Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 14: Problem 153

At \(25^{\circ} \mathrm{C}\), a saturated solution of benzoic acid \(\left(K_{\mathrm{a}}=6.4 \times 10^{-5}\right)\) has a pH of \(2.80\). Calculate the water solubility of benzoic acid in moles per liter.

Short Answer

Expert verified
The solubility of benzoic acid in water at 25°C can be calculated using the given Ka value and the pH of the solution. First, determine the concentration of hydronium ions (\([\mathrm{H_3O^+}]\)) using the pH value: \([\mathrm{H_3O^+}] = 10^{-2.80}\). Then, use the Ka expression \(\frac{[\mathrm{C_6H_5COO^-}][\mathrm{H_3O^+}]}{[\mathrm{C_6H_5COOH}]}\) and the relationship \([\mathrm{C_6H_5COO^-}]=[\mathrm{H_3O^+}]\) to find the solubility (S) in moles per liter: \(6.4 \times 10^{-5} = \frac{[\mathrm{H_3O^+}]^2}{S - [\mathrm{H_3O^+}]}\).

Step by step solution

01

Write the chemical equation

Write down the equilibrium reaction for the benzoic acid (\(\mathrm{C_6H_5COOH}\)) in water. The benzoic acid donates a proton to the water, resulting in the formation of benzoate ion (\(\mathrm{C_6H_5COO^-}\)) and hydronium ion (\(\mathrm{H_3O^+}\)): \[ \mathrm{C_6H_5COOH \rightleftharpoons C_6H_5COO^- + H_3O^+} \]
02

Relate pH to the concentration of hydronium ions

Calculate the concentration of hydronium ions (\([\mathrm{H_3O^+}]\)) to find the concentration of benzoic acid in the solution using the pH value: \[ [\mathrm{H_3O^+}] = 10^{-\mathrm{pH}} \] Given a pH of 2.80, the concentration of hydronium ions can be calculated as follows: \[ [\mathrm{H_3O^+}] = 10^{-2.80} \]
03

Use the Ka expression

Write down the Ka expression for benzoic acid and look for relationships between the variables: \[ K_a = \frac{[\mathrm{C_6H_5COO^-}][\mathrm{H_3O^+}]}{[\mathrm{C_6H_5COOH}]} \] Since the benzoic acid, when dissociated, forms a 1:1 ratio between the benzoate ion \(\mathrm{C_6H_5COO^-}\) and the hydronium ion \(\mathrm{H_3O^+}\), we can write the concentrations as follows: \[ 60 \] \[ [\mathrm{C_6H_5COO^-}]=[\mathrm{H_3O^+}] \] Let the solubility of benzoic acid in water be S mol/L. Then, \[ [\mathrm{C_6H_5COOH}] = S - [\mathrm{H_3O^+}] \] Substitute these expressions in the Ka equation: \[ K_a = \frac{[\mathrm{H_3O^+}]^2}{S - [\mathrm{H_3O^+}]} \]
04

Solve for benzoic acid solubility

Use the given Ka value of \(6.4 \times 10^{-5}\) and the calculated \([\mathrm{H_3O^+}]\) value to solve for the solubility (S) in moles per liter: \[ 6.4 \times 10^{-5} = \frac{[\mathrm{H_3O^+}]^2}{S - [\mathrm{H_3O^+}]} \] Once calculated, the value of S will represent the solubility of benzoic acid in moles per liter.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

What are the major species present in \(0.015 M\) solutions of each of the following bases? a. \(\mathrm{KOH}\) b. \(\mathrm{Ba}(\mathrm{OH})_{2}\) What is \(\left[\mathrm{OH}^{-}\right]\) and the \(\mathrm{pH}\) of each of these solutions?

Write out the stepwise \(K_{\mathrm{a}}\) reactions for citric acid \(\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right)\), a triprotic acid.

Monochloroacetic acid, \(\mathrm{HC}_{2} \mathrm{H}_{2} \mathrm{ClO}_{2}\), is a skin irritant that is used in "chemical peels" intended to remove the top layer of dead skin from the face and ultimately improve the complexion. The value of \(K_{\mathrm{a}}\) for monochloroacetic acid is \(1.35 \times 10^{-3}\). Calculate the \(\mathrm{pH}\) of a \(0.10 \mathrm{M}\) solution of monochloroacetic acid.

The \(\mathrm{pH}\) of a sample of gastric juice in a person's stomach is \(2.1\). Calculate the \(\mathrm{pOH},\left[\mathrm{H}^{+}\right]\), and \(\left[\mathrm{OH}^{-}\right]\) for this sample. Is gastric juice acidic or basic?

Identify the Lewis acid and the Lewis base in each of the following reactions. a. \(\mathrm{B}(\mathrm{OH})_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{B}(\mathrm{OH})_{4}^{-}(a q)+\mathrm{H}^{+}(a q)\) b. \(\mathrm{Ag}^{+}(a q)+2 \mathrm{NH}_{3}(a q) \rightleftharpoons \mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}^{+}(a q)\) c. \(\mathrm{BF}_{3}(g)+\mathrm{F}^{-}(a q) \rightleftharpoons \mathrm{BF}_{4}^{-}(a q)\)
See all solutions

Recommended explanations on Chemistry Textbooks

Organic Chemistry

Read Explanation

Inorganic Chemistry

Read Explanation

Chemical Reactions

Read Explanation

Chemical Analysis

Read Explanation

Physical Chemistry

Read Explanation

Making Measurements

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free