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The Ka and Kb of it

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Autoionization of Water Because water is amphiprotic, one water molecule can react with another to form an OH – ion and an H 3 O + ion in an autoionization process: 2H 2 O (l) ⇋ H 3 O + (aq) + OH – (aq) Equilibrium constant K for this reaction can be written as [H 3 O + ] [OH – ] [H 2 O] 2 1 L of water contains 55.5 moles of water. In dilute aqueous solutions: The water concentration is many orders of magnitude greater than the ion concentrations. The concentration is essentially that of pure water. Recall that the activity of pure water is 1. When pure liquid water is in equilibrium with hydronium and hydroxide ions at 25ºC, the concentrations of hydronium ion and hydroxide ion are equal: [H 3 O + ]=[OH – ] = 1.0 x 10 –7 M [H 3 O + ][OH – ] = 1.0 x 10 –14 M = K w [H 3 O + ]=[OH – ] = 1.0 x 10 –7 M [H 3 O + ][OH – ] = 1.0 x 10 –14 M = K w pH = pOH = 7 pH + pOH = pK w = 14 pH = pOH = 7 pH + pOH = pK w = 14 K c = K c [H 2 O] 2 = K w = [H 3 O + ][OH – ] = 1.0 x 10 –14

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No acid stronger than H 3 O + and no base stronger than OH – can exist in aqueous solution, leading to the phenomenon known as the leveling effect. Any species that is a stronger acid than the conjugate acid of water (H 3 O + ) is leveled to the strength of H 3 O + in aqueous solution because H 3 O + is the strongest acid that can exist in equilibrium with water. In aqueous solution, any base stronger than OH – is leveled to the strength of OH – because OH – is the strongest base that can exist in equilibrium with water Any substance whose anion is the conjugate base of a compound that is a weaker acid than water is a strong base that reacts quantitatively with water to form hydroxide ion Leveling Effect It’s all because of Gibbs Free Energy

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Acid-Base Equilibrium Constants: K a, K b, pK a, and pK b The magnitude of the equilibrium constant for an ionization reaction can determine the relative strengths of acids and bases The general equation for the ionization of a weak acid in water, where HA is the parent acid and A – is its conjugate base, is HA(aq) + H 2 O(l) ⇋ H 3 O+(aq) + A – (aq) The equilibrium constant for this dissociation is K = [H 3 O + ] [A – ] [H 2 O] [HA] The concentration of water is constant for all reactions in aqueous solution, so [H 2 O] can be incorporated into a new quantity, the acid ionization constant (K a ): K a = K[H 2 O] = [H 3 O + ] [A – ] [HA]

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Strong acids and bases ionize essentially completely in water; the percent ionization is always approximately 100%, regardless of the concentration The percent ionization in solutions of weak acids and bases is small and depends on the analytical concentration of the weak acid or base; percent ionization of a weak acid or a weak base actually increases as its analytical concentration decreases and percent ionization increases as the magnitude of the ionization constants K a and K b increases Ionization Constants for Weak Monoprotic Acids and Bases

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A 1 M solution is prepared by dissolving 1 mol of acid or base in water and adding enough water to give a final volume of exactly 1 L. If the actual concentrations of all species present in the solution were listed, it would be determined that none of the values is exactly 1 M because a weak acid or a weak base always reacts with water to some extent. Only the total concentration of both the ionized and unionized species is equal to 1 M. The analytical concentration (C) is defined as the total concentration of all forms of an acid or base that are present in solution, regardless of their state of protonation. Thus; a 1 M solution has an analytical concentration of 1 M, which is the sum of the actual concentrations of unionized acid or base and the ionized form. Ionization Constants for Weak Acids and Bases When is a 1M solution not a 1 M solution?

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Ionization Constants for Weak Monoprotic Acids and Bases Let’s look at the dissolution of acetic acid, a weak acid, in water as an example. The equation for the ionization of acetic acid is: The equilibrium constant for this ionization is expressed as:

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Ionization Constants for Weak Monoprotic Acids and Bases The water concentration in dilute aqueous solutions is very high. 1 L of water contains 55.5 moles of water. Thus in dilute aqueous solutions: The water concentration is many orders of magnitude greater than the ion concentrations. Thus the water concentration is essentially that of pure water. –Recall that the activity of pure water is 1.

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Ionization Constants for Weak Monoprotic Acids and Bases We can define a new equilibrium constant for weak acid equilibria that uses the previous definition. – This equilibrium constant is called the acid ionization constant. – The symbol for the ionization constant is K a.

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The ionization constant values for several acids are given below. – Which acid is the strongest? – Are all of these acids weak acids? – What is the relationship between K a and strength? – What is the relationship between pK a and strength? – What is the relationship between pH and strength? AcidFormulaK a valuepK a value -log K a pH of 1M analytical [HA] AceticCH 3 COOH1.8 x NitrousHNO x HydrofluoricHF7.2 x HypochlorousHClO3.5 x HydrocyanicHCN4.0 x Ionization Constants for Weak Monoprotic Acids and Bases

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Determining K a and K b The ionization constants K a and K b are equilibrium constants that are calculated from experimentally measured concentrations. What does the concentration of an aqueous solution of a weak acid or base exactly mean? – A 1 M solution is prepared by dissolving 1 mol of acid or base in water and adding enough water to give a final volume of exactly 1 L. – If the actual concentrations of all species present in the solution were listed, it would be determined that none of the values is exactly 1 M – Only the total concentration of both the ionized and unionized species is equal to 1 M. – The analytical concentration (C) is defined as the total concentration of all forms of an acid or base that are present in solution, regardless of their state of protonation. – 1 M solution has an analytical concentration of 1 M, the sum of the actual concentrations of unionized acid or base and the ionized form. Two common ways to obtain the concentrations 1.By measuring the electrical conductivity of the solution, which is related to the total concentration of ions present 2.By measuring the pH of the solution, which gives [H + ] or [OH – ]

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RICE Procedure for determining K a for a weak acid and K b for a weak base 1. The analytical concentration of the acid or base ionization Reaction is the Initial concentration 2. The stoichiometry of the reaction with water determines the Change in concentrations 3. The final (Equilibrium) concentrations of all species are calculated from the initial concentrations and the changes in the concentrations 4. Inserting the final concentration into the equilibrium constant expression enables the value of K a or K b to be calculated Determining K a and K b

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Use the concentrations that were just determined in the ionization constant expression to get the value of K a. R HY H 3 O + + Y - I C E In a 0.12 M solution of a weak monoprotic acid, HY, the acid is 5.0% ionized. Calculate the ionization constant for the weak acid. Ionization Constants for Weak Monoprotic Acids: the math

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The pH of a 0.10 M solution of a weak monoprotic acid, HA, is found to be What is the value for its ionization constant? Use the [H 3 O + ] and the stoichiometry of the ionization reaction to determine concentrations of all species. Calculate the ionization constant from this information. R HA H 3 O + + A - I C E Simplifying Assumption: Is the change significant? Later we will find that in general, if the K a /[] is < 1x10 -3 you can apply the simplifying assumption. Ionization Constants for Weak Monoprotic Acids the MATH

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Calculate the concentrations of the various species in 0.15 M acetic acid, CH 3 COOH, solution. 1.It is always a good idea to write down the ionization reaction and the ionization constant expression. 2.Next we combine the basic chemical concepts with some algebra to solve the problem RCH 3 COOH H 3 O + + CH 3 COO - I C E Ionization Constants for Weak Monoprotic Acids the MATH

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Substitute these algebraic quantities into the ionization expression. Ionization Constants for Weak Monoprotic Acids and Bases Solve the algebraic equation, using a simplifying assumption that is appropriate for all weak acid and base ionizations.

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Complete the algebra and solve for the concentrations of the species. Ionization Constants for Weak Monoprotic Acids and Bases Note that the properly applied simplifying assumption gives the same result as solving the quadratic equation does.

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Calculate the concentrations of the species in 0.15 M hydrocyanic acid, HCN, solution. K a = 4.0 x for HCN R HCN H 3 O + + CN - I C E Substitute these algebraic quantities into the ionization expression. Solve the algebraic equation, using the simplifying assumption that is appropriate for all weak acid and base ionizations. Ionization Constants for Weak Monoprotic Acids: the MATH

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Ionization Constants for Weak Monoprotic Acids and Bases Let’s look at the percent ionization of two weak acids as a function of their ionization constants. Note that the [H + ] in 0.15 M acetic acid is 200 times greater than for 0.15 M HCN. SolutionKaKa [H + ]pH% ionization 0.15 M acetic acid 1.8 x x M HCN 4.0 x x % ionization = x 100% [unionized HY] [ionized HY]

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Ionization Constants for Weak Monoprotic Acids and Bases All of the calculations and understanding we have at present can be applied to weak acids and weak bases. Calculate the concentrations of the various species in 0.15 M aqueous ammonia.

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All of the calculations and understanding we have at present can be applied to weak acids and weak bases. Calculate the concentrations of the various species in 0.15 M aqueous ammonia. K b = 1.8 E -5 R NH 3 NH OH - I C E Ionization Constants for Weak Monoprotic Bases: the MATH

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The pH of an aqueous ammonia solution is Calculate the molarity (original concentration) of the aqueous ammonia solution R NH 3 NH OH - I C E Examination of the last equation suggests that our simplifying assumption can be applied. In other words (x-2.3x10 -3 ) x. –Making this assumption simplifies the calculation. Ionization Constants for Weak Monoprotic Bases: the MATH

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