The remaining weak base is present as the unreacted form. The equilibrium constant for the ionization of a weak base, K b , is called the ionization constant of the weak base, and is equal to the reaction quotient when the reaction is at equilibrium. For trimethylamine, at equilibrium:. The ionization constants of several weak bases are given in Table 3 and in Appendix I. What is the value of K a for acetic acid?
Relative Strengths of Acids and Bases – Chemistry
Solution We are asked to calculate an equilibrium constant from equilibrium concentrations. At equilibrium, the value of the equilibrium constant is equal to the reaction quotient for the reaction:. Check Your Learning What is the equilibrium constant for the ionization of the ion, the weak acid used in some household cleansers:. K a for.
Solution At equilibrium, the value of the equilibrium constant is equal to the reaction quotient for the reaction:. Check Your Learning What is the equilibrium constant for the ionization of the ion, a weak base:.
K b for. What is its K a? Solution We determine an equilibrium constant starting with the initial concentrations of HNO 2 , , and as well as one of the final concentrations, the concentration of hydronium ion at equilibrium. Remember that pH is simply another way to express the concentration of hydronium ion. We can solve this problem with the following steps in which x is a change in concentration of a species in the reaction:. We can summarize the various concentrations and changes as shown here the concentration of water does not appear in the expression for the equilibrium constant, so we do not need to consider its concentration :.
To get the various values in the ICE Initial, Change, Equilibrium table, we first calculate , the equilibrium concentration of , from the pH:. The change in concentration of is equal to the change in concentration of.
8.4 Solvent Effects
For each 1 mol of that forms, 1 mol of forms. The equilibrium concentration of HNO 2 is equal to its initial concentration plus the change in its concentration. Now we can fill in the ICE table with the concentrations at equilibrium, as shown here:. Finally, we calculate the value of the equilibrium constant using the data in the table:.
Strengths of Acids and Bases
Check Your Learning. The pH of a solution of household ammonia, a 0. What is K b for NH 3. What is the concentration of hydronium ion and the pH in a 0. The concentration of water does not appear in the expression for the equilibrium constant, so we do not need to consider its change in concentration when setting up the ICE table. The table shows initial concentrations concentrations before the acid ionizes , changes in concentration, and equilibrium concentrations follows the data given in the problem appear in color :.
Solve for x and the equilibrium concentrations.
At equilibrium: Now solve for x. This gives:. To check the assumption that x is small compared to 0. We find the equilibrium concentration of hydronium ion in this formic acid solution from its initial concentration and the change in that concentration as indicated in the last line of the table:. The pH of the solution can be found by taking the negative log of the , so:. Check Your Learning Only a small fraction of a weak acid ionizes in aqueous solution. What is the percent ionization of acetic acid in a 0. Hint: Determine at equilibrium. The following example shows that the concentration of products produced by the ionization of a weak base can be determined by the same series of steps used with a weak acid.
Equilibrium Concentrations in a Solution of a Weak Base Find the concentration of hydroxide ion in a 0. Solution This problem requires that we calculate an equilibrium concentration by determining concentration changes as the ionization of a base goes to equilibrium. The solution is approached in the same way as that for the ionization of formic acid in Example 6. The reactants and products will be different and the numbers will be different, but the logic will be the same:.
If we assume that x is small relative to 0. Solving the simplified equation gives:. Recall that, for this computation, x is equal to the equilibrium concentration of hydroxide ion in the solution see earlier tabulation :. Check Your Learning a Show that the calculation in Step 2 of this example gives an x of 4.
Some weak acids and weak bases ionize to such an extent that the simplifying assumption that x is small relative to the initial concentration of the acid or base is inappropriate. As we solve for the equilibrium concentrations in such cases, we will see that we cannot neglect the change in the initial concentration of the acid or base, and we must solve the equilibrium equations by using the quadratic equation. What is the pH of a 0. Solution We need to determine the equilibrium concentration of the hydronium ion that results from the ionization of so that we can use to determine the pH.
As in the previous examples, we can approach the solution by the following steps:. We need the quadratic formula to find x. Solving for x gives a negative root which cannot be correct since concentration cannot be negative and a positive root:. In solvents less basic than water, we find HCl, HBr, and HI differ markedly in their tendency to give up a proton to the solvent.
The inability to discern differences in strength among strong acids dissolved in water is known as the leveling effect of water. Water also exerts a leveling effect on the strengths of strong bases. In the absence of any leveling effect, the acid strength of binary compounds of hydrogen with nonmetals A increases as the H-A bond strength decreases down a group in the periodic table.
Across a row in the periodic table, the acid strength of binary hydrogen compounds increases with increasing electronegativity of the nonmetal atom because the polarity of the H-A bond increases. Compounds containing oxygen and one or more hydroxyl OH groups can be acidic, basic, or amphoteric, depending on the position in the periodic table of the central atom E, the atom bonded to the hydroxyl group. If the central atom, E, has a low electronegativity, its attraction for electrons is low. Little tendency exists for the central atom to form a strong covalent bond with the oxygen atom, and bond a between the element and oxygen is more readily broken than bond b between oxygen and hydrogen.
Hence bond a is ionic, hydroxide ions are released to the solution, and the material behaves as a base—this is the case with Ca OH 2 and KOH. Lower electronegativity is characteristic of the more metallic elements; hence, the metallic elements form ionic hydroxides that are by definition basic compounds. If, on the other hand, the atom E has a relatively high electronegativity, it strongly attracts the electrons it shares with the oxygen atom, making bond a relatively strongly covalent.
The oxygen-hydrogen bond, bond b , is thereby weakened because electrons are displaced toward E. Bond b is polar and readily releases hydrogen ions to the solution, so the material behaves as an acid. High electronegativities are characteristic of the more nonmetallic elements.
Increasing the oxidation number of the central atom E also increases the acidity of an oxyacid because this increases the attraction of E for the electrons it shares with oxygen and thereby weakens the O-H bond. In each of these pairs, the oxidation number of the central atom is larger for the stronger acid Figure 9. Hydroxy compounds of elements with intermediate electronegativities and relatively high oxidation numbers for example, elements near the diagonal line separating the metals from the nonmetals in the periodic table are usually amphoteric.
This means that the hydroxy compounds act as acids when they react with strong bases and as bases when they react with strong acids. The amphoterism of aluminum hydroxide, which commonly exists as the hydrate Al H 2 O 3 OH 3 , is reflected in its solubility in both strong acids and strong bases.
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In strong bases, the relatively insoluble hydrated aluminum hydroxide, Al H 2 O 3 OH 3 , is converted into the soluble ion, , by reaction with hydroxide ion:. In this reaction, a proton is transferred from one of the aluminum-bound H 2 O molecules to a hydroxide ion in solution. On the other hand, when dissolved in strong acids, it is converted to the soluble ion by reaction with hydronium ion:. In this case, protons are transferred from hydronium ions in solution to Al H 2 O 3 OH 3 , and the compound functions as a base.
Stronger acids form weaker conjugate bases, and weaker acids form stronger conjugate bases. Thus strong acids are completely ionized in aqueous solution because their conjugate bases are weaker bases than water. Weak acids are only partially ionized because their conjugate bases are strong enough to compete successfully with water for possession of protons. Strong bases react with water to quantitatively form hydroxide ions.
Weak bases give only small amounts of hydroxide ion. What is the effect on the concentration of hydrofluoric acid, hydronium ion, and fluoride ion when the following are added to separate solutions of hydrofluoric acid? Why is the hydronium ion concentration in a solution that is 0. From the equilibrium concentrations given, calculate K a for each of the weak acids and K b for each of the weak bases. The salt ionizes in solution, but the anion slightly reacts with water to form the weak acid.
The stronger base or stronger acid is the one with the larger K b or K a , respectively. In these two examples, they are CH 3 2 NH and. Thus, PH 3 is weaker than HI. Br is to the left and below S, so HBr is the stronger acid. The larger number of oxygen atoms on the central atom giving it a higher oxidation state also creates a greater release of hydrogen atoms, resulting in a stronger acid. As a salt, the acidity increases in the same manner. The acidity increases as the electronegativity of the central atom increases. Cl is more electronegative than Br, and I is the least electronegative of the three.
In a periodic group, the more electronegative element has the more basic anion. Equilibrium calculations are necessary when one or more of the ions is a weak acid or a weak base. Assume that the change in initial concentration of the acid as the equilibrium is established can be neglected, so this concentration can be assumed constant and equal to the initial value of the total acid concentration. The equilibrium will shift to the right, increasing the concentration of HNO 2 , and decreasing the concentration of ions.
This is a case in which the solution contains a mixture of acids of different ionization strengths. Therefore, the HCO 2 H contributes a negligible amount of hydronium ions to the solution. The stronger acid, HCl, is the dominant producer of hydronium ions because it is completely ionized. Skip to content Increase Font Size. Chapter Acid-Base Equilibria. Learning Objectives By the end of this section, you will be able to:. Assess the relative strengths of acids and bases according to their ionization constants Rationalize trends in acid—base strength in relation to molecular structure Carry out equilibrium calculations for weak acid—base systems.
Solution The percent ionization for an acid is:. Answer: 1. Figure 6. Vinegar is a solution of acetic acid, a weak acid. Answer: K a for. It is usually not easy to separate these three effects and, in particular, the effects of dielectric constant and solvation merge into one another. These points are illustrated with examples of several of the more important solvents. In this discussion the solvents are classified as amphoteric both acidic and basic , acidic in which the acidic properties are much more prominent than the basic , basic in which the reverse is true , and aprotic in which both acidic and basic properties are almost entirely absent.
Finally, concentrated aqueous acids are mentioned as an example—a particularly important one—of mixed solvents. The most important nonaqueous solvents of this class are the lower alcohols methanol and ethanol. They resemble water in their acid—base properties but, because of their lower dielectric constants, facilitate processes producing ions to a much smaller extent. The most important strongly acidic solvent is sulfuric acid , which is able to protonate a wide variety of compounds containing oxygen or nitrogen.
Thus, water, alcohols, ethers , ketones, nitro compounds, and sulfones all act as bases in sulfuric acid. Many substances undergo reactions in sulfuric acid that are more complicated than simple proton transfers, often yielding species important because of their chemical reactivity. This ion frequently is the active agent in the nitration of organic compounds.
Hydrogen fluoride has solvent properties resembling those of sulfuric acid but is less acidic and has negligible basic properties. Acetic acid is another acidic solvent that has been extensively studied. Because of its low dielectric constant, ions exist in it largely in the form of ion pairs, and more complex associates are frequently formed. For this reason a quantitative interpretation of acid—base equilibria in acetic acid is often difficult, but some general conclusions can be drawn. All such bases therefore give solutions with indistinguishable acid—base properties; this is often referred to as a levelling effect of the solvent.