Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 16: Problem 107

Which of the following solutions has the higher pH? (a) a \(0.1 M\) solution of a strong acid or a \(0.1 M\) solution of a weak acid, (b) a \(0.1 \mathrm{M}\) solution of an acid with \(K_{a}=2 \times 10^{-3}\) or one with \(K_{a}=8 \times 10^{-6},(\mathrm{c}) \mathrm{a} 0.1 \mathrm{M}\) solution of a base with \(\mathrm{p} K_{b}=4.5\) or one with \(\mathrm{p} K_{b}=6.5\).

Short Answer

Expert verified
(a) The 0.1 M solution of a weak acid has a higher pH than the 0.1 M solution of a strong acid. (b) The 0.1 M solution of an acid with \(K_{a}=8 \times 10^{-6}\) has a higher pH. (c) The 0.1 M solution of a base with \(pK_{b}=4.5\) has a higher pH.

Step by step solution

01

(a) Comparing a 0.1 M solution of a strong acid and a 0.1 M solution of a weak acid

Recall that the pH of a solution is defined as the negative base 10 logarithm of the hydrogen ion concentration, given by the formula: pH = -log10([H+]). For strong acids, they ionize completely in water and, for weak acids, only partially ionize. For the 0.1 M solution of a strong acid, since it ionizes completely, the concentration of H+ ions would be 0.1 M and the pH would be -log10(0.1) = 1. For the 0.1 M solution of a weak acid, the concentration of H+ ions would be less than 0.1 M. Therefore, the pH would be greater than 1 since the pH is inversely proportional to the concentration of H+ ions. Conclusion: The 0.1 M solution of a weak acid has a higher pH than the 0.1 M solution of a strong acid.
02

(b) Comparing 0.1 M solution of an acid with \(K_{a}=2 \times 10^{-3}\) and one with \(K_{a}=8 \times 10^{-6}\)

For weak acids, the presence of the dissociation constant (\(K_a\)) is crucial. A higher \(K_a\) value indicates the acid is stronger (dissociates to a greater extent) and will have a higher concentration of H+ ions, which means a lower pH. Comparing the given acids with \(K_{a}\) values of \(2 \times 10^{-3}\) and \(8 \times 10^{-6}\), we can see that the first one has a higher \(K_a\) value and thus will be stronger than the second one. Hence, the second acid will have higher pH than the first one. Conclusion: The 0.1 M solution of an acid with \(K_{a}=8 \times 10^{-6}\) has a higher pH.
03

(c) Comparing 0.1 M solution of a base with \(pK_{b}=4.5\) and \(pK_{b}=6.5\)

For bases, we look at their dissociation constant (\(K_b\)) or their \(pK_b\) value. A lower \(pK_b\) means a stronger base (dissociates more in water). The pH of a solution of a base will be more than 7. We are given the bases with \(pK_b\) values of 4.5 and 6.5. The base with a \(pK_b\) of 4.5 is stronger than the base with a \(pK_b\) of 6.5. As a stronger base dissociates more in water and produces a larger amount of hydroxide ions, this will result in a higher pH. Conclusion: The 0.1 M solution of a base with \(pK_{b}=4.5\) has a higher pH.

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

Phenylacetic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{COOH}\right)\) is one of the substances that accumulates in the blood of people with phenylketonuria, an inherited disorder that can cause mental retardation or even death. A \(0.085 \mathrm{M}\) solution of \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{COOH}\) has a \(\mathrm{pH}\) of \(2.68 .\) Calculate the \(K_{a}\) value for this acid.

The structural formula for acetic acid is shown in Table 16.2 . Replacing hydrogen atoms on the carbon with chlorine atoms causes an increase in acidity, as follows: $$ \begin{array}{lll} \hline \text { Acid } & \text { Formula } & \boldsymbol{K}_{\boldsymbol{a}}\left(\mathbf{2 5}^{\circ} \mathbf{C}\right) \\\ \hline \text { Acetic } & \mathrm{CH}_{3} \mathrm{COOH} & 1.8 \times 10^{-5} \\\ \text {Chloroacetic } & \mathrm{CH}_{2} \mathrm{ClCOOH} & 1.4 \times 10^{-3} \\\ \text {Dichloroacetic } & \mathrm{CHCl}_{2} \mathrm{COOH} & 3.3 \times 10^{-2} \\\ \text {Trichloroacetic } & \mathrm{CCl}_{3} \mathrm{COOH} & 2 \times 10^{-1} \\\ \hline \end{array} $$ Using Lewis structures as the basis of your discussion, explain the observed trend in acidities in the series. Calculate the \(\mathrm{pH}\) of a \(0.010 \mathrm{M}\) solution of each acid.

Butyric acid is responsible for the foul smell of rancid butter. The \(\mathrm{p} K_{a}\) of butyric acid is \(4.84 .\) (a) Calculate the \(\mathrm{p} K_{b}\) for the butyrate ion. (b) Calculate the \(\mathrm{pH}\) of a \(0.050 \mathrm{M}\) solution of butyric acid. (c) Calculate the pH of a \(0.050 \mathrm{M}\) solution of sodium butyrate.

Calculate the \(\mathrm{pH}\) of a solution made by adding \(2.50 \mathrm{~g}\) of lithium oxide \(\left(\mathrm{Li}_{2} \mathrm{O}\right)\) to enough water to make \(1.500 \mathrm{~L}\) of solution.

If a neutral solution of water, with \(\mathrm{pH}=7.00\), is heated to \(50^{\circ} \mathrm{C}\), the pH drops to 6.63 . Does this mean that the concentration of \(\left[\mathrm{H}^{+}\right]\) is greater than the concentration of \(\left[\mathrm{OH}^{-}\right] ?\) Explain.
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Analysis

Read Explanation

Inorganic Chemistry

Read Explanation

Making Measurements

Read Explanation

Chemical Reactions

Read Explanation

The Earths Atmosphere

Read Explanation

Physical Chemistry

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