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Chapter 16: Problem 47

A \(0.040 M\) solution of a monoprotic acid is 14 percent ionized. Calculate the ionization constant of the acid.

Short Answer

Expert verified
The Ionization constant (Ka) of the acid is approximately \(8.8 * 10^{-3}\).

Step by step solution

01

Understand what is given and what is asked

We know that the molar concentration of acid is \(0.040 M\) and the percentage of ionization is \(14\%\). We're asked to determine the Ionization constant (Ka) of the acid.
02

Correlate the percentage ionization with the amount of hydronium ions

The 14 percent ionized means 14 percent of the acid molecules have donated their protons and therefore became hydronium ions. So, we have \(0.040 M * 0.14 = 0.0056 M\) hydronium ions. Note that for every one acid molecule that ionizes, it donates one proton (H+) and becomes one hydronium ion (H3O+). So, the concentration of protons is equal to the concentration of hydronium ions.
03

Determine the Ionization Constant

The ionization constant for a weak acid (Ka) is given by: \[Ka = [H3O+][A鈥揮 / [HA]\] Where \([HA]\) is the concentration of the un-ionized acid, \([H3O+]\) is the concentration of the hydronium ion, \([A鈥揮\) is the concentration of the conjugate base. For a monoprotic weak acid, \([H3O+]\) = \([A鈥揮\). Therefore, \[Ka = [H3O+]^2 / (0.040 - [H3O+])\] Substituting the value we have for \([H3O+]\) (which is 0.0056), we find \[Ka= [(0.0056)]^2 / (0.040-0.0056)\] After calculation, we find that the Ionization Constant, Ka, is approximately \(8.8 * 10^{-3}\).

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Most popular questions from this chapter

Define pOH. Write an equation relating pH and pOH.

Prove the statement that when the concentration of a weak acid HA decreases by a factor of 10 , its percent ionization increases by a factor of \(\sqrt{10}\). State any assumptions.

About half of the hydrochloric acid produced annually in the United States \((3.0\) billion pounds \()\) is used for metal pickling. This process involves the removal of metal oxide layers from metal surfaces to prepare them for coating. (a) Write the overall and net ionic equations for the reaction between iron(III) oxide, which represents the rust layer over iron, and HCl. Identify the Bronsted acid and base. (b) Hydrochloric acid is also used to remove scale (which is mostly \(\mathrm{CaCO}_{3}\) ) from water pipes. Hydrochloric acid reacts with calcium carbonate in two stages; the first stage forms the bicarbonate ion, which then reacts further to form carbon dioxide. Write equations for these two stages and for the overall reaction. (c) Hydrochloric acid is used to recover oil from the ground. It dissolves rocks (often \(\mathrm{CaCO}_{3}\) ) so that the oil can flow more easily. In one process, a 15 percent (by mass) HCl solution is injected into an oil well to dissolve the rocks. If the density of the acid solution is \(1.073 \mathrm{~g} / \mathrm{mL}\), what is the \(\mathrm{pH}\) of the solution?

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Write all the species (except water) that are present in a phosphoric acid solution. Indicate which species can act as a Bronsted acid, which as a Bronsted base, and which as both a Bronsted acid and a Bronsted base.
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