathrm{concentration}\times\mathrm{volume}\) \(\textrm{moles} = 0.207 \mathrm{M}\times 1.00\mathrm{ L}\) \(\textrm{moles} = 0.207\, \textrm{moles}\)
06

Calculate the grams of sodium lactate needed

Finally, we can calculate the mass of sodium lactate needed. The molar mass of sodium lactate (NaC3H5O3) is approximately 112.06 g/mol. So, the mass of sodium lactate needed can be calculated as follows: \(\textrm{mass} = \textrm{moles}\times\mathrm{molar \ mass}\) \(\textrm{mass} = 0.207 \textrm{ moles} \times 112.06 \frac{\textrm{g}}{\textrm{mol}}\) \(\textrm{mass} \approx 23.2\, \textrm{g}\) To create a buffer solution with a pH of 4.00, approximately 23.2 grams of sodium lactate should be added to the 1.00 L of 0.150 M lactic acid solution.

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Most popular questions from this chapter

(a) What is the common-ion effect? (b) Give an example of a salt that can decrease the ionization of \(\mathrm{HNO}_{2}\) in solution.

(a) Consider the equilibrium \(\mathrm{B}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons\) \(\mathrm{HB}^{+}(a q)+\mathrm{OH}^{-}(a q) .\) Using Le Ch芒telier's principle, explain the effect of the presence of a salt of \(\mathrm{HB}^{+}\) on the ionization of B. (b) Give an example of a salt that can decrease the ionization of \(\mathrm{NH}_{3}\) in solution.

How many milliliters of \(0.0850 \mathrm{M} \mathrm{NaOH}\) are required to titrate each of the following solutions to the equivalence point: (a) \(40.0 \mathrm{~mL}\) of \(0.0900 \mathrm{M} \mathrm{HNO}_{3}\), (b) \(35.0 \mathrm{~mL}\) of \(0.0850 \mathrm{MCH}_{3} \mathrm{COOH}\), (c) \(50.0 \mathrm{~mL}\) of a solution that contains \(1.85 \mathrm{~g}\) of \(\mathrm{HCl}\) per liter?

Suppose that a 10-mL sample of a solution is to be tested for \(\mathrm{Cl}^{-}\) ion by addition of 1 drop \((0.2 \mathrm{~mL})\) of \(0.10 \mathrm{M}\) \(\mathrm{AgNO}_{3}\). What is the minimum number of grams of \(\mathrm{Cl}^{-}\) that must be present for \(\mathrm{AgCl}(\mathrm{s})\) to form?

(a) Will \(\mathrm{Ca}(\mathrm{OH})_{2}\) precipitate from solution if the \(\mathrm{pH}\) of a \(0.050 \mathrm{M}\) solution of \(\mathrm{CaCl}_{2}\) is adjusted to \(8.0 ?\) (b) Will \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\) precipitate when \(100 \mathrm{~mL}\) of \(0.050 \mathrm{M} \mathrm{AgNO}_{3}\) is mixed with \(10 \mathrm{~mL}\) of \(5.0 \times 10^{-2} \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}\) solution?
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