Br0nsted-Lowry acids can be placed into two big categories: strong and weak. Whether an acid is strong or weak depends on how completely it ionizes in water. A strong acid is one that
dissociates completely (or very nearly so) in water; hydrochloric acid, HCl, is an example:
HCl(aq) + H20(l) ~ H30+(aq) + Cl-(aq) This reaction goes essentially to completion.
On the other hand, hydrofluoric acid, HF, is an example of a weak acid, since its dissolution in water,
HF(aq) + H20(l) ~ H3Q+(aq) + F-(aq) does not go to completion; most of the HF remains undissociated.
If we use HA to denote a generic acid, its dissolution in water has the form HA(aq) + H20(l) ~ã H30+(aq) + A-(aq)
The strength of the acid is directly related toãhow much the products are favored _over the reactants.
The equilibrium expression for this reaction is
K = (H30+][A -]
a [HA]
This is written as Ka, rather than Ke , to emphasize that this is the equilibrium expression for an i!dd-dissociation reaction. In fact, Ka is known as the acid-ionization (or acid-dissociation)
constant of the acid (H.A). If Ka > 1, then the products are favored, and we say the acid is strong; if Ka < 1 then the reactants are favored and the acid is weak. We can also rank the relative strengths of
426 MCAT PHYSICAL SCIENCES REVIEW
acids by comparing their Ka values: The larger the Ka value, the stronger the acid; the smaller the Ka value, the weaker the acid.
The acids for which Ka > 1-the strong acids-are so few that you should memorize them:
Common Strong Acids Hydroiodic acid HI Hydrobromic acid HBr Hydrochloric acid HCl Perchloric acid HClO 4 Chloric acid HC103 Sulfuric acid H2SO4
Nitric acid HN03
\Aif.A h
1--1 :5 o 3 1-\, Po~.;
';).: L Q
l i f 'l ~} (/3
{4Ct0 / HCt6 J-.
ltc.Jv
The values of Ka for these acids are so large that most tables of acid ionization constants don't even list them. On the MCAT, you may assume that any acid that's not in this list is a weak acid. (Other acids that fit the definition of strong-such as thiocyanic acid, selenic acid, and permanganic acid- are so uncommon that it's very unlikely they'd appear on the test.)
.... Example 8-3: In a 1 M aqueous solution of boric acid (H3B031 Ka = 5.8 x l0-10),
which of the following species will be present in solution in the greatest quantity?
A. H3B03 B. H2B03-
C. HBO/- D. H30+
Solution. The equilibrium here is H3B03(aq) + H20(1) H30+(aq) + H2B03-(aq).
Boric acid is a weak acid (ifs not on the list of strong acids), so the equilibrium lies to the left (also, notice how small its Ka value is). So, there'll be very few H30+ or H2B03- ions in solution but plenty of undissociated H3B03• The answer is A .
..._ Example 8-4: Of the following, which statement best explains why HF is a weak acid, but HCl, HBr, and HI are strong acids?
A. F has a lower, ionization energy than Cl, Br, or I.
B. F has a larger 'radius than Cl, Br, or I.
C. p- has a larger radius than Cl-, Be, or I-.
D. The H-F bond is stronger than the H-Cl, H-Br, or H-I bonds.
Solution. Because F is smaller than Cl, Br, or I (eliminating choices Band C), choice Dis true and explains why HF doesn't dissociate as easily as HCl, HBr, or HI.
Choice A is false.
MCAT GENERAL CHEMISTRY- CHAPTER 8: ACIDS AND BASES 427 .._ Example 8-5: Of the following acids, which one would dissociate to the greatest
extent (in water)?
A. HCN (hydrocyanic acid), Ka = 6.2 x 10-10 B. HNCO (cyanic add), Ka = 3.3 x 10-4 . C. HCIO (hypochlorous acid), Ka = 2.9 x 10-s D. HBrO (hypobromous add), Ka = 2.2 x 10-9
Solution.ã The acid that w~uld dissociate to the greatest extent would haveãthe greatest Ka value. Of the choices given, HNCO (choice B) has the greatest Ka value.
We can apply the same ideas as above to identify strong and weak bases. If we use B to denote a generic base, its dissolution in water has the form
B(aq) + liaO(l) ~ HB+(aq) + OH-(aq)
The strength of the base is directly related to how much the products are favored over the reactants. If we write down the equilibrium constant for this reaction, we get
Kb = [HB+][oH-]
[B]
This is written as Kb, rather than Ke, to emphasize that this is the equilibrium expression for a :b.ase-dissociation reaction. In fact, Kb is known as the base-ionization (or base-dissociation) constant. We can rank the relative strengths of bases by comparing their Kb values: The larger the Kb value, the stronger the base; the smaller the Kb vahte, the weaker the. base. The common soluble .strong bases are the Group l hydroxides: LiOH, NaOH, KOH, RbOH, CsOH. Metal amides, such as NaNH2, are also strong bases, since the amide ion, NHa~, will react completely with:water to form NH3 and OH- ions. [Some of the Group 2 hydroxides, such as Ca(OHh, Sr(OHh, and Ba(OH}2, are also often classified as '1strong," although their base-dissoCiation constants are smaller than those of the Group 1 hydroxides.] Weak bases include ammonia (NH3) and amines.
THE RELATIVE STRENGTHS OF .CONJUGATE ACID-BASE PAIRS Let's once again look at.the dissociation of HCl in water:
HCl(aq) + H20(1) -t HaO+(aq) + Cl-(aq)
The chloride ion (Cl-) is the conjugate base of HCL :Since this reaction goes toã completion, there must be no reverse reaction. Therefore, Cl- has no tendency to accept a proton and thus does not act as a base. The conjugate base of a strong acid has no basic properties in water.
On the other hand, hydrofluoric acid, HF, is a weak acid since its dissolution is not complete:
HF(aq) + H20(l) ~ H3<;'+(aq) + F-(aq)
Since the reverse reaction does takeplace to a significant extent, the conjugate base of HF, the fluoride ion, F:", does have some tendency to accept a proton, and so behaves as a weak base.
The conjugate base of a weak acid is a weak base.
428 MCAT PHYSICAL SCIENCES REVIEW
In fact, the weaker the acid, the more the reverse reaction is favored, and the stronger its conjugate base. For example, hydrocyanic acid (HCN) has aKa value of about 5 x 10-10, which is much smaller than that of hydrofluodc acid (Ka = 7 x 10--4). Therefore, the conjugate base of HCN, the cyanide ion, CN-, is a stronger base than F-.
The same ideas can be applied to bases: (1) The conjugate add of a strong base has no acidic properties in water. For example, the conjugate acid of LiOH is Li+, which does not act as an acid in water. (2) The conjugate acid of a weak base is a weak acid (and the weaker the base, the stronger the conjugate acid). For example, the conjugate acid of NH3 is NH4 +, which is a weak acid.
~ Example 8-6: Of the following anions, which is the strongest base?
A. I- B. CN- C. N0
3-
D. Br-
Solution. Here's another way to ask the same question: Which of the following anions has the weakest conjugate acid? Since HI, HN03, and HBr are all strong acids, while HCN is a weak acid, CN- (choice B) has the weakest conjugate acid, and is thus the strongest base.
~ Example 8-7: Of the following, which acid has the weakest conjugate base?
A. HC104 B. HCOOH C. HjP04
n~ H2C03
Solution. Here's another way to ask the same question: Which of the following acids is the strongest? Thought about this way, the answer's easy: it's choice A- perchloric acid. It's the only strong acid in the list.
AMPHOTERIC SUBSTANCES
Take a look at the dissociation of carbonic acid (H2C03), a weak acid:
H2C03(aq) + H20(l) ~ H30+(aq) + HC03-(aq) (Ka = 4.5 X 10-7)
The conjugate base of carbonic acid is HC03 -, which also has an ionizable proton. Carbonic acid is said to be polyprotic, because it has more than one proton to donate.
Let's look at how the conjugate base of carbonic acid dissociates:
HC03-(aq) + H20(l) ~ H30+(aq) + CO/-(aq) (Ka = 4.8 X .l0-11)
In the first reaction, HC03- acts as a base, but in the second reaction it acts as an acid. Whenever a substance can act as either an acid or a base, we say that it is amphoteric. The conjugate base of a weak polyprotic acid is always amphoteric, because it can either donate or accept another proton.
Also notice that HC03- is a weaker acid than H2C03; in general, every time a polyproticacid donates a proton, the resulting species will be a weaker acid than its predecessor.
MCAT GENERAL CHEMISTRY- CHAPTER 8: ACIDS AND BASES 429
§8.4 THE ION-PRODUCT CONSTANT OF WATER
Water is amphoteric. It reacts with itself in a Brensted-Lowry acid-base reaction, one molecule acting as the acid, the other as the base:
H20(l) + H20(l) ~ H3Q+(aq) + QH-(aq)
This is called the autoionization (or self-ionization) of water. The equilibrium expression is Kw = [H3Q+][QH-]
This is written as Kw, rather than Keq'. to emphasize that this is the equilibrium expression for the autoionization of n_ater; Kw is known as the ion-product constant of water. Only a very small.
fraction of the water molecules will undergo this reaction, and it's known that at 25°C,
I Kw =l.Ox10"14 I
(Like all other equilibrium constants, Kw varies with temperature; it increases as the temperature increases. However, because 25°C is so common, this is the value you should memorize.) Since the number of H3Q+ ions in pure water will be equal to the number of QH- ions, if we call each of their concentrations x, then x2 = ~~ which gives x = 1 x 10-7• That is, the concentration of both types of ions in pure water is 1 x 10-7M. (In addition ~is constant at a given temperature, regardless of the H30+ concentration.)
If the introduction of an add increases the concentration of H3Q+ ions, then the equilibrium is disturbed, and the reverse reaction is favored, decreasing the concentration of OH- ions. Similarly, if the introduction of a base increases the concentration of QH- ions, then the equilibrium is again disturbed; the reverse reaction is favored, decreasing the concentration of H3Q+ ions. However, in either case, the product of [H3Q+] and [QH-] will remain equal to~ã
For example, suppose we add 0.002 moles of HCl to water to create a 1-liter solution. Since the dissolution of HCl goes to completion (it's a strong acid), it will create 0.002 moles of H3Q+ ions, so [H3Q+] = 0.002 M. Since the H3Q+ concentration has been increased, we expect the OR-
concentration to decrease, which it does:
[OH-]= Kw _1x1o-t4
[H30+] - 2 X 10 ... 3 = 5 X 10-12 M
§8.5 pH
The pH scale measures the concentration of H+ (or H3Q+) ions in a solution. Because the
molarity of H+ tends to be quite small and can vary over many orders of magrutude, the pH scale isã
logarithmic:
pH=-log[W) I
This formula implies that [H+] = 10:-PH. Since [H+] =ãl0-7 Min pure water, the pH of water is 7.
At 25°C, this defines a pH neutral solution. If [H+] is greater than 10-7M, then the pH w.ill be less than 7, and the solution is said to be acidic. If [H+] is less than 10-7M, the pH will be greater than 7,
430 MCAT PHYSICAL SCIENCES REVIEW
and the solution is basic (or alkaline). Notice that a low pH means a high [H+] and the solution is acidic; a high pH means a low [H+] and the solution is basic.
pH > 7 basic solution pH = 7 neutral solution pH < 7 acidic solution
The range of the pH scale for most solutions falls between 0 and 14, but some strong acids and bases extend the scale past this range. For example, a 10M solution of HCl will fully dissociate into H+ and Cl-. Therefore, the[H+] = 10M, and the pH= -l.
An alternate measurement expresses the acidity or basicity in terms of the hydroxide ion concentration, [OH-], by using pOH. The same formula applies for hydroxide ions as for hydrogen ions.
I pOH=-log[OH-]1 This formula implies that [OH-] = 10-pOH.
Acids and bases are inversely related: The greater the concentration of H+ ions, the lower the concentration of OH- ions, and vice versa. Since [H+][OH-] = l0-14 at 25 °C, the values of pH and pOH satisfy a special relationship at 25 °C:
I..-_p_H_+_p_O_H_=-14---.1
So, if you know the pOH of a solution, you can find the pH, and vice versa. For example, if the pH of a solution is 5, then the pOH must be 9. If the pOH of a solution is 2, then the pH must be 12.
On the MCAT, it will be helpful to be able to figure out the pH even in cases where the H+
concentration isn't exactly equal to a whole-number power of 10. In general, if y is a number between 1 and 10, and you're told that [H+] = y x 10-n (where n is a whole number) then the pH will be between (n-1) and n. For exttmple, if [H+] = 6.2 x l0-5, then the pH is between 4 and 5.
~ Example 8-8: Of the following liquids, which one contains the lowest concentration of H30t ions?
A. Lemon juice (pH = 2.3) B. Blood (pH= 7.4) C. Seawater (pH = 8.5) D. Coffee (pH = 5.1)
Solution. SincepH = -log[H30+], we know that [H30+]= 1/lOPH. This fraction is smallest when the pH is greatest. Of the choices given, seawater (choice C) has the highest pH.
~ Example 8-9: What is the pH of a solution at 25 °C whose hydroxide ion concentration is 1 x l0-4 M?
Solution. Since pOH = -log[OH-], we know that pOH = 4. Therefore, the pH is 10.
MCAT GENERAL CHEMISTRY- CHAPTER 8: ACIDS AND BASES 431
~ Example 8-10: Orange juice has a pH of 3.5. What is its [H+]?
Solution. Because pH= -log[H+], we know that [H_j_ = 10-pH. For orange juice, then, we have [H+] = l0-3ã5 = 10°ã5-4 = 10°ã5 x 10-4 = .J10 x 10-4 === 3.2 x 10-4M.
~ Example 8-11: If 99% of the H30+ ions are removed from a solution whose pH was originally 3, what will be its new pH?
Solution. If 99% of the H3Q+ ions are removed, then only 1% remain. This means that the number of H30+ ions is now only 1/100 of the original. If [H30+] is decreased by a factor of 100, then the pH is increased by 2-to pH 5, in this case- since log 100 = 2.
~Example 8-12: Let Ka be the acid-dissociation constant for formic acid (HCOOH) and let Kb stand for the base-dissociation constant of its conjugate base (the formate ion, HCOO-). If K8 is equal to 5.6 x 10-11, what is Ka. Kb?
Solution. The equilibrium for the dissociation of HCOOH is
HCOOH(aq) + H20(l) ~ H3Q+(aq) + HCOO-(aq) so
K [H30+][HCOO-]
a [HCOOH]
The equilibrium for the dissociation of HCOO- is
so
Therefore,
HCOO-(aq) + H20(l) ~ . HCOOH(aq) + OH-(aq)
K _ [HCOOHIOH-]
b - [Hcoo-1
[H30+][HCOO-] . [HCOOH][OH-] = [H
3
o+][oH-]
KaKb = [HCOOH] [:HCOO-]
We now immediate~y recognize this product as Kw, the ion-product constant of water, whose value (at 25 °C) is 1 X 10-14•
This calculation wasn't special for HCOOH; we can see that the same thing will happen for any acid and its conjugate base. So, for any acid-base conjugate pair, we'll have
K K a b = K w = 1 X l0-14
This gives us a way to quantitatively relate the strength of an acid and its conjugate base. For example, the value of K
8 for HF is about 7 x 10-4; therefore, the value of Kb for its conjugate base, F-, is about 1.4 X l0-9 •• For HCN, Ka =:: 5 X l0-10, so Kb for eN-is 2 x 10-5•
432 MCAT PHYSICAL SCIENCES REVIEW
~Example 8-13: Given that the self-ionization of water is endothermic, what is the value of the sum pH + pOH at 50°C?
H20(I) + H20(I) ~ H3Q+(aq) + OH-(aq) A. Less than 14
B. Equal to 14 C. Greater than 14
D. Cannot determine from the information given
Solution. This is aLe Chatelier's principle question in disguise. Imagine we start at equilibrium at 25°C; which way would the self-ionization reaction shift if we increase the temperature to 50°C? Since the question tells us this reaction is
endothermic, the system would shift to the right. Shifting to the right means that at equilibrium, [H+] and [OH-] will increase. So pH and pOH will both be lower than 7 at 50°C, and the sum of pH and pOH will be less than 14 at 50°C. Choice A is the correct answer.
pH CALCULATIONS FOR STRONG ACIDS
Strong acids dissociate completely, so the hydrogen ion concentration will be the same as the concentration of the acid. That means that you can calculate the pH directly from the molarity of the solution. For example, a 0.01 M solution of HCl will have [H+] = 0.01 M and pH = 2.
FOR WEAK ACIDS
Weak acids come to equilibrium with their dissociated ions. In fact, for a weak acid at
equilibrium, the concentration of undissociated acid will be much greater than the concentration of hydrogen ion. To get the pH of a weak acid solution, you need to use the equilibrium expression.
Let's say you add 0.2 mol of HCN (hydrocyanic acid, a weak acid) to water to create a 1-liter solution, and you want to find the pH .. Initially, [HCN] = 0.2 M, and none of it has dissociated. If x moles of HCN are dissociated at equilibrium, then the equilibrium concentration of HCN is 0.2 - x.
Now, since each molecule of HCN dissociates into one H+ ion and one CN- ion, if x moles of HCN have dissociated, there'll be x moles of H+ and x moles of CN-:
initial:
at equilibrium:
HCN 0.2M.
(0.2 -x) M
~
~ H+ + eN-
OM OM
xM xM
(Actually, the initial concentration of H+ is 10-7M, but it's so small that it can be neglected for this calculation.) Our goal is to find x, because once we know [H+], we'll know the pH. So, we set up the equilibrium expression:
[H+][cN-] x2
Kã= = - -
a [HCN] 0.2-X
MCAT GENERAL CHEMISTRY - CHAPTER 8: ACIDS AND BASES 433 It's known that the value of Ka for HCN is 4.9 x l0-10. Because the K11 is so small, not that much of the HCN is going to dissociate. ã[This assumption, that x added to or subtracted from a number is negligible, is always a good one when K < 10-4 (the usual case found on the MCAn.J That is, we can assume that x is going to be a very small number, insignificant compared to 0.2; therefore, the value (0.2- x) is almost exactly the same as 0.2. By substituting 0.2 for (0.2- x), we can solve the equation above for x:
0.x2
2 :::: 4.9 X 10-10 x2 = lx 10-10 :.x= lxlo-5 Since [H+] is approximately 1 x lo-s M, the pH is about 5.
We simplified the computation by assuming that the concentration of hydrogen ion [H+] was insignificant compared to the concentration of undissociated acid [HCN]. Since it turned out that [H+] :::: lo-s M, which is much less than [HCN] = 0.2 M, our assumption was valid. On the MCAT, you should always simplify the math wherever possible .
.._.Example 8-14: If 0.7 mol of benzoic acid (C6HsCOOH, Ka = 6.6 x lO-S) is added to water to create a 1-liter solution, what will be the pH?
Solution. Initially, [C6HsCOOH] = 0.7 M, and none of it has dissociated. If x moles of C6HsCOOH are dissociated at equilibrium, then the equilibrium concentration of C6H5COOH is 0.7-x. Now, since each molecule of C6H5COOH dissociates into one H+ ion and one C6H5COO- ion, if x moles of C6H5COOH have dissociated, there'll be x moles of H+ and x moles of C6H5COO-:
C6H5COOH ~ H+ + C6H5COO-
initial: 0.7M OM OM
at equilibrium: (0.7 -x) M xM xM
(Again, the initial concentration of H+is l0-7 M, but it's so small that it can be neglected.) Our goal is to find x, because once we know [H+], we'll know the pH.
So, we set up the equilibrium expression:
K = [H+][C6H5COO-] _i_ =.t_
a [C6H5COOH] 0.7 -X 0.7 and then solve the equation for x:
~ 0.
7 =6.6xlo-s
~ =4.6xlo-5
= 46x10-6
:. X:::: 7 xl0-3
Since [H+] is approximately 7 x l0-3 M = l0-2 M, the pH is a little more than 2, say 2.2.
434 MCAT PHYSICAL SCIENCES REVIEW
pK8ANDpKb
The definitions of pH and pOH both involved the opposite of a logarithm. In general, "p" of something is equal to the -log of that something. Therefore, the following definitions won't be surprising:
pKa =-logKa pKb =-logKb
Because H+ concentrations are generally very small and can vary over such a wide range, the pH scale gives us more convenient numbers to work with. The same is true for pK8 and pKb.
Remember that the larger the K8 value, the stronger the acid. Since "p" means "take the negative log of ... ," the lower the pK8 value, the stronger the acid. For example, acetic acid (CH3COOH) has a K8 of 1.75 x 10-5, and hypochlorous acid (HClO) has aKa of 2.9 x 10-a. Since the Ka of acetic acid is largerã than that of hypochlorous acid, we know this means that more molecules of acetic acid than hypochlorous acid will dissociate into ions in aqueous solution~ In other words, acetic acid is stronger than hypochlorous. The pK8 of acetic acid is 4.8, and the pKa of hypochlorous acid is 7.5.
The acid with the lower pKa value is the stronger acid. The same logic applies to pKb: the lower the pKb value, the stronger the base.
It also follows from our definitions and the general equatiqn we derived at the end of the solution to Example 8ã12 above that for an acid-base conjugate pair at 25 °C, we'll have
I pK.+pKb=141
§8.6 ~EUTRALIZATION REACTIONS
When an acid and a base are combined, they react with each other to form a salt and water.
This is called a neutralization reaction. Here's an example:
HCl + NaOH ~ NaCl + H20
acid base salt water
This type of reaction takes place when you take an antacid to relieve excess stomach acid.
The antacid is a weak base, usually carbonate, that reacts in the stomach to neutralize acid.
If a strong acid and strong base react (as in the example above), the resulting solution will be pH neutral (which is why we call it a neutralization reaction). However, if the reaction involves a weak add or weak base, the resulting solution will generally not be pH neutral.
As you can see from the reaction above, equal molar amounts of HCl and NaOH are needed to complete the neutralization. To determine just how much base (B) to add to an acidic solution (or how much acid (A) to add to a basic solution) in order to cause complete neutralization, we just the following formula:
a X [A] X VA = b X [B] X VB
where a is the number of acidic hydrogens per formula unit and b is a constant that tells us how many H3Q+ ions the base can accept.