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Chapter 17: Problem 19

You are asked to prepare a buffer solution with a pH of 3.50. The following solutions, all \(0.100 \mathrm{M},\) are available to you: HCOOH, CH \(_{3} \mathrm{COOH}, \mathrm{H}_{3} \mathrm{PO}_{4}, \mathrm{NaCHOO}\) \(\mathrm{NaCH}_{3} \mathrm{COO},\) and \(\mathrm{NaH}_{2} \mathrm{PO}_{4} . \quad\) Describe how you would prepare this buffer solution. [Hint: What volumes of which solutions would you use?

Short Answer

Expert verified
To make a buffer solution of pH 3.50, we should mix the formic acid HCOOH and sodium formate NaHCOO solutions, taking 1 liter of formic acid for every 0.58 liters of sodium formate solution.

Step by step solution

01

Choosing the right solution to create a buffer

From the given \(0.100 \mathrm{M}\) solutions, the correct one to choose would be the one that yields a buffer with a pH of 3.50. We choose the weak acid and its conjugate base fron the list provided: HCOOH (Formic acid) and NaCHO (\( \text {Sodium formate}\))
02

Calculate the dissociation constant for Formic acid

The first step in preparing a buffer solution is to find the dissociation constant, pKa, of the chosen weak acid from a standard chemistry data tables. pKa of a substance is related to pH and indicates how readily hydrogen ions are given off by the acid in the solution. For Formic acid the pKa value is 3.74.
03

Applying the Henderson-Hasselbalch equation

For preparing a buffer solution, the Henderson-Hasselbalch equation is used which is \(pH = pKa + log \left( \frac {[Base]}{[Acid]} \right)\). Here, [Base] indicates the concentration of the base (Sodium formate) and [Acid] indicates the concentration of the acid (Formic acid). Substituting the given and found values in the equation we have, 3.50 = 3.74 + log \left( \frac {[Base]}{[Acid]} \right). Now we can solve for the ratio [Base]/[Acid].
04

Calculating concentrations

From the previous step, we can find the ratio [Base]/[Acid] = 0.58. Now to find the concentrations, one can keep the acid concentration at 0.100 M, and accordingly adjust the base concentration to achieve the required ratio. In this case, the base concentration will be 0.58 x 0.100 M = 0.058 M.
05

Finding the final volumes

Now, to prepare a buffer solution with the desired pH, you should mix the solutions in the right proportions. Since the sodium formate is 0.100 M and we need it to be 0.058 M, we take 0.58 L of sodium formate solution for each 1 L of formic acid solution. So preparing a buffer solution then depends on the total volume needed. If 1 L of buffer solution is needed, use 0.58 L of sodium formate and 1 L of formic acid. If less or more is needed, use the same ratios.

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Most popular questions from this chapter

A very common buffer agent used in the study of biochemical processes is the weak base TRIS, \(\left(\mathrm{HOCH}_{2}\right)_{3} \mathrm{CNH}_{2},\) which has a \(\mathrm{pK}_{\mathrm{b}}\) of 5.91 at \(25^{\circ} \mathrm{C} . \mathrm{A}\) student is given a sample of the hydrochloride of TRIS together with standard solutions of \(10 \mathrm{M}\) NaOH and HCl. (a) Using TRIS, how might the student prepare 1 L of a buffer of \(\mathrm{pH}=7.79 ?\) (b) In one experiment, 30 mmol of protons are released into \(500 \mathrm{mL}\) of the buffer prepared in part (a). Is the capacity of the buffer sufficient? What is the resulting pH? (c) Another student accidentally adds \(20 \mathrm{mL}\) of \(10 \mathrm{M}\) HCl to 500 mL of the buffer solution prepared in part (a). Is the buffer ruined? If so, how could the buffer be regenerated?

The Henderson-Hasselbalch equation can be written as \(\mathrm{pH}=\mathrm{p} K_{\mathrm{a}}-\log \left(\frac{1}{\alpha}-1\right)\) where \(\alpha=\frac{\left[\mathrm{A}^{-}\right]}{\left[\mathrm{A}^{-}\right]+[\mathrm{HA}]}\) Thus, the degree of ionization \((\alpha)\) of an acid can be determined if both the \(\mathrm{pH}\) of the solution and the \(\mathrm{p} K_{\mathrm{a}}\) of the acid are known. (a) Use this equation to plot the pH versus the degree of ionization for the second ionization constant of phosphoric acid \(\left(K_{\mathrm{a}}=6.3 \times 10^{-8}\right)\) (b) If \(\mathrm{pH}=\mathrm{p} K_{\mathrm{a}}\) what is the degree of ionization? (c) If the solution had a pH of 6.0 what would the value of \(\alpha\) be?

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?

Indicate whether you would expect the equivalence point of each of the following titrations to be below, above, or at \(\mathrm{pH}\) 7. Explain your reasoning. (a) \(\mathrm{NaHCO}_{3}(\mathrm{aq})\) is titrated with \(\mathrm{NaOH}(\mathrm{aq})\) (a) (b) \(\mathrm{HCl}(\mathrm{aq})\) is titrated with \(\mathrm{NH}_{3}(\mathrm{aq}) ;\) (c) \(\mathrm{KOH}(\mathrm{aq})\) is titrated with HI(aq).

In your own words, define or explain the following terms or symbols: (a) mmol; (b) HIn; (c) equivalence point of a titration; (d) titration curve.
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