An Increased Concentration Of What Ion Characterizes A Solution Of A Base In Water?
15: Acrid-Base Equilibrium
- Folio ID
- 85557
Foundation
We accept developed an agreement of equilibrium involving phase transitions and involving reactions entirely in the gas phase. Nosotros will assume an agreement of the principles of dynamic equilibrium, reaction equilibrium constants, and Le Chatelier'southward Principle. To understand awarding of these principles to reactions in solution, we will now assume a definition of certain classes of substances as beingness either acids or bases. An acid is a substance whose molecules donate positive hydrogen ions (protons) to other molecules or ions. When dissolved in pure water, acid molecules will transfer a hydrogen ion to a water molecule or to a cluster of several water molecules. This increases the concentration of \(\ce{H^+}\) ions in the solution. A base is a substance whose molecules accept hydrogen ions from other molecules. When dissolved in pure h2o, base of operations molecules will accept a hydrogen ion from a water molecule, leaving behind an increased concentration of \(\ce{OH^-}\) ions in the solution. To empathize what determines acid-base behavior, we will assume an understanding of the bonding, structure, and properties of private molecules.
Goals
Acids and bases are very common substances whose properties vary greatly. Many acids are known to be quite corrosive, with the ability to dissolve solid metals or burn flesh. Many other acids, however, are not simply beneficial just vital to the processes of life. Far from destroying biological molecules, they carry out reactions critical for organisms. Similarly, many bases are caustic cleansers while many others are medications to calm indigestion pains.
In this concept study, nosotros will develop an understanding of the characteristics of molecules which brand them either acids or bases. We volition examine measurements well-nigh the relative strengths of acids and bases, and nosotros will apply these to develop a quantitative understanding of the relative strengths of acids and bases. From this, we tin can develop a qualitative understanding of the properties of molecules which determine whether a molecule is a strong acid or a weak acid, a stiff base or a weak base. This agreement is valuable in predicting the outcomes of reactions, based on the relative quantitative strengths of acids and bases. These reactions are commonly referred to as neutralization reactions. A surprisingly large number of reactions, particularly in organic chemical science, tin can exist understood as transfer of hydrogen ions from acid molecules to base molecules.
Ascertainment 1: Strong Acids and Weak Acids
From the definition of an acid given in the Foundation, a typical acid can be written as \(\ce{HA}\), representing the hydrogen ion which will be donated and the balance of the molecule which volition remain as a negative ion after the donation. The typical reaction of an acrid in aqueous solution reacting with h2o can exist written every bit
\[\ce{HA} \left( aq \right) + \ce{H_2O} \left( l \right) \rightarrow \ce{H_3O^+} \left( aq \correct) + \ce{A^-} \left( aq \right)\]
In this reaction, \(\ce{HA} \left( aq \right)\) represents an acid molecule dissolved in aqueous solution. \(\ce{H_3O^+} \left( aq \right)\) is a notation to indicate that the donate proton has been dissolved in solution. Observations indicate that the proton is associated with several water molecules in a cluster, rather than attached to a single molecule. \(\ce{H_3O^+}\) is a simplified notation to represent this consequence. Similarly, the \(\ce{A^-} \left( aq \right)\) ion is solvated by several water molecules. This equation is referred to every bit acid ionization.
The equation above implies that a \(0.ane \: \text{M}\) solution of the acid \(\ce{HA}\) in h2o should produce \(\ce{H_3O^+}\) ions in solution with a concentration of \(0.1 \: \text{M}\). In fact, the concentration of \(\ce{H_3O^+}\) ions, \(\left[ \ce{H_3O^+} \correct]\), can be measured by a variety of techniques. Chemists unremarkably use a measure of the \(\ce{H_3O^+}\) ion concentration called the pH, defined past:
\[\text{pH} = -\text{log} \: \left[ \ce{H_3O^+} \right]\]
We now observe the concentration \(\left[ \ce{H_3O^+} \correct]\) produced by dissolving a variety of acids in solution at a concentration of \(0.1 \: \text{Thousand}\), and the results are tabulated in Table 15.1.
| Acid | \(\left[ \ce{H_3O^+} \right] \: \left( \text{M} \correct)\) | pH |
|---|---|---|
| \(\ce{H_2SO_4}\) | 0.1 | 1 |
| \(\ce{HNO_3}\) | 0.1 | 1 |
| \(\ce{HCl}\) | 0.ane | 1 |
| \(\ce{HBr}\) | 0.1 | 1 |
| \(\ce{HI}\) | 0.1 | 1 |
| \(\ce{HClO_4}\) | 0.1 | i |
| \(\ce{HClO_3}\) | 0.1 | 1 |
| \(\ce{HNO_2}\) | \(6.2 \times 10^{-3}\) | two.2 |
| \(\ce{HCN}\) | \(7 \times 10^{-half dozen}\) | five.ane |
| \(\ce{HIO}\) | \(1 \times 10^{-vi}\) | 5.8 |
| \(\ce{HF}\) | \(v.5 \times ten^{-3}\) | ii.3 |
| \(\ce{HOCN}\) | \(5.5 \times 10^{-3}\) | ii.3 |
| \(\ce{HClO_2}\) | \(ii.8 \times 10^{-ii}\) | i.six |
| \(\ce{CH_3COOH}\) (acetic acid) | \(i.3 \times 10^{-3}\) | 2.9 |
| \(\ce{CH_3CH_2COOH}\) (propanoic acid) | \(ane.1 \times 10^{-3}\) | 2.nine |
Notation that there are several acids listed for which \(\left[ \ce{H_3O^+} \right] = 0.ane \: \text{One thousand}\), and pH = 1. This shows that, for these acids, the acid ionization is complete: essentially every acid molecule is ionized in the solution co-ordinate to the equation above. All the same, there are other acids listed for which \(\left[ \ce{H_3O^+} \right]\) is considerably less than \(0.ane \: \text{M}\) and the pH is considerably greater than 1. For each of these acids, therefore, not all of the acid molecules ionize according to the equation higher up. In fact, it is articulate in Table 15.i that in these acids the vast majority of the acid molecules do not ionize, and only a pocket-size percent does ionize.
From these observations, we distinguish two classes of acids: potent acids and weak acids. Potent acids are those for which almost \(100\%\) of the acid molecules ionize, whereas weak acids are those for which only a small pct of molecules ionize. There are seven strong acids listed in Tabular array 15.one. From many observations, it is possible to make up one's mind that these seven acids are the only commonly observed strong acids. The vast majority of all substances with acidic properties are weak acids. We seek to narrate weak acrid ionization quantitatively and to determine what the differences in molecular properties are between strong acids and weak acids.
Observation 2: Per centum Ionization in Weak Acids
Table 15.i shows that the pH of \(0.i \: \text{Yard}\) acid solutions varies from ane weak acrid to another. If we dissolve 0.1 moles of acrid in a \(1.0 \: \text{L}\) solution, the fraction of those acid molecules which will ionize varies from weak acid to weak acid. For a few weak acids, using the data in Tabular array fifteen.1 we summate the pct of ionized acid molecules in \(0.1 \: \text{M}\) acrid solutions in Table 15.2.
| Acid | \(\left[ \ce{H_3O^+} \right] \: \left( \text{M} \correct)\) | \(\%\) Ionization |
|---|---|---|
| \(\ce{HNO_2}\) | \(vi.ii \times 10^{-3}\) | \(6.2\%\) |
| \(\ce{HCN}\) | \(7 \times 10^{-6}\) | \(0.007\%\) |
| \(\ce{HIO}\) | \(1 \times ten^{-vi}\) | \(0.001\%\) |
| \(\ce{HF}\) | \(v.5 \times x^{-three}\) | \(five.five\%\) |
| \(\ce{HOCN}\) | \(5.5 \times 10^{-three}\) | \(5.5\%\) |
| \(\ce{HClO_2}\) | \(two.viii \times 10^{-2}\) | \(28.2\%\) |
| \(\ce{CH_3COOH}\) (acerb acid) | \(ane.3 \times x^{-3}\) | \(i.three\%\) |
| \(\ce{CH_3CH_2COOH}\) (propanoic acid) | \(1.1 \times ten^{-three}\) | \(i.1\%\) |
We might be tempted to conclude from Tabular array 15.ii that we can characterize the force of each acrid past the percent ionization of acid molecules in solution. Even so, before doing and then, we detect the pH of a single acid, nitrous acid, in solution every bit a role of the concentration of the acrid.
\[\ce{HNO_2} \left( aq \right) + \ce{H_2O} \left( l \right) \rightarrow \ce{H_3O^+} \left( aq \right) + \ce{NO_2^-} \left( aq \correct)\]
In this case, "concentration of the acid" refers to the number of moles of acrid that we dissolved per liter of h2o. Our observations are listed in Table 15.3, which gives \(\left[ \ce{H_3O^+} \right]\), pH, and percent ionization every bit a function of nitrous acid concentration.
| \(c_0 \: \left( K \right)\) | \(\left[ \ce{H_3O^+} \right]\) | pH | \(\%\) Ionization |
|---|---|---|---|
| 0.fifty | \(ane.7 \times x^{-two}\) | 1.8 | \(3.3\%\) |
| 0.twenty | \(1.0 \times ten^{-2}\) | 2.0 | \(v.1\%\) |
| 0.10 | \(7.0 \times 10^{-3}\) | 2.ii | \(7.0\%\) |
| 0.050 | \(four.8 \times 10^{-iii}\) | 2.iii | \(ix.7\%\) |
| 0.020 | \(two.ix \times 10^{-3}\) | 2.5 | \(14.7\%\) |
| 0.010 | \(2.0 \times 10^{-3}\) | 2.7 | \(twenty.0\%\) |
| 0.005 | \(1.iii \times x^{-3}\) | ii.9 | \(26.7\%\) |
| 0.001 | \(4.ix \times ten^{-4}\) | iii.3 | \(49.1\%\) |
| 0.0005 | \(3.0 \times 10^{-4}\) | 3.5 | \(60.8\%\) |
Surprisingly, perhaps, the percent ionization varies considerably every bit a function of the concentration of the nitrous acid. Nosotros recall that this means that the fraction of molecules which ionize, according to the acid ionization equation, depends on how many acid molecules there are per liter of solution. Since some just not all of the acrid molecules are ionized, this means that nitrous acid molecules are nowadays in solution at the aforementioned time equally the negative nitrite ions and the positive hydrogen ions. Recalling our observation of equilibrium in gas phase reactions, we can conclude that the acid dissociation equation achieves equilibrium for each concentration of the nitrous acid.
Since we know that gas phase reactions come to equilibrium under weather determined past the equilibrium constant, we might speculate that the same is true of reactions in aqueous solution, including acrid ionization. Nosotros therefore ascertain an illustration to the gas phase reaction equilibrium abiding. In this example, we would not be interested in the pressures of the components, since the reactants and products are all in solution. Instead, we attempt a office composed of the equilibrium concentrations:
\[K = \frac{\left[ \ce{H_3O^+} \right] \left[ \ce{NO_2^-} \right]}{\left[ \ce{HNO_2} \correct] \left[ \ce{H_2O} \right]}\]
The concentrations at equilibrium tin can be calculated from the data in Table xv.3 for nitrous acrid. \(\left[ \ce{H_3O^+} \right]\) is listed and \(\left[ \ce{NO_2^-} \correct] = \left[ \ce{H_3O^+} \right]\). Furthermore, if \(c_0\) is the initial concentration of the acid defined past the number of moles of acid dissolved in solution per liter of solution, and then \(\left[ \ce{HA} \right] = c_0 - \left[ \ce{H_3O^+} \correct]\). Note that the contribution of \(\left[ \ce{H_2O} \left( l \right) \right]\) to the value of the function \(One thousand\) is simply a constant. This is because the "concentration" of water in the solution is simply the molar density of water, \(\frac{n_{H_2O}}{V} = 55.5 \: \text{Thousand}\), which is non affected by the presence or absence of solute. All of the relevant concentrations, along with the function in the equilibrium constant equation are calculated and tabulated in Table fifteen.4.
| \(c_0 \: \left( \text{Yard} \right)\) | \(\left[ \ce{H_3O^+} \correct]\) | \(\left[ \ce{NO_2^-} \right]\) | \(\left[ \ce{HNO_2} \right]\) | \(Thou\) |
|---|---|---|---|---|
| 0.50 | \(1.7 \times x^{-2}\) | \(ane.7 \times x^{-2}\) | 0.48 | \(1.0 \times 10^{-5}\) |
| 0.20 | \(1.0 \times 10^{-2}\) | \(1.0 \times 10^{-two}\) | 0.nineteen | \(9.9 \times 10^{-half dozen}\) |
| 0.ten | \(7.0 \times 10^{-3}\) | \(seven.0 \times 10^{-3}\) | \(ix.3 \times ten^{-2}\) | \(9.half dozen \times ten^{-half-dozen}\) |
| 0.050 | \(4.8 \times ten^{-iii}\) | \(iv.8 \times 10^{-3}\) | \(4.5 \times x^{-two}\) | \(9.4 \times ten^{-6}\) |
| 0.020 | \(2.9 \times 10^{-three}\) | \(2.9 \times 10^{-3}\) | \(4.v \times 10^{-2}\) | \(9.iv \times 10^{-6}\) |
| 0.010 | \(ii.0 \times 10^{-three}\) | \(2.0 \times x^{-3}\) | \(eight.0 \times ten^{-3}\) | \(8.ix \times 10^{-6}\) |
| 0.005 | \(one.3 \times x^{-3}\) | \(1.three \times 10^{-3}\) | \(3.6 \times 10^{-3}\) | \(8.viii \times 10^{-6}\) |
| 0.001 | \(four.9 \times 10^{-four}\) | \(iv.9 \times x^{-4}\) | \(5.1 \times x^{-iv}\) | \(8.five \times \10^{-6}\) |
| 0.0005 | \(three.0 \times 10^{-4}\) | \(iii.0 \times 10^{-four}\) | \(2.0 \times 10^{-4}\) | \(eight.5 \times x^{-six}\) |
We note that the function \(K\) in the equation above is approximately, though merely approximately, the same for all conditions analyzed in Table 15.4. Variation of the concentration by a cistron of 1000 produces a alter in \(K\) of only \(x\%\) to \(15\%\). Hence, we can regard the function \(K\) as a constant which approximately describes the acrid ionization equilibrium for nitrous acid. By convention, chemists omit the constant concentration of water from the equilibrium expression, resulting in the acrid ionization equilibrium abiding, \(K_a\), divers as
\[K_a = \frac{\left[ \ce{H_3O^+} \correct] \left[ \ce{NO_2^-} \right]}{\left[ \ce{HNO_2} \right]}\]
From an average of the data in Tabular array 15.4, we can calculate that, at \(25^\text{o} \text{C}\) for nitrous acid, \(K_a = v \times ten^{-4}\). Acrid ionization constants for the other weak acids in Table 15.three are listed in Table 15.5.
| Acrid | \(K_a\) | p\(K_a\) |
|---|---|---|
| \(\ce{HNO_2}\) | \(5 \times 10^{-four}\) | 3.3 |
| \(\ce{HCN}\) | \(four.9 \times x^{-ten}\) | 9.iii |
| \(\ce{HIO}\) | \(2.3 \times x^{-11}\) | x.6 |
| \(\ce{HF}\) | \(3.5 \times 10^{-4}\) | 3.4 |
| \(\ce{HOCN}\) | \(3.5 \times 10^{-iv}\) | 3.iv |
| \(\ce{HClO_2}\) | \(i.1 \times ten^{-two}\) | two.0 |
| \(\ce{CH_3COOH}\) (acetic acid) | \(1.seven \times 10^{-five}\) | 4.8 |
| \(\ce{CH_3CH_2COOH}\) | \(i.4 \times 10^{-5}\) | 4.9 |
We brand ii final notes about the results in Tabular array fifteen.five. First, information technology is clear the larger the value of \(K_a\), the stronger the acid. That is, when \(K_a\) is a big number, the percent ionization of the acid is larger, and vice versa. Second, the values of \(K_a\) vary over many orders of magnitude. Every bit such, it is frequently convenient to define the quantity p\(K_a\), analogous to pH, for purposes of comparing acid strengths:
\[\text{p} K_a = -\text{log} \: K_a\]
The value of p\(K_a\) for each acid is also listed in Tabular array 15.5. Note that a small-scale value of p\(K_a\) implies a big value of \(K_a\) and thus a stronger acid. Weaker acids take larger values of p\(K_a\). \(K_a\) and p\(K_a\) thus give a simple quantitative comparison of the strength of weak acids.
Ascertainment iii: Autoionization of H2o
Since nosotros have the ability to measure pH for acid solutions, we can measure pH for pure water as well. Information technology might seem that this would brand no sense, equally we would wait \(\left[ \ce{H_3O^+} \right]\) to equal zero exactly in pure water. Surprisingly, this is incorrect: a measurement on pure water at \(25^\text{o} \text{C}\) yields pH = 7, so that \(\left[ \ce{H_3O^+} \right] = 1.0 \times 10^{-vii} \: \text{M}\). There can be only one possible source for these ions: water molecules. The process
\[\ce{H_2O} \left( 50 \right) + \ce{H_2O} \left( l \right) \rightarrow \ce{H_3O^+} \left( aq \right) + \ce{OH^-} \left( aq \correct)\]
is referred to as the autoionization of h2o. Annotation that, in this reaction, some water molecules behave equally acid, donating protons, while other water molecules behave as base, accepting protons.
Since at equilibrium \(\left[ \ce{H_3O^+} \right] = 1.0 \times 10^{-7} \: \text{M}\), it must also be truthful that \(\left[ \ce{OH^-} \correct] = ane.0 \times 10^{-vii} \: \text{M}\). Nosotros can write the equilibrium constant for the to a higher place equation, following our previous convention of omitting the pure water from the expression, and we find that, at \(25^\text{o} \text{C}\),
\[\begin{align} K_w &= \left[ \ce{H_3O^+} \right] \left[ \ce{OH^-} \right] \\ &= 1.0 \times x^{-14} \: \text{G} \end{align}\]
(In this instance, the subscript "w" refers to "water".)
Autoionization of water occurs in pure h2o just must likewise occur when ions are dissolved in aqueous solutions. This includes the presence of acids ionized in solution. For example, nosotros consider a solution of \(0.1 \: \text{M}\) acetic acrid. Measurements show that, in this solution \(\left[ \ce{H_3O^+} \right] = 1.3 \times 10^{-iii} \: \text{G}\) and \(\left[ \ce{OH^-} \right] = seven.seven \times 10^{-12} \: \text{M}\). We note ii things from this observation: get-go, the value of \(\left[ \ce{OH^-} \right]\) is considerably less than in pure water; second, the autoionization equilibrium constant remains the same at \(1.0 \times x^{-xiv}\). From these notes, we tin can conclude that the autoionization equilibrium of water occurs in acrid solution, but the extent of autoionization is suppressed past the presence of the acid in solution.
We consider a final note on the autoionization of water. The pH of pure water is 7 at \(25^\text{o} \text{C}\). Calculation any acid to pure water, no matter how weak the acid, must increment \(\left[ \ce{H_3O^+} \right]\), thus producing a pH below 7. As such, we tin conclude that, for all acidic solutions, pH is less than 7, or on the other hand, any solution with pH less than 7 is acidic.
Ascertainment four: Base of operations Ionization, Neutralization and Hydrolysis of Salts
Nosotros have not yet examined the beliefs of base molecules in solution, nor have we compared the relative strengths of bases. We take divers a base molecule as one which accepts a positive hydrogen ion from another molecule. Ane of the nearly common examples is ammonia, \(\ce{NH_3}\). When ammonia is dissolved in aqueous solution, the following reaction occurs:
\[\ce{NH_3} \left( aq \right) + \ce{H_2O} \left( l \right) \rightarrow \ce{NH_4^+} \left( aq \correct) + \ce{OH^-} \left( aq \right)\]
Due to the lone pair of electrons on the highly electronegative \(\ce{North}\) atom, \(\ce{NH_3}\) molecules will readily attach a free hydrogen ion forming the ammonium ion \(\ce{NH_4^+}\). When we measure the concentration of \(\ce{OH^-}\) for various initial concentrations of \(\ce{NH_3}\) in water, nosotros detect the results in Table 15.half dozen. We should conceptualize that a base of operations ionization equilibrium abiding might exist comparable to the acid ionization equilibrium constant, and in Table 15.6, we have also calculated the value of the function \(K_b\) defined as:
\[K_b = \frac{\left[ \ce{NH_4^+} \correct] \left[ \ce{OH^-} \correct]}{\left[ \ce{NH_3} \right]}\]
| \(c_0 \: \left( \text{Thou} \right)\) | \(\left[ \ce{OH^-} \right]\) | \(K_b\) | pH |
|---|---|---|---|
| 0.50 | \(3.2 \times 10^{-3}\) | \(2.0 \times 10^{-5}\) | 11.5 |
| 0.20 | \(2.0 \times 10^{-iii}\) | \(2.0 \times 10^{-5}\) | 11.3 |
| 0.ten | \(ane.four \times ten^{-three}\) | \(2.0 \times 10^{-five}\) | 11.1 |
| 0.050 | \(9.vii \times 10^{-4}\) | \(ane.9 \times 10^{-v}\) | eleven.0 |
| 0.020 | \(6.0 \times 10^{-4}\) | \(ane.nine \times 10^{-5}\) | 10.8 |
| 0.010 | \(4.ii \times 10^{-4}\) | \(ane.9 \times ten^{-5}\) | 10.half dozen |
| 0.005 | \(3.0 \times x^{-4}\) | \(1.9 \times 10^{-v}\) | x.five |
| 0.001 | \(1.iii \times 10^{-iv}\) | \(one.viii \times 10^{-v}\) | x.1 |
| 0.0005 | \(8.vii \times x^{-five}\) | \(i.8 \times ten^{-5}\) | 9.9 |
Given that we have dissolved a base in pure water, we might be surprised to discover the presence of positive hydrogen ions, \(\ce{H_3O^+}\), in solution, but a measurement of the pH for each of the solutions reveals small amounts. The pH for each solution is as well listed in Table 15.6. The source of these \(\ce{H_3O^+}\) ions must exist the autoionization of h2o. Annotation, yet, that in each instance in basic solution, the concentration of \(\ce{H_3O^+}\) ions is less than that in pure water. Hence, the presence of the base in solution has suppressed the autoionization. Because of this, in each case the pH of a bones solution is greater than vii.
Base ionization is therefore quite analogous to acid ionization observed earlier. We at present consider a comparing of the forcefulness of an acid to the strength of the base. To do so, nosotros consider a class of reactions called "neutralization reactions" which occur when we mix an acid solution with a base of operations solution. Since the acid donates protons and the base of operations accepts protons, we might wait, when mixing acid and base of operations, to accomplish a solution which is no longer acidic or bones. For instance, if we mix together equal volumes of \(0.1 \: \text{M}\) \(\ce{HCl} \left( aq \correct)\) and \(0.one \: \text{One thousand}\) \(\ce{NaOH} \left( aq \right)\), the post-obit reaction occurs:
\[\ce{HCl} \left( aq \right) + \ce{NaOH} \left( aq \right) \rightarrow \ce{Na^+} \left( aq \correct) + \ce{Cl^-} \left( aq \correct) + \ce{H_2O} \left( fifty \right)\]
The resultant solution is just a table salt solution with \(\ce{NaCl}\) dissolved in water. This solution has neither acidic nor bones properties, and the pH is vii; hence the acid and base of operations have neutralized each other. In this case, nosotros have mixed together a strong acid with a stiff base. Since both are strong and since we mixed equal molar quantities of each, the neutralization reaction is essentially consummate.
We next consider mixing together a weak acid solution with a stiff base of operations solution, again with equal molar quantities of acrid and base of operations. Equally an case, we mix \(100 \: \text{mL}\) of \(0.1 \: \text{Thou}\) acerb acrid \(\left( \ce{HA} \right)\) solution with \(100 \: \text{mL}\) of \(0.1 \: \text{M}\) sodium hydroxide. In this discussion, nosotros volition abridge the acetic acid molecular formula \(\ce{CH_3COOH}\) as \(\ce{HA}\) and the acetate ion \(\ce{CH_3COO^-}\) equally \(\ce{A^-}\). The reaction of \(\ce{HA}\) and \(\ce{NaOH}\) is:
\[\ce{HA} \left( aq \right) + \ce{NaOH} \left( aq \correct) \rightarrow \ce{Na^+} \left( aq \right) + \ce{A^-} \left( aq \right) + \ce{H_2O} \left( 50 \correct)\]
\(\ce{A^-} \left( aq \correct)\) is the acetate ion in solution, formed when an acetic acid molecule donates the positive hydrogen ion. We have thus created a salt solution again, in this instance of sodium acetate in h2o. Note that the book of the combined solution is \(200 \: \text{mL}\), so the concentration of sodium acetate \(\left( \ce{NaA} \right)\) in solution is \(0.050 \: \text{M}\).
Unlike our previous \(\ce{NaCl}\) table salt solution, a measurement in this instance reveals that the pH of the product salt solution is 9.four, so the solution is basic. Thus, mixing equal tooth quantities of strong base of operations with weak acid produces a basic solution. In essence, the weak acid does not fully neutralize the strong base. To sympathize this, we examine the behavior of sodium acetate in solution. Since the pH is greater than 7, then at that place is an excess of \(\ce{OH^-}\) ions in solution relative to pure water. These ions must have come from the reaction of sodium acetate with the water. Therefore, the negative acetate ions in solution must behave as a base, accepting positive hydrogen ions:
\[\ce{A^-} \left( aq \right) + \ce{H_2O} \left( l \correct) \rightarrow \ce{HA} \left( aq \right) + \ce{OH^-} \left( aq \right)\]
The reaction of an ion with water to grade either an acrid or a base of operations solution is referred to equally hydrolysis. From this case, the salt of a weak acrid behaves equally a base in water, resulting in a pH greater than 7.
To understand the extent to which the hydrolysis of the negative ion occurs, we need to know the equilibrium abiding for this reaction. This turns out to exist determined by the acid ionization constant for \(\ce{HA}\). To come across this, we write the equilibrium constant for the hydrolysis of \(\ce{A^-}\) as
\[K_h = \frac{\left[ \ce{HA} \right] \left[ \ce{OH^-} \right]}{\left[ \ce{A^-} \right]}\]
Multiplying numerator and denominator by \(\left[ \ce{H_3O^+} \correct]\), we discover that
\[\begin{marshal} K_h &= \frac{\left[ \ce{HA} \right] \left[ \ce{OH^-} \right]}{\left[ \ce{A^-} \right]} \frac{\left[ \ce{H_3O^+} \right]}{\left[ \ce{H_3O^+} \right]} \\ &= \frac{K_w}{K_a} \end{align}\]
Therefore, for the hydrolysis of acetate ions in solution, \(K_h = v.8 \times ten^{-10}\). This is fairly small, and then the acetate ion is a very weak base.
Observation 5: Acrid strength and molecular properties
We at present take a adequately complete quantitative description of acrid-base equilibrium. To complete our understanding of acid-base of operations equilibrium, we need a predictive model which relates acid strength or base of operations strength to molecular properties. In general, we expect that the strength of an acrid is related either to the relative ease by which it tin donate a hydrogen ion or by the relative stability of the remaining negative ion formed afterward the deviation of the hydrogen ion.
To begin, we note that at that place are 3 basic categories of acids which we take examined in this study. First, there are simple binary acids: \(\ce{HF}\); \(\ce{HCl}\); \(\ce{HBr}\); \(\ce{HI}\). 2nd, there are acids formed from main group elements combined with i or more oxygen atoms, such equally \(\ce{H_2SO_4}\) or \(\ce{HNO_3}\). These are called oxyacids. Third, there are the carboxylic acids, organic molecules which contain the carboxylic functional grouping in Figure 15.1.
Figure 15.1: Carboxylic acid functional group
We consider showtime the simple binary acids. \(\ce{HCl}\), \(\ce{HBr}\), and \(\ce{How-do-you-do}\) are all strong acids, whereas \(\ce{HF}\) is a weak acid. In comparing the experimental values of p\(K_a\) values in Tabular array 15.vii, nosotros notation that the acrid strength increases in the guild \(\ce{HF} < \ce{HCl} < \ce{HBr} < \ce{Hi}\). This means that the hydrogen ion can more readily split from the covalent bond with the halogen atom \(\left( \ce{X} \correct)\) every bit nosotros move down the periodic table, equally shown in Table 15.7.
| p\(K_a\) | Bail Energy \(\left( \frac{\text{kJ}}{\text{mol}} \correct)\) | |
|---|---|---|
| \(\ce{HF}\) | 3.ane | 567.7 |
| \(\ce{HCl}\) | -6.0 | 431.6 |
| \(\ce{HBr}\) | -ix.0 | 365.9 |
| \(\ce{Hullo}\) | -9.5 | 298.0 |
The decreasing forcefulness of the \(\ce{H-10}\) bond is primarily due to the increment in the size of the \(\ce{Ten}\) atom as we motility downward the periodic table. Nosotros conclude that one cistron which influences acidity is the strength of the \(\ce{H-X}\) bond: a weaker bond produces a stronger acid, and vice versa.
In the acids in the other two categories, the hydrogen atom which ionizes is fastened direct to an oxygen atom. Thus, to sympathise acidity in these molecules, we must examine what the oxygen atom is in turn bonded to. It is very interesting to note that, in examining compounds like \(\ce{R-O-H}\), where \(\ce{R}\) is an cantlet or group of atoms, we can get either acidic or basic backdrop. For instance, \(\ce{NaOH}\) is a potent base of operations, whereas \(\ce{HOCl}\) is a weak acrid. This ways that, when \(\ce{NaOH}\) ionizes in solution, the \(\ce{Na-O}\) linkage ionizes, whereas when \(\ce{HOCl}\) ionizes in solution, the \(\ce{H-O}\) bond ionizes.
To understand this behavior, we compare the strength of the elementary oxyacids \(\ce{HOI}\), \(\ce{HOBr}\), and \(\ce{HOCl}\). The p\(K_a\)'s for these acids are establish experimentally to be, respectively, x.6, 8.6, and 7.five. The acid strength for \(\ce{HOX}\) increases as we move up the periodic table in the element of group vii group. This ways that the \(\ce{H-O}\) bond ionizes more than readily when the oxygen cantlet is bonded to a more electronegative cantlet.
Nosotros tin can add to this ascertainment by comparison the strengths of the acids \(\ce{HOCl}\), \(\ce{HOClO}\), \(\ce{HOClO_2}\), and \(\ce{HOClO_3}\). (Note that the molecular formulae are more than usually written every bit \(\ce{HClO}\), \(\ce{HClO_2}\), \(\ce{HClO_3}\), and \(\ce{HClO_4}\). Nosotros have written them instead to emphasize the molecular structure.) The p\(K_a\)'south of these acids are, respectively, 7.5, 2.0, -2.7, and -8.0. In each case, the molecule with more than oxygen atoms on the fundamental \(\ce{Cl}\) atom is the stronger acid: \(\ce{HOClO}\) is more acidic than \(\ce{HOCl}\), etc. A like event is found in comparing the oxyacids of nitrogen. \(\ce{HONO_2}\), nitric acrid, is one of the strong acids, whereas \(\ce{HONO}\), nitrous acid, is a weak acid. Since oxygen atoms are very strongly electronegative, these trends add to our observation that increasing electronegativity of the attached atoms increases the ionization of the \(\ce{O-H}\) bond.
Why would electronegativity play a role in acid forcefulness? There are two conclusions we might draw. Kickoff, a greater electronegativity of the cantlet or atoms fastened to the \(\ce{H-O}\) in the oxyacid apparently results in a weaker \(\ce{H-O}\) bail, which is thus more readily ionized. We know that an electronegative atom polarizes bonds by cartoon the electrons in the molecule towards it. In this case, the \(\ce{Cl}\) in \(\ce{HOCl}\) and the \(\ce{Br}\) in \(\ce{HOBr}\) must polarize the \(\ce{H-O}\) bond, weakening information technology and facilitating the ionization of the hydrogen. In comparing \(\ce{HOCl}\) to \(\ce{HOClO}\), the added oxygen atom must increase the polarization of the \(\ce{H-O}\) bond, thus weakening the bail further and increasing the extent of ionization.
A 2d conclusion has to do with the ion created by the acid ionization. The negative ion produced has a surplus electron, and the relative energy of this ion volition depend on how readily that extra electron is attracted to the atoms of the ion. The more electronegative those atoms are, the stronger is the attraction. Therefore, the \(\ce{OCl^-}\) ion can more than readily accommodate the negative charge than can the \(\ce{OBr^-}\) ion. And the \(\ce{OClO^-}\)ion tin can more readily adjust the negative charge than can the \(\ce{OCl^-}\) ion.
Nosotros conclude that the presence of strongly electronegative atoms in an acrid increases the polarization of the \(\ce{H-O}\) bond, thus facilitating ionization of the acid, and increases the attraction of the extra electron to the negative ion, thus stabilizing the negative ion. Both of these factors increase the acid strength. Chemists commonly use both of these conclusions in agreement and predicting relative acid strength.
The relative acidity of carbon compounds is a major subject of organic chemistry, which we can only visit briefly here. In each of the carboxylic acids, the \(\ce{H-O}\) group is attached to a carbonyl \(\ce{C=O}\) group, which is in turn bonded to other atoms, the comparison we observe here is between carboxylic acid molecules, denoted as \(\ce{RCOOH}\), and other organic molecules containing the \(\ce{H-O}\) grouping, such as alcohols denoted as \(\ce{ROH}\). (\(\ce{R}\) is simply an atom or group of atoms attached to the functional group.) The sometime are obviously acids whereas the latter group contains molecules which are mostly extremely weak acids. One interesting comparing is for the acid and alcohol when \(\ce{R}\) is the benzene ring, \(\ce{C_6H_5}\). Benzoic acrid, \(\ce{C_6H_5COOH}\), has p\(K_a\) = 4.2, whereas phenol, \(\ce{C_6H_5OH}\), has p\(K_a\) = 9.9. Thus, the presence of the doubly bonded oxygen cantlet on the carbon atom side by side to the \(\ce{O-H}\) clearly increases the acidity of the molecule, and thus increases ionization of the \(\ce{O-H}\) bond.
This ascertainment is quite reasonable in the context of our previous determination. Adding an electronegative oxygen atom in near proximity to the \(\ce{O-H}\) bond both increases the polarization of the \(\ce{O-H}\) bail and stabilizes the negative ion produced past the acid ionization. In addition to the electronegativity outcome, carboxylate anions, \(\ce{RCOO^-}\), exhibit resonance stabilization, as seen in Effigy xv.ii.
Effigy 15.ii: Resonance stabilization of carboxylate anion
The resonance results in a sharing of the negative charge over several atoms, thus stabilizing the negative ion. This is a major contributing factor in the acidity of carboxylic acids versus alcohols.
Review and Discussion Questions
Strong acids have a college percent ionization than practice weak acids. Why don't we use per centum ionization as a mensurate of acrid strength, rather than \(K_a\)?
Using the data in Table 15.4 for nitrous acid, plot \(\left[ \ce{H_3O^+} \right]\) versus \(c_0\), the initial concentration of the acrid, and versus \(\left[ \ce{HNO_2} \right]\), the equilibrium concentration of the acid. On a second graph, plot \(\left[ \ce{H_3O^+} \correct]^2\) versus \(c_0\), the initial concentration of the acid, and versus \(\left[ \ce{HNO_2} \right]\), the equilibrium concentration of the acid. Which of these results gives a directly line? Using the equilibrium constant expression, explicate your respond.
Using Le Chatelier's principle, explain why the concentration of \(\left[ \ce{OH^-} \right]\) is much lower in acidic solution than it is in neutral solution.
We considered mixing a potent base with a weak acid, but we did not consider mixing a strong acrid with a weak acid. Consider mixing \(0.one \: \text{M} \: \ce{HNO_3}\) and \(0.1 \: \text{M} \ce{HNO_2}\). Predict the pH of the solution and the percent ionization of the nitrous acrid. Rationalize your prediction using Le Chatelier's principle.
Imagine taking a \(0.five \: \text{M}\) solution of nitrous acid and slowly adding water to information technology. Looking at Table fifteen.three, we run across that, as the concentration of nitrous acid decreases, the percent ionization increases. By contrast, \(\left[ \ce{H_3O^+} \right]\) decreases. Rationalize these results using Le Chatelier'due south principle.
Nosotros observed that mixing a strong acid and a strong base, in equal amounts and concentrations, produces a neutral solution, and that mixing a potent base with a weak acid, in equal amounts and concentrations, produces a basic solution. Imagine mixing a weak acid and a weak base, in equal amounts and concentrations. Predict whether the resulting solution will be acidic, basic, or neutral, and explain your prediction.
Using the electronegativity arguments presented to a higher place, explicate why, in general, compounds like \(\ce{One thousand-O-H}\) are bases rather than acids, when \(\ce{M}\) is a metal cantlet. Predict the relationship between the backdrop of the metal atom \(\ce{M}\) and the strength of the base \(\ce{MOH}\).
Ionization of sulfuric acid \(\ce{H_2SO_4}\) produces \(\ce{HSO_4^-}\), which is also an acrid. However, \(\ce{HSO_4^-}\) is a much weaker acid than \(\ce{H_2SO_4}\). Using the conclusions from above, explain why \(\ce{HSO_4^-}\) is a much weaker acid.
Predict and explain the relative acid strengths of \(\ce{H_2S}\) and \(\ce{HCl}\). Predict and explain the relative acid strengths of \(\ce{H_3PO_4}\) and \(\ce{H_3AsO_4}\).
Using arguments from above, predict and explicate the relative acidity of phenol and methanol.
(a)
(b)
Figure 15.3: Structural formulae for (a) phenol and (b) methanol.
An Increased Concentration Of What Ion Characterizes A Solution Of A Base In Water?,
Source: https://chem.libretexts.org/Bookshelves/General_Chemistry/Book:_Concept_Development_Studies_in_Chemistry_%28Hutchinson%29/15:_Acid-Base_Equilibrium
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