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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) Why is the concentration of undissolved solid not explicitly included in the expression for the solubilityproduct constant? (b) Write the expression for the solubility-product constant for each of the following strong electrolytes: \(\mathrm{AgI}, \mathrm{SrSO}_{4}, \mathrm{Fe}(\mathrm{OH})_{2}\), and \(\mathrm{Hg}_{2} \mathrm{Br}_{2}\).

Predict whether the equivalence point of each of the following titrations is below, above, or at \(\mathrm{pH} 7\) : (a) formic acid titrated with \(\mathrm{NaOH}\), (b) calcium hydroxide titrated with perchloric acid, (c) pyridine titrated with nitric acid.

Describe the solubility of \(\mathrm{CaCO}_{3}\) in each of the following solutions compared to its solubility in water: (a) in \(0.10 \mathrm{M} \mathrm{NaCl}\) solution; \((\mathrm{b})\) in \(0.10 \mathrm{M} \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) solution; (c) \(0.10 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3}\); (d) \(0.10 \mathrm{M}\) HCl solution. (Answer same, less soluble, or more soluble.)

Suppose you want to do a physiological experiment that calls for a pH \(6.5\) buffer. You find that the organism with which you are working is not sensitive to the weak acid \(\mathrm{H}_{2} \mathrm{X}\left(K_{a 1}=2 \times 10^{-2} ; K_{a 2}=5.0 \times 10^{-7}\right)\) or its sodium salts. You have available a \(1.0 \mathrm{M}\) solution of this acid and a \(1.0 \mathrm{M}\) solution of \(\mathrm{NaOH}\). How much of the \(\mathrm{NaOH}\) solution should be added to \(1.0 \mathrm{~L}\) of the acid to give a buffer at \(\mathrm{pH}\) 6.50? (lgnore any volume change.)

A hypothetical weak acid, HA, was combined with \(\mathrm{NaOH}\) in the following proportions: \(0.20 \mathrm{~mol}\) of \(\mathrm{HA}\), \(0.080 \mathrm{~mol}\) of \(\mathrm{NaOH}\). The mixture was diluted to a total volume of \(1.0 \mathrm{~L}\), and the pH measured. (a) If \(\mathrm{pH}=4.80\), what is the \(\mathrm{p} K_{a}\) of the acid? (b) How many additional moles of \(\mathrm{NaOH}\) should be added to the solution to increase the \(\mathrm{pH}\) to \(5.00 ?\)
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