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Chapter 17: Problem 82

Benzenesulfonic acid is a monoprotic acid with \(\mathrm{p} K_{a}=2.25\). Calculate the \(\mathrm{pH}\) of a buffer composed of \(0.150 \mathrm{M}\) benzenesulfonic acid and \(0.125 M\) sodium benzenesulfonate.

Short Answer

Expert verified
The pH of the buffer solution composed of \(0.150 M\) benzenesulfonic acid and \(0.125 M\) sodium benzenesulfonate can be calculated using the Henderson-Hasselbalch equation: \(pH = pK_a + \log \frac{[\text{base}]}{[\text{acid}]}\). Plugging in the given values, we get \(pH = 2.25 + \log \frac{0.125}{0.150} \approx 2.07\). Therefore, the pH of the buffer solution is approximately \(2.07\).

Step by step solution

01

Identify the components of the buffer solution

The weak acid and its conjugate base are identified as benzenesulfonic acid and sodium benzenesulfonate, respectively.
02

Write the given concentrations and pKa value

The concentration of benzenesulfonic acid is 0.150 M, the concentration of sodium benzenesulfonate is 0.125 M, and the pKa of benzenesulfonic acid is 2.25.
03

Use the Henderson-Hasselbalch equation to calculate the pH of the buffer solution

The Henderson-Hasselbalch equation is: \( pH=pK_{a}+\log \frac{[\text{base}]}{[\text{acid}]} \) Plug in the given values to obtain the pH of the buffer solution: \( pH = 2.25 + \log \frac{0.125}{0.150} \)
04

Calculate the logarithm and find the pH

Calculate the logarithm term: \( \log \frac{0.125}{0.150} \approx -0.177 \) Now find the pH: \( pH = 2.25 - 0.177 \approx 2.07 \) The pH of the buffer solution composed of 0.150 M benzenesulfonic acid and 0.125 M sodium benzenesulfonate is approximately 2.07.

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Most popular questions from this chapter

Tooth enamel is composed of hydroxyapatite, whose simplest formula is \(\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH},\) and whose corresponding \(K_{s p}=6.8 \times 10^{-27} .\) As discussed in the "Chemistry and Life" box on page 730 , fluoride in fluorinated water or in toothpaste reacts with hydroxyapatite to form fluoroapatite, \(\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{~F},\) whose \(K_{s p}=1.0 \times 10^{-60} \cdot(\mathrm{a})\) Write the expres- sion for the solubility-constant for hydroxyapatite and for fluoroapatite. (b) Calculate the molar solubility of each of these compounds.

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