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Chapter 14: Problem 48

A \(0.1375 \mathrm{M}\) solution of potassium hydroxide is used to titrate \(35.00 \mathrm{~mL}\) of \(0.257 M\) hydrobromic acid. (Assume that volumes are additive.) (a) Write a balanced net ionic equation for the reaction that takes place during titration. (b) What are the species present at the equivalence point? (c) What volume of potassium hydroxide is required to reach the equivalence point? (d) What is the \(\mathrm{pH}\) of the solution before any \(\mathrm{KOH}\) is added? (e) What is the \(\mathrm{pH}\) of the solution halfway to the equivalence point? (f) What is the \(\mathrm{pH}\) of the solution at the equivalence point?

Short Answer

Expert verified
Question: Write the balanced net ionic equation for the reaction between potassium hydroxide (KOH) and hydrobromic acid (HBr), and state the species present at the equivalence point. Calculate the volume of KOH required to reach the equivalence point, and determine the pH of the solution before any KOH is added, halfway to the equivalence point, and at the equivalence point. Answer: The balanced net ionic equation is OH⁻(aq) + H⁺(aq) → H2O(l). At the equivalence point, K⁺(aq), Br⁻(aq), and H2O(l) are present. The volume of KOH required is 64.73 mL. The pH before adding any KOH is 0.59, halfway to the equivalence point is 1.29, and at the equivalence point is 7.

Step by step solution

01

(a) Balanced net ionic equation

The balanced net ionic equation for the reaction between potassium hydroxide and hydrobromic acid is given by: OH⁻(aq) + H⁺(aq) → H2O(l)
02

(b) Species present at the equivalence point

At the equivalence point, all of the hydrobromic acid (HBr) has reacted with the potassium hydroxide (KOH) and their respective cations and anions are present in the solution. Therefore, the species present at the equivalence point are K⁺(aq), Br⁻(aq), and H2O(l).
03

(c) Volume of potassium hydroxide

To find the volume of potassium hydroxide (KOH) required to reach the equivalence point, we can use the equation: \(n_{O H^{-}}=n_{H^+}\) moles of OH⁻ = moles of H⁺ \(V_{KOH}×C_{KOH}=V_{HBr}×C_{HBr}\) Where \(V_{KOH}\) is the volume of KOH, and \(C_{KOH}\), \(V_{HBr}\), and \(C_{HBr}\) are known. Plugin the values: \(V_{KOH} = \frac{V_{HBr} * C_{HBr}}{C_{KOH}} = \frac{35.00 \mathrm{~mL} * 0.257 \mathrm{M}}{0.1375 \mathrm{M}}\) \(V_{KOH} = 64.73 \mathrm{~mL}\)
04

(d) pH before any KOH is added

The pH of the solution before adding any KOH is the pH of the hydrobromic acid (HBr) solution. Since HBr is a strong acid, it will dissociate completely in water: \([\mathrm{H^+}] = 0.257 \mathrm{M}\) pH \(= -\log([\mathrm{H^+}])\) pH \(= -\log(0.257) \approx 0.59\)
05

(e) pH halfway to the equivalence point

Halfway to the equivalence point, half of the strong acid has been neutralized by the strong base. The resulting solution is a mixture of the strong acid and its conjugate weak base. At this point: \([\mathrm{H^+}] = \frac{0.257 \,\mathrm{M}}{2}\) pH \(= -\log([\mathrm{H^+}])\) pH \(= -\log(\frac{0.257}{2}) \approx 1.29\)
06

(f) pH at the equivalence point

At the equivalence point, all of the strong acid has reacted with the strong base. Since both are strong, the resulting solution is neutral (pH = 7), and any remaining ions do not affect the pH. pH at the equivalence point \(= 7\).

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Most popular questions from this chapter

A sodium hydrogen carbonate-sodium carbonate buffer is to be prepared with a \(\mathrm{pH}\) of \(9.40\). (a) What must the \(\left[\mathrm{HCO}_{3}^{-}\right] /\left[\mathrm{CO}_{3}^{2-}\right]\) ratio be? (b) How many moles of sodium hydrogen carbonate must be added to a liter of \(0.225 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3}\) to give this \(\mathrm{pH}\) ? (c) How many grams of sodium carbonate must be added to \(475 \mathrm{~mL}\) of \(0.336 \mathrm{M} \mathrm{NaHCO}_{3}\) to give this \(\mathrm{pH}\) ? (Assume no volume change.) (d) What volume of \(0.200 \mathrm{M} \mathrm{NaHCO}_{3}\) must be added to \(735 \mathrm{~mL}\) of a \(0.139 \mathrm{M}\) solution of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) to give this \(\mathrm{pH}\) ? (Assume that volumes are additive.)

Consider the titration of \(\mathrm{HF}\left(K_{\mathrm{a}}=6.7 \times 10^{-4}\right)\) with \(\mathrm{NaOH}\). What is the \(\mathrm{pH}\) when a third of the acid has been neutralized?

A painful arthritic condition known as gout is caused by an excess of uric acid HUric in the blood. An aqueous solution contains \(4.00 \mathrm{~g}\) of uric acid. A \(0.730 \mathrm{M}\) solution of \(\mathrm{KOH}\) is used for titration. After \(12.00 \mathrm{~mL}\) of KOH is added, the resulting solution has pH 4.12. The equivalence point is reached after a total of \(32.62 \mathrm{~mL}\) of KOH is added. $$\operatorname{HUric}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{Uric}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}$$ (a) What is the molar mass of uric acid? (b) What is its \(K_{\mathrm{a}}\) ?

WEB Write a balanced net ionic equation for the reaction of each of the following aqueous solutions with \(\mathrm{OH}^{-}\) ions. (a) ammonium nitrate (b) sodium dihydrogen phosphate \(\left(\mathrm{NaH}_{2} \mathrm{PO}_{4}\right)\) (c) \(\mathrm{Al}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}{ }^{3+}\)

A solution of \(\mathrm{NaOH}\) with \(\mathrm{pH} 13.68\) requires \(35.00 \mathrm{~mL}\) of \(0.128 \mathrm{M}\) \(\mathrm{HClO}_{4}\) to reach the equivalence point. (a) What is the volume of the \(\mathrm{NaOH}\) solution? (b) What is the \(\mathrm{pH}\) at the equivalence point? that volumes are additive.)
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