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Chapter 16: Problem 117

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.

Short Answer

Expert verified
The original statement is incorrect. When the concentration of a weak acid decreases by a factor of 10, its percent ionization increases by a factor of 10, but not \(\sqrt{10}\).

Step by step solution

01

Understanding Weak Acid Ionization

A weak acid HA ionizes in water to produce H+ and A-. This process can be represented as HA <-> H+ + A-. This dynamic equilibrium is governed by the acid ionization constant, or Ka. The expression for Ka can be written as Ka = \([H^+][A^-] / [HA]\) where \([H^+]\), \([A^-]\) and \([HA]\) represent the molar concentrations of the ions and the weak acid respectively at equilibrium.
02

Representing Percent Ionization

As per the definition, the percent ionization of a weak acid is given by the ratio of the ion concentration to the initial acid concentration, multiplied by 100, expressed as \(( [H^+] / [HA]_0 ) * 100\%\). Since the degree of ionization of a weak acid is small, we can assume that \([HA]\) is approximately equal to the initial concentration \([HA]_0\) at equilibrium. Thus, the percent ionization can also be expressed as \((Ka / [HA]_0 ) * 100\%\).
03

Testing the given Statement

According to the given statement, when the concentration of acid ( [HA] ) decreases by a factor of 10, the percent ionization must increase by a factor of \(\sqrt{10}\). We can test this by substituting [HA] with [HA]/10 in our percent ionization formula, resulting in the formula \((Ka / ([HA]/10) ) * 100\%\), which simplifies to \((Ka*10 / [HA]) * 100\%\). Dividing this by original percent ionization formula, we get the factor as \(\sqrt{100} = 10\) not the \(\sqrt{10}\). Hence, the original statement is incorrect.

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Most popular questions from this chapter

A 0.0560 -g quantity of acetic acid is dissolved in enough water to make \(50.0 \mathrm{~mL}\) of solution. Calculate the concentrations of \(\mathrm{H}^{+}, \mathrm{CH}_{3} \mathrm{COO}^{-},\) and \(\mathrm{CH}_{3} \mathrm{COOH}\) at equilibrium. \(\left(K_{\mathrm{a}}\right.\) for acetic acid \(=\) \(\left.1.8 \times 10^{-5} .\right)\)

The \(\mathrm{pH}\) of an HF solution is 6.20 . Calculate the ratio [conjugate base]/[acid] for HF at this pH.

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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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