Strong and Weak Acids and Bases

Strong and Weak Acids and Bases

• Many medicines are acids or bases.
  • Tylenol (acetaminophen) and Aspirin (acetylsalicylic acid, or ASA) are two common painkillers that are acids.
  • The pH of a $0.25 mol/L$ solution of acetaminophen is $5.3$, while the pH of an equally concentrated solution of ASA is $2.0$.
  • The $K<em>a$ of acetaminophen is $1.2 \times 10^{-10}$, while the $K</em>a$ of ASA is $3.27 \times 10^{-4}$. Acetaminophen is much less likely than ASA to ionize to form $H^+(aq)$ ions in aqueous solution.

Acid and Base Strength

• The strength of an acid or base depends on the equilibrium position of the compound’s ionization reaction.
• Stronger acids and bases have ionization equilibrium positions farther to the right.
• Weaker acids and bases have equilibrium positions farther to the left.
• In water, strong acids or bases will ionize more than weak acids or bases.
• ASA is a stronger acid than acetaminophen.

Strong Acids and Weak Acids

• When acids dissolve and ionize in water, they form a dynamic equilibrium between reactants and products.

Strong Acid

• A strong acid is an acid for which the equilibrium position in an aqueous solution lies far to the right.
• Almost all the $HA$ molecules have broken apart to produce ions.
• Ionizes almost $100 \%$ in water, producing hydrogen ions.

Weak Acid

*A weak acid is one for which the equilibrium position is far to the left.
*Most of the acid originally placed in the solution is $HA$ molecules at equilibrium.
*A weak acid ionizes only to a very small extent in aqueous solution and exists primarily as non-ionized molecules.
*Only partly ionizes in water, producing hydrogen ions.

Acid Strength

• Value of acid ionization constant, $K_a$.
  • Strong acid: $K_a$ is large.
  • Weak acid: $K_a$ is small.
• Position of the ionization equilibrium
  • Strong acid: far to the right.
  • Weak acid: far to the left.
• Equilibrium concentration of $H^+(aq)$ compared with original concentration of HA
  • Strong acid: $[H^+(aq)]<em>{equilibrium} < [HA(aq)]</em>{initial}$
  • Weak acid: $[H^+(aq)]<em>{equilibrium} << [HA(aq)]</em>{initial}$

Acid Ionization Constant

• The acid ionization constant, $K_a$, is the equilibrium constant for the ionization of an acid.
• The general equation is $K<em>a = \frac{[H^+(aq)][A^-(aq)]}{[HA(aq)]}$, where $K</em>a$ always refers to the reaction of an acid, $HA(aq)$, with water to form the conjugate base, $A^-(aq)$, and the hydrogen ion, $H^+(aq)$ (representing the hydronium ion, $H_3O^+(aq)$).
• Since the concentration (density) of water is a constant, it is incorporated into the value of $K_a$.

Acid and Conjugate Base Strength

• There is an important connection between the strength of an acid and the strength of its conjugate base.
• The stronger an acid, the weaker its conjugate base, and conversely, the weaker an acid, the stronger its conjugate base.

Oxyacids and Organic Acids

Oxyacids

• Most familiar acids are oxyacids, which have the acidic hydrogen (ionizable hydrogen) atom attached to an oxygen atom.
• Sulfuric acid is a typical example of a strong oxyacid.
• Many common weak acids, such as phosphoric acid $H<em>3PO</em>4(aq)$, nitrous acid $HNO_2(aq)$, and hypochlorous acid $HClO(aq)$, are also oxyacids.

Organic Acids

• An organic acid has a carbon backbone and a carboxyl group.
• Most organic acids are weak acids.
• Examples are ethanoic acid, $HC<em>2H</em>3O<em>2(aq)$, and benzoic acid, $HC</em>7H<em>5O</em>2(aq)$.
• The acidic hydrogen atom is written at the beginning of the chemical formula.
• The remaining hydrogen atoms are not acidic—they do not form $H^+(aq)$ in water.

Acids of Halogens

• There are some important acids in which the acidic hydrogen atom is attached to an atom other than oxygen.
• The most significant of these are the acids of the halogens (specifically, $HF(aq)$, $HCl(aq)$, $HBr(aq)$, and $HI(aq)$).

Strong Bases and Weak Bases

• Like acids, bases may be either strong or weak, depending on the position of their equilibrium in solution.
• A strong base forms an equilibrium that lies farther to the right (toward products) when it reacts with water.
• A weak base forms an equilibrium that lies farther to the left (toward reactants) when it reacts with water.

Strong Bases

• The bases sodium hydroxide, $NaOH$, and potassium hydroxide, $KOH$, dissociate completely in aqueous solution to form cations and hydroxide ions, leaving virtually no undissociated base entities in the solution.
• $NaOH(s) \rightarrow Na^+(aq) + OH^-(aq)$
• $KOH(s) \rightarrow K^+(aq) + OH^-(aq)$
• A $1.0 mol/L$ sodium hydroxide solution contains $1.0 mol/L Na^+(aq)$ and $1.0 mol/L OH^-(aq)$.
• Since it dissociates completely, sodium hydroxide is called a strong base: a base that dissociates completely in aqueous solution.
• All the hydroxides of the Group 1 elements—$LiOH$, $NaOH$, $KOH$, $RbOH$, and $CsOH$—are strong bases.
• The Group 2 (alkaline earth) hydroxides—$Ca(OH)<em>2$, $Ba(OH)</em>2$, and $Sr(OH)_2$—are also strong bases.
• For the Group 2 bases, $2 mol$ of hydroxide ions are produced for every $1 mol$ of metal hydroxide dissolved:
  • $Ca(OH)_2(aq) \rightarrow Ca^{2+}(aq) + 2OH^-(aq)$
• Although the alkaline earth hydroxides are strong bases, they are only slightly soluble.
• The low solubility of these bases can sometimes be an advantage.
• Many antacid medicines are suspensions of metal hydroxides, such as aluminum hydroxide, $Al(OH)<em>3(s)$, and magnesium hydroxide, $Mg(OH)</em>2(s)$.
• The low solubility of these compounds prevents a quick dissociation, which would release a high concentration of hydroxide ions that could harm the tissues lining the mouth, esophagus, and stomach.
• The hydroxide compounds in the antacid dissolve in the highly acidic solution of the stomach.
• Dissolved $OH^-(aq)$ ions react with $H^+(aq)$ ions in stomach acid, the dissociation equilibrium position shifts to the right and more base dissociates.
• Calcium hydroxide, $Ca(OH)_2$, often called slaked lime, is used in “scrubbers” to remove sulfur dioxide from the exhaust of power plants and refineries.

Weak Bases

• Many compounds are bases even though they do not contain the hydroxide ion.
• These compounds increase the concentration of hydroxide ions in aqueous solution because of their reaction with water.
• These bases are Brønsted–Lowry bases.
• Ammonia, $NH_3(aq)$, is a base because it reacts with water to form aqueous hydroxide ions:
  • $NH<em>3(aq) + H</em>2O(l) \rightleftharpoons NH_4^+(aq) + OH^-(aq)$
• In this reaction, water is a Brønsted–Lowry acid, and ammonia is a Brønsted–Lowry base.
• Even though ammonia contains no hydroxide ions, it still increases the concentration of hydroxide ions in solution because of its reaction with water.
• Since the equilibrium position of this reaction is far to the left, ammonia is considered to be a weak base.
• Compounds that react with water as ammonia does are generally weak bases.
• Bases such as ammonia have at least one unshared pair of electrons that is capable of forming a coordinate covalent bond with a hydrogen ion.

Base Ionization Constant

• For the reaction of a generic base with water, the equilibrium law equation, $K$ is written as follows:
  • $K = \frac{[OH^-(aq)][BH^+(aq)]}{[B(aq)][H_2O(l)]}$
• Since the concentration (density) of water is a constant, it can be incorporated into the value of $K$ (just as it was in the equilibrium law equation for $K_a$).
• This yields a new constant, $K_b$, called the base ionization constant:
  • $K_b = \frac{[BH^+(aq)][OH^-(aq)]}{[B(aq)]}$
• Consider the ionization of ammonia in water. When ammonia reacts with water, the equilibrium equation is as follows:
  • $NH<em>3(aq) + H</em>2O(l) \rightleftharpoons OH^-(aq) + NH_4^+(aq)$
• The $K_b$ equation for this reaction is
  • $K<em>b = \frac{[OH^-(aq)][NH</em>4^+(aq)]}{[NH_3(aq)]}$
• The equilibrium position of the reaction between ammonia and water lies far to the left as is the case with all weak bases.
• The $K<em>b$ values of ammonia and other weak bases tend to be small (for example, for ammonia, $K</em>b = 1.8 \times 10^{-5}$).
• Weak bases are the conjugate bases of weak acids.
• The ethanoate ion, $C<em>2H</em>3O<em>2^-(aq)$, is the conjugate base of ethanoic acid, $HC</em>2H<em>3O</em>2(aq)$.
• The hypochlorite ion, $ClO^-(aq)$, is the conjugate base for hypochlorous acid, $HClO(aq)$.

Organic Bases

• An organic compound that increases the concentration of hydroxide ions in aqueous solution is called an organic base.
• All organic bases contain carbon atoms, and many also contain nitrogen atoms.
• One group of organic bases is called the alkaloids.
• Most alkaloids are derived from plants, fungi, and bacteria.
• Many drugs are based on alkaloids.
• These drugs include powerful painkillers such as codeine and morphine and illicit drugs such as cocaine.
• Caffeine and nicotine are also alkaloids.
• All contain at least one nitrogen atom with an unbonded pair of electrons that can accept a hydrogen ion, $H^+(aq)$, from water, leaving behind a hydroxide ion that makes the solution more basic.

Water as an Acid and a Base

• Water is the most common amphiprotic substance: it can behave as either an acid or a base.
• Water can behave as both an acid and a base in the same reaction.
• This reaction is called the autoionization of water and involves the transfer of a hydrogen ion from one water molecule to another water molecule.
• The products are a hydroxide ion and a hydronium ion.
• One water molecule acts as a Brønsted–Lowry acid by releasing a hydrogen ion, and the other acts as a Brønsted–Lowry base by accepting the hydrogen ion.
• The chemical equation for the autoionization of water:
  • $2H<em>2O(l) \rightleftharpoons H</em>3O^+(aq) + OH^-(aq)$
• The equilibrium law equation:
  • $K = \frac{[H<em>3O^+(aq)][OH^-(aq)]}{[H</em>2O(l)]^2}$
• We omit $[H_2O(l)]$, leaving the simplified equation:
  • $K = [H_3O^+(aq)][OH^-(aq)]$
• This constant is called the ion-product constant for water, $K_w$.
• We can also write $K<em>w$ in an even simpler way if we use $H^+$ instead of $H</em>3O^+$:
  • $K_w = [H^+(aq)][OH^-(aq)]$

Value of $K_w$

• Experiments show that, at $25 \degree C$ in pure water, $[H^+(aq)] = 1.0 \times 10^{-7} mol/L$ and $[OH^-(aq)] = 1.0 \times 10^{-7} mol/L$
• We can calculate the value of $K_w$ at $25 \degree C$ as follows:
  • $K_w = [H^+(aq)][OH^-(aq)]$
  • $K_w = (1.0 \times 10^{-7})(1.0 \times 10^{-7})$
  • $K_w = 1.0 \times 10^{-14}$

Meaning of $K_w$

• In any aqueous solution at $25 \degree C$, no matter what the solution contains, the product of $[H^+(aq)]$ and $[OH^-(aq)]$ must always equal $1.0 \times 10^{-14}$.
• There are three possible situations:
  • A neutral solution, where $[H^+(aq)] = [OH^-(aq)]$
  • An acidic solution, where [H^+(aq)] > [OH^-(aq)]
  • A basic solution, where [OH^-(aq)] > [H^+(aq)]
• In each case, however, at $25 \degree C$, $[H^+(aq)][OH^-(aq)] = 1.0 \times 10^{-14}$.

Relationship between $K<em>w, K</em>a$, and $K_b$

• The ionization reaction of a weak acid, $HA(aq)$, is represented as
  • $HA(aq) + H<em>2O(l) \rightleftharpoons A^-(aq) + H</em>3O^+(aq)$
• The acid ionization constant equation is
  • $K<em>a = \frac{[H</em>3O^+(aq)][A^-(aq)]}{[HA(aq)]}$
• $A^-$ is the conjugate base of $HA$.
• We can write an ionization equation for the reaction of $A^-$ with water:
  • $A^-(aq) + H_2O(l) \rightleftharpoons HA(aq) + OH^-(aq)$
• The corresponding base ionization constant equation:
  • $K_b = \frac{[HA][OH^-]}{[A^-]}$
• If we add together the ionization reactions for $HA(aq)$ and $A^-(aq)$, we can obtain an overall equation:
  • $HA(aq) + H<em>2O(l) \rightleftharpoons A^-(aq) + H</em>3O^+(aq)$
  • $A^-(aq) + H_2O(l) \rightleftharpoons HA(aq) + OH^-(aq)$
  • $2H<em>2O(l) \rightleftharpoons H</em>3O^+(aq) + OH^-(aq)$

Mathematical Relationship

• Since there is a mathematical relationship between these three equations, there is also a mathematical relationship between their corresponding equilibrium constants, $K<em>a, K</em>b$, and $K_w$.
• If we multiply the $K<em>a$ for the acid, $HA(aq)$, by the $K</em>b$ for its conjugate base, $A^-(aq)$, the product is $K_w$:
  • $K<em>aK</em>b = \frac{[H<em>3O^+(aq)][A^-(aq)]}{[HA(aq)]} \times \frac{[HA(aq)][OH^-(aq)]}{[A^-(aq)]} = [H</em>3O^+(aq)][OH^-(aq)]$
  • $K<em>aK</em>b = K_w$
• This relationship holds for all weak acids and bases: for a weak acid $HA(aq)$ and its conjugate base $A^-(aq)$, or for a weak base $B(aq)$ and its conjugate acid $BH(aq)$
• This relationship explains the trend we observed earlier: as the strength of the acid increases, the strength of its conjugate base decreases, and vice versa.

General Assumptions

• A strong acid or base has a very weak conjugate.
• A weak acid or base has a weak conjugate.
• A very weak acid or base has a strong conjugate.

pH and pOH

• In pure water at $25 \degree C$, the autoionization of water produces a hydrogen ion concentration of $1.0 \times 10^{-7} mol/L$ and a hydroxide ion concentration of $1.0 \times 10^{-7} mol/L$.
• We may convert these very small concentration values into more convenient positive integer values by using logarithms.
• The negative logarithm of the hydrogen ion concentration is called pH.
• The negative logarithm of the hydroxide ion concentration is called pOH.
• $pH = -log[H^+(aq)]$
• $pOH = -log[OH^-(aq)]$
• Since pH is a logarithmic value based on 10, the pH changes by 1 for every 10-fold change in $[H^+(aq)]$.
• A solution of pH 3 has a $H^+(aq)$ ion concentration 10 times greater than a solution of pH 4 and 100 times greater than a solution of pH 5.
• Since pH is defined as –log[$H^+(aq)$], pH decreases as $[H^+(aq)]$ increases and vice versa.
• The pH of common aqueous solutions at $25 \degree C$ ranges from 0 to 14.

Calculating pH of Pure Water

• $[H^+(aq)] = 1.0 \times 10^{-7} mol/L$
• $pH = -log(1.0 \times 10^{-7})$
• $pH = -(-7.00)$
• $pH = 7.00$

Calculating pOH of Pure Water

• $[OH^-(aq)] = 1.0 \times 10^{-7} mol/L$
• $pOH = -log(1.0 \times 10^{-7})$
• $pOH = -(-7.00)$
• $pOH = 7.00$
• In pure water, therefore, pH = 7 and pOH = 7.
• This result does not only apply to pure (neutral) water but to all neutral aqueous solutions.
• In all neutral aqueous solutions, both pH and pOH are equal to 7.
• In pure water and all aqueous solutions, the product of $[H^+(aq)]$ and $[OH^-(aq)]$ always equals $1.0 \times 10^{-14}$, the value of $K_w$.
• For a solution to be neutral, the concentration of hydrogen ions must equal the concentration of hydroxide ions.
• These conditions can only be met if the concentration of hydrogen ions and hydroxide ions are both $1.0 \times 10^{-7} mol/L$.
• In pure water and all neutral aqueous solutions, $[H^+(aq)] = 1.0 \times 10^{-7} mol/L$ and pH = 7 and $[OH^-(aq)] = 1.0 \times 10^{-7} mol/L$ and pOH = 7

pH and pOH of Acidic and Basic Solutions

• Acidic and basic solutions are formed when acids and bases are dissolved in water.
• Acids increase the concentration of $H^+(aq)$ ions in solution, and bases increase the concentration of $OH^-(aq)$ ions in solution.
• If we add an acid to pure water, the $[H^+(aq)]$ will increase to a value higher than $10^{-7} mol/L$, and the pH will be lower than 7.

Example

• In a $0.010 mol/L HCl(aq)$ solution,
  • $[H^+(aq)] = 1.0 \times 10^{-2} mol/L$
  • $pH = -log(1.0 \times 10^{-2})$
  • $pH = 2$
• When we dissolve an acid in water, there is an increase in $[H^+(aq)]$ and a decrease in pH.
• While there is an increase in $[H^+(aq)]$, there is also a proportional decrease in the concentration of hydroxide ions because, in all aqueous solutions at $25 \degree C$, $[H^+(aq)][OH^-(aq)] = 1.0 \times 10^{-14}$.
• Since $[H^+(aq)] = 1.0 \times 10^{-2} mol/L$ and $[H^+(aq)][OH^-(aq)] = 1.0 \times 10^{-14}$, then
  • $(1.0 \times 10^{-2})[OH^-(aq)] = 1.0 \times 10^{-14}$
  • $[OH^-(aq)] = \frac{1.0 \times 10^{-14}}{1.0 \times 10^{-2}}$
  • $[OH^-(aq)] = 1.0 \times 10^{-12} mol/L$
• We may now calculate the pOH of this solution:
  • $pOH = -log(1.0 \times 10^{-12})$
  • $pOH = 12$
• For a $0.010 mol/L HCl(aq)$ solution,
  • $[H^+(aq)] = 1.0 \times 10^{-2} mol/L$ and pH = 2
  • $[OH^-(aq)] = 1.0 \times 10^{-12} mol/L$ and pOH = 12
• We may use the equation $[H^+(aq)][OH^-(aq)] = 1.0 \times 10^{-14}$ to determine $[H^+(aq)]$ or $[OH^-(aq)]$ (and then pH and pOH) of any aqueous solution at $25 \degree C$ when the concentration of one ion or the other is known.

Mathematical Relationship

• $[H^+(aq)][OH^-(aq)] = K_w$
• $-log([H^+(aq)][OH^-(aq)]) = -log K_w$
• $(−log [H^+(aq)]) + (−log[OH(aq)]) = −log K_w$
• $pH + pOH = -log K_w$
• Since $K_w = 1.0 \times 10^{-14}$ and $−log (1.0 \times 10^{-14}) = 14$ for all aqueous solutions at $25 \degree C$, then
  • $pH + pOH = 14$
• This equation allows us to calculate the pH or pOH of an aqueous solution at $25 \degree C$ if one or the other value is already known.
• If we add a base pure water, $[OH^-(aq)]$ will temporarily increase.
  As most of the hydroxide ions react with hydrogen ions, $[H^+(aq)]$ will decrease to a value below $1.0 \times 10^{-7} mol/L$, and the pH will be greater than 7.
• At the same time, $[OH^-(aq)]$ will be higher than $1.0 \times 10^{-7} mol/L$, and the pOH will be lower than 7.

Characteristics of Solutions

Neutral Solutions

• $[H^+(aq)] = 1.0 \times 10^{-7} mol/L$ and pH = 7
• $[OH^-(aq)] = 1.0 \times 10^{-7} mol/L$ and pOH = 7

Acidic Solutions

• [H^+(aq)] > 1.0 \times 10^{-7} mol/L and pH < 7
• $[OH^-(aq)] < 1.0 \times 10^{-7} mol/L$ and pOH > 7

Basic Solutions

• $[H^+(aq)] < 1.0 \times 10^{-7} mol/L$ and pH > 7
• [OH^-(aq)] > 1.0 \times 10^{-7} mol/L and pOH < 7

Measuring pH

pH Meter

• A pH meter is an electronic device with a probe that can be inserted into a solution of unknown pH.
• The probe contains an acidic aqueous solution enclosed by a special glass membrane that allows $H^+(aq)$ ions to pass through.
• If the unknown solution has a different pH than the solution in the probe, the meter registers the resulting electric potential and displays the data as a pH reading.

Acid-Base Indicator

• An acid–base indicator is a substance that has different colours in solutions with different pH values.
• Since the colour of an acid–base indicator varies with the pH of the solution, you can use an indicator to determine the approximate pH of a solution.
• Juice from red cabbage can range in colour from red to brown, depending on the pH of the solution with which it is mixed.
• Many plants produce naturally coloured substances that are acid–base indicators.
• Tea, red grape juice, and blueberries all change colour with pH.

Litmus paper

• Litmus paper is another widely used acid–base indicator.
• It is a common indicator because it is readily available, inexpensive, and stores well.
• The dye used in litmus paper comes from lichen.
• After the water-soluble dye compound is extracted from the lichen, absorbent paper is soaked in the solution.
• When the paper dries, the litmus indicator is bonded to the paper.
• There are two types of litmus paper: blue and red.
• Acidic solutions turn blue litmus red; basic solutions turn red litmus blue.
• A neutral solution leaves red litmus red and blue litmus blue.

Relating pH or pOH, and Ion Concentration

• The following equations allow you to calculate pH from $[H^+(aq)]$ and $[H^+(aq)]$ from pH:
  • $pH = -log[H^+(aq)]$
  • $10^{-pH} = [H^+(aq)]$
• The following equations allow you to calculate pOH from $[OH^-(aq)]$ and $[OH^-(aq)]$ from pOH:
  • $pOH = -log[OH^-(aq)]$
  • $10^{-pOH} = [OH^-(aq)]$