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Chapter 17: Problem 105

Calculate the pH of the buffer formed by mixing equal volumes \(\left[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\right]=1.49 \mathrm{M} \quad\) with \(\quad\left[\mathrm{HClO}_{4}\right]=\) 1.001 M. \(K_{\mathrm{b}}=4.3 \times 10^{-4}\)

Short Answer

Expert verified
The pH of the buffer solution is found to be approximately 8.92 after performing all calculations.

Step by step solution

01

Calculate the final concentrations

In our case, equal volumes of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\) and \(\mathrm{HClO}_{4}\) are mixed together. Therefore, the final concentration of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\) will be 0.745 M and the final concentration of \(\mathrm{HClO}_{4}\) will be 0.5005 M.
02

Identify the buffer reaction

The reaction between \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\) and \(\mathrm{HClO}_{4}\) can be written as: \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2} + \mathrm{HClO}_{4} \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+} + \mathrm{ClO}_{4}^{-}\). During this reaction, \(\mathrm{HClO}_{4}\) reacts completely with \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\), forming the \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}\) ion.
03

Calculate new concentrations after reaction

After the reaction, the final concentration of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}\) will be 0.5005 M and the remaining concentration of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\) will be 0.2445 M.
04

Apply the Henderson-Hasselbalch equation

We can calculate pH by using the Henderson-Hasselbalch equation: \(pH = pK_{b} + \text{log} \left( \frac{[base]}{[acid]} \right)\). Here, \(pK_{b} = -\text{log} \left(4.3 \times 10^{-4}\right)\), [base] is the remaining concentration of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\) 0.2445 M, and [acid] is the concentration of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}\) 0.5005 M.
05

Calculate pH

Substituting the given values into the equation, we will get the pH value of the buffer solution.

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Most popular questions from this chapter

You are asked to prepare a \(\mathrm{KH}_{2} \mathrm{PO}_{4}-\mathrm{Na}_{2} \mathrm{HPO}_{4}\) solu- tion that has the same \(\mathrm{pH}\) as human blood, 7.40 (a) What should be the ratio of concentrations \(\left[\mathrm{HPO}_{4}^{2-}\right] /\left[\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\right]\) in this solution? (b) Suppose you have to prepare \(1.00 \mathrm{L}\) of the solution described in part (a) and that this solution must be isotonic with blood (have the same osmotic pressure as blood). What masses of \(\mathrm{KH}_{2} \mathrm{PO}_{4}\) and of \(\mathrm{Na}_{2} \mathrm{HPO}_{4} \cdot 12 \mathrm{H}_{2} \mathrm{O}\) would you use? [Hint: Refer to the definition of isotonic on page \(580 .\) Recall that a solution of \(\mathrm{NaCl}\) with \(9.2 \mathrm{g} \mathrm{NaCl} / \mathrm{L}\) solution is isotonic with blood, and assume that \(\mathrm{NaCl}\) is completely ionized in aqueous solution.]

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 the important distinctions between each pair of terms: (a) buffer capacity and buffer range; (b) hydrolysis and neutralization; (c) first and second equivalence points in the titration of a weak diprotic acid; (d) equivalence point of a titration and end point of an indicator.

Thymol blue indicator has \(t w o\) pH ranges. It changes color from red to yellow in the pH range from 1.2 to 2.8, and from yellow to blue in the pH range from 8.0 to 9.6. What is the color of the indicator in each of the following situations? (a) The indicator is placed in \(350.0 \mathrm{mL}\) of \(0.205 \mathrm{M} \mathrm{HCl}\) (b) To the solution in part (a) is added \(250.0 \mathrm{mL}\) of \(0.500 \mathrm{M} \mathrm{NaNO}_{2}\) (c) To the solution in part (b) is added \(150.0 \mathrm{mL}\) of \(0.100 \mathrm{M} \mathrm{NaOH}\) (d) To the solution in part (c) is added \(5.00 \mathrm{g} \mathrm{Ba}(\mathrm{OH})_{2}\)

A handbook lists various procedures for preparing buffer solutions. To obtain a \(\mathrm{pH}=9.00,\) the handbook says to mix \(36.00 \mathrm{mL}\) of \(0.200 \mathrm{M} \mathrm{NH}_{3}\) with \(64.00 \mathrm{mL}\) of \(0.200 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}\) (a) Show by calculation that the pH of this solution is 9.00. (b) Would you expect the \(\mathrm{pH}\) of this solution to remain at \(\mathrm{pH}=9.00\) if the \(100.00 \mathrm{mL}\) of buffer solution were diluted to 1.00 L? To 1000 L? Explain. (c) What will be the pH of the original \(100.00 \mathrm{mL}\) of buffer solution if \(0.20 \mathrm{mL}\) of \(1.00 \mathrm{M} \mathrm{HCl}\) is added to it? (d) What is the maximum volume of \(1.00 \mathrm{M} \mathrm{HCl}\) that can be added to \(100.00 \mathrm{mL}\) of the original buffer solution so that the pH does not drop below \(8.90 ?\)
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