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Chapter 17: Problem 22

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?

Short Answer

Expert verified
The effective pH range for this buffer solution is from 9.64 to 11.64. The buffer capacity of this solution is 6.25 mmol of strong acid or base.

Step by step solution

01

Determine the pKA

Firstly, calculate the pKa of the weak base, CH3NH2. Looking at a table of Ka values for weak acids, one can find that the Ka value for the conjugate acid CH3NH3+ is 2.29x10^-11. Since pKa= -log(Ka), the pKa is 10.64.
02

Effective Buffer Range

A buffer solution is most effective when the pH value is within 1 unit of pKa, meaning the effective buffer range is from (pKa - 1) to (pKa + 1). So, the effective buffer pH of this solution ranges from 9.64 to 11.64.
03

Buffer Capacity

For part (b), determine the buffer capacity. This solution can handle equal amounts of acid or base because the weak base and its conjugate acid present are at the same concentration. Look at the lesser concentration, which in this case is 0.0500 M (we multiply by 125 ml to convert the concentration to millimoles, giving us 6.25 mmol). So, this (6.25 mmol) is the maximum amount of strong acid or base that can be added before the pH changes significantly.
04

Conclusion

Therefore, the solution can act as an effective buffer within the pH range 9.64 to 11.64 and the buffer capacity equals 6.25 mmol. That is, until 6.25 mmol of strong acid or base are added, the pH of the solution will not change significantly.

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Most popular questions from this chapter

Write equations to show how each of the following buffer solutions reacts with a small added amount of a strong acid or a strong base: (a) HCOOH-KHCOO; (b) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}-\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}^{+} \mathrm{Cl}^{-}\) (c) \(\mathrm{KH}_{2} \mathrm{PO}_{4}-\mathrm{Na}_{2} \mathrm{HPO}_{4}\)

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Carbonic acid is a weak diprotic acid \(\left(\mathrm{H}_{2} \mathrm{CO}_{3}\right)\) with \(K_{a_{1}}=4.43 \times 10^{-7}\) and \(K_{\mathrm{a}_{2}}=4.73 \times 10^{-11} .\) The equiv- alence points for the titration come at approximately pH 4 and 9. Suitable indicators for use in titrating carbonic acid or carbonate solutions are methyl orange and phenolphthalein. (a) Sketch the titration curve that would be obtained in titrating a sample of \(\mathrm{NaHCO}_{3}(\mathrm{aq})\) with \(1.00 \mathrm{M} \mathrm{HCl}\) (b) Sketch the titration curve for \(\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{aq})\) with 1.00 M HCl. (c) What volume of \(0.100 \mathrm{M} \mathrm{HCl}\) is required for the complete neutralization of \(1.00 \mathrm{g} \mathrm{NaHCO}_{3}(\mathrm{s}) ?\) (d) What volume of \(0.100 \mathrm{M} \mathrm{HCl}\) is required for the complete neutralization of \(1.00 \mathrm{g} \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s}) ?\) (e) A sample of NaOH contains a small amount of \(\mathrm{Na}_{2} \mathrm{CO}_{3} .\) For titration to the phenolphthalein end point, \(0.1000 \mathrm{g}\) of this sample requires \(23.98 \mathrm{mL}\) of \(0.1000 \mathrm{M} \mathrm{HCl} .\) An additional \(0.78 \mathrm{mL}\) is required to reach the methyl orange end point. What is the percent \(\mathrm{Na}_{2} \mathrm{CO}_{3},\) by mass, in the sample?

Is a solution of sodium dihydrogen citrate, \(\mathrm{NaH}_{2} \mathrm{Cit}\) likely to be acidic, basic, or neutral? Explain. Citric \(\mathrm{acid}, \mathrm{H}_{3} \mathrm{Cit}, \mathrm{is} \mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\)

What stoichiometric concentration of the indicated substance is required to obtain an aqueous solution with the pH value shown: (a) aniline, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\), for \(\mathrm{pH}=8.95 ;(\mathrm{b}) \mathrm{NH}_{4} \mathrm{Cl}\) for \(\mathrm{pH}=5.12 ?\)
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