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Chapter 17: Problem 40

Assume that \(30.0 \mathrm{~mL}\) of a \(0.10 \mathrm{M}\) solution of a weak base \(\mathrm{B}\) that accepts one proton is titrated with a \(0.10 \mathrm{M}\) solution of the monoprotic strong acid HX. (a) How many moles of \(\mathrm{HX}\) have been added at the equivalence point? (b) What is the predominant form of \(\mathrm{B}\) at the equivalence point? (c) What factor determines the \(\mathrm{pH}\) at the equivalence point? (d) Which indicator, phenolphthalein or methyl red, is likely to be the better choice for this titration?

Short Answer

Expert verified
(a) The moles of HX at the equivalence point is 0.003 moles. (b) The predominant form of B at the equivalence point is its protonated form, BH+. (c) The factor determining pH at the equivalence point is the extent of hydrolysis of the BH+ ions in the solution. (d) Methyl red is the better indicator for this titration, as its color change range (pH 4.4 - 6.3) is more suitable for detecting the acidic pH shift at the equivalence point.

Step by step solution

01

Moles of HX at equivalence point

At the equivalence point in a titration, the number of moles of the titrant (in this case, HX) is equal to the number of moles of the analyte (in this case, B). Since we have the volume and concentration of the weak base B, we can calculate the moles of B and, consequently, the moles of HX at the equivalence point: Moles of B = Volume of B × Concentration of B Moles of B = 30.0 mL × 0.10 M \(\) To convert the volume in mL to L, we need to divide by 1000: \( 30.0 \mathrm{~mL} = 30.0 \div 1000 = 0.03 \mathrm{~L} \) So, moles of B = 0.03 L × 0.10 M = 0.003 moles. Then, the moles of HX at the equivalence point is also 0.003 moles. #b) Predominant form of B at equivalence point#
02

Predominant form of B

At the equivalence point, all of the weak base B has reacted with the strong acid HX. The weak base B has accepted one proton from HX, so the predominant form of B at the equivalence point is the protonated form, BH+. #c) Factor determining pH at equivalence point#
03

Determining pH factor

The factor that determines the pH at the equivalence point is the extent of hydrolysis of the BH+ ions in the solution. At the equivalence point, BH+ ions will undergo hydrolysis and produce H3O+ ions, which will influence the pH of the solution. By calculating the concentration of H3O+ ions, we can determine the pH at the equivalence point. In the case of weak base - strong acid titration, the pH at the equivalence point is always less than 7. #d) Choice of indicator#
04

Choosing the Indicator

Phenolphthalein has a color change range of approximately pH 8.2 - 10.0, while methyl red has a color change range of approximately pH 4.4 - 6.3. Since this is a weak base - strong acid titration, we expect the pH at the equivalence point to be less than 7. Therefore, methyl red would be the better indicator for this titration, as its color change range is more suitable to detect the acidic pH shift at the equivalence point.

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Most popular questions from this chapter

A sample of \(0.1687 \mathrm{~g}\) of an unknown monoprotic acid was dissolved in \(25.0 \mathrm{~mL}\) of water and titrated with \(0.1150 \mathrm{M} \mathrm{NaOH}\). The acid required \(15.5 \mathrm{~mL}\) of base to reach the equivalence point. (a) What is the molecular weight of the acid? (b) After \(7.25 \mathrm{~mL}\) of base had been added in the titration, the \(\mathrm{pH}\) was found to be 2.85 . What is the \(K_{a}\) for the unknown acid?

(a) Consider the equilibrium \(\mathrm{B}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons\) \(\mathrm{HB}^{+}(a q)+\mathrm{OH}^{-}(a q) .\) Using Le Châtelier's principle, explain the effect of the presence of a salt of \(\mathrm{HB}^{+}\) on the ionization of B. (b) Give an example of a salt that can decrease the ionization of \(\mathrm{NH}_{3}\) in solution.

The solubility of \(\mathrm{CaCO}_{3}\) is pH dependent. (a) Calculate the molar solubility of \(\mathrm{CaCO}_{3}\left(K_{s p}=4.5 \times 10^{-9}\right)\) neglecting the acid-base character of the carbonate ion. (b) Use the \(K_{b}\) expression for the \(\mathrm{CO}_{3}^{2-}\) ion to determine the equilibrium constant for the reaction \(\mathrm{CaCO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{Ca}^{2+}(a q)+\mathrm{HCO}_{3}^{-}(a q)+\mathrm{OH}^{-}(a q)\) (c) If we assume that the only sources of \(\mathrm{Ca}^{2+}, \mathrm{HCO}_{3}^{-},\) and \(\mathrm{OH}^{-}\) ions are from the dissolution of \(\mathrm{CaCO}_{3},\) what is the molar solubility of \(\mathrm{CaCO}_{3}\) using the preceding expression? What is the \(\mathrm{pH} ?\) (d) If the \(\mathrm{pH}\) is buffered at 8.2 (as is historically typical for the ocean), what is the molar solubility of \(\mathrm{CaCO}_{3} ?\) (e) If the \(\mathrm{pH}\) is buffered at \(7.5,\) what is the molar solubility of \(\mathrm{CaCO}_{3} ?\) How much does this drop in \(\mathrm{pH}\) increase solubility? solution remains \(0.50 \mathrm{~L},\) calculate the \(\mathrm{pH}\) of the resulting solution.

The osmotic pressure of a saturated solution of strontium sulfate at \(25^{\circ} \mathrm{C}\) is 21 torr. What is the solubility product of this salt at \(25^{\circ} \mathrm{C} ?\)

To what final concentration of \(\mathrm{NH}_{3}\) must a solution be adjusted to just dissolve \(0.020 \mathrm{~mol}\) of \(\mathrm{NiC}_{2} \mathrm{O}_{4}\left(K_{s p}=4 \times 10^{-10}\right)\) in \(1.0 \mathrm{~L}\) of solution? (Hint: You can neglect the hydrolysis of \(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\) because the solution will be quite basic.)
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