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Chapter 17: Problem 33

In the titration of \(10.00 \mathrm{mL}\) of \(0.04050 \mathrm{M} \mathrm{HCl}\) with \(0.01120 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) in the presence of the indicator 2,4-dinitrophenol, the solution changes from colorless to yellow when 17.90 mL of the base has been added. What is the approximate value of \(\mathrm{p} K_{\mathrm{HIn}}\) for 2,4 -dinitrophenol? Is this a good indicator for the titration?

Short Answer

Expert verified
The approximate value of \(pK_{\mathrm{HIn}}\) for 2,4 -dinitrophenol is slightly less than 7. 2,4 -dinitrophenol is a suitable indicator for this titration, although it is not the ideal one since its color change does not exactly coincide with the equivalence point.

Step by step solution

01

Identify the stoichiometry of the reaction

We need to first understand the reaction between \(HCl\) and \(Ba(OH)_2\). This reaction can be represented by the equation \(2HCl + Ba(OH)_2 \rightarrow BaCl_2 + 2H_2O\). Hence, the ratio of \(HCl\) to \(Ba(OH)_2\) in a balanced reaction is 2:1.
02

Calculate the moles of \(HCl\) and find equivalence point

The volume of \(HCl\) is given as 10.00 mL and its molarity as 0.04050 M. We can calculate the moles of \(HCl\) using the formula Molarity = moles/volume. Therefore, moles of \(HCl\) = volume * molarity = 10.00 mL * 0.04050 M = 0.000405 mol. At the equivalence point, all the \(HCl\) would have reacted with \(Ba(OH)_2\) based on the 2:1 ratio, meaning the moles of \(Ba(OH)_2\) needed is half the moles of \(HCl\), which is 0.0002025 mol.
03

Calculate volume of \(Ba(OH)_2\) required

Next, we calculate the volume of \(Ba(OH)_2\) required to reach the equivalence point by using the formula Volume = moles/Molarity. Therefore, Volume = 0.0002025 mol/0.01120 M = 18.08 mL.
04

Calculate the pH at equivalence point

The pH at the equivalence point of a titration of a strong acid with a strong base is 7.
05

Find \(pK_{\mathrm{HIn}}\)

Based on the color change of the indicator, the pH at which 2,4-dinitrophenol changes color is the same as the \(pK_{\mathrm{HIn}}\). Since the color change occurred before the equivalence point (17.90 mL compared to 18.08 mL), the pH is slightly less than 7. Since pH decreases with increasing H+ concentration, \(pK_{\mathrm{HIn}}\) would be slightly less than 7.
06

Evaluate the suitability of the indicator

A good indicator for a titration would change color at the same pH as the equivalence point. In this case, the \(pK_{\mathrm{HIn}}\) is slightly less than the pH at equivalence point, and so 2,4-dinitrophenol is not a perfect indicator for the titration but still a fairly good one since the difference is small.

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Most popular questions from this chapter

Two aqueous solutions are mixed: \(50.0 \mathrm{mL}\) of 0.0150 \(\mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) and \(50.0 \mathrm{mL}\) of \(0.0385 \mathrm{M} \mathrm{NaOH} .\) What is the pH of the resulting solution?

\(\begin{array}{lll}\text { Given } & 1.00 & \mathrm{L}\end{array}\) of a solution that is \(0.100 \mathrm{M}\) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH}\) and \(0.100 \mathrm{M} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COO}\) (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?

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?

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 \(\mathrm{pH}=5.12 ?\)

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?
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