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The pOH of a solution can also be calculated It is defined as pOH = log[OH ] The pH and the pOH are related: pH + pOH = p K w = 14 00 at 25 C
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pH 14 13 12 MORE BASIC 11 10 9 8 7 6 5 MORE ACIDIC 4 3 2 1 0 Vinegar (24 34) Lemon juice (22 24) Stomach acid (10 30) 1 M HCl (00) Milk of magnesia (105) Detergent solution (~10) Seawater (70 83) Blood (74) NEUTRAL Milk (64) Urine (48 75) Rain water (56) 1 M NaOH (140)
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Household ammonia (119)
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The pH scale
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In any of the problems above in which [H+ ] or [OH ] was calculated, you can now calculate the pH or pOH of the solution + You can estimate the pH of a solution by looking at its [H ] For example, if a solution + 5 has an [H ] = 1 10 , its pH would be 5 This value was determined from the value of + the exponent in the [H ]
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Kb The Base Dissociation Constant
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Weak bases (B), when placed into water, also establish an equilibrium system much like weak acids: B(aq) + H2O(l) HB+ (aq) + OH ( aq)
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Equilibrium 221
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The equilibrium constant expression is called the weak base dissociation constant, Kb, and has the form: [HB+ ][OH ] Kb= [HB] The same reasoning that was used in dealing with weak acids is also true here: [HB+] = 2 [OH ]; [HB] Minitially; the numerator can be represented as [OH ] ; and knowing the ini tial molarity and Kb of the weak base, the [OH ] can easily be calculated And if the initial molarity and [OH ] are known, Kb can be calculated For example, a 0500 M solution of ammonia has a pH of 1148 What is the Kb of ammonia pH = 1148
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+ 1148 [H ] = 10
[H+] = 33 10 12 M
+ 14 Kw = [H ][OH ] = 10 10
[OH ] = 30 10 M NH3 + H 2O 0500 x NH+ + OH 4 x x
[ NH+ ][OH ] 4 Kb= [ NH3 ]
3 [OH ] = [NH4 ] = 30 10 M 3 [NH3] = 0500 30 10 = 0497 M +
(3 0 10 3 )2 = 1 8 10 5 (0 497 )
The Ka and Kb of conjugate acid base pairs are related through the Kw expression: Ka Kb = Kw This equation shows an inverse relationship between Ka and Kb for any conjugate acid base pair This relationship may be used in problems such as: Determine the pH of a solution made by adding 0400 mol of strontium acetate to sufficient water to produce 2000 L of solution Solution: The initial molarity is 0400 mol/2000 L = 0200 M When a salt is added to water dissolution will occur: Sr (C 2H3O2 )2 Sr 2+ ( aq) + 2C 2H3O ( aq) 2
222 U Step 4 Review the Knowledge You Need to Score High
The resultant solution, since strontium acetate is soluble, has 0200 M Sr2+ and 0400 M C2H3O2 2+ Ions such as Sr , which come from strong acids or strong bases, may be ignored in this type of problem Ions such as C2H3O2 , from weak acids or bases, will undergo hydrolysis 5 The acetate ion is the conjugate BASE of acetic acid (Ka = 18 10 ) Since acetate is not a strong base this will be a Kb problem, and OH will be produced The equilibrium is: C 2 H 3O + H 2 O 2 0 400 x OH + HC 2H3O2 +x +x
Determining Kb from Ka (using Kw = KaKb = 10 10 [ x ][x ] = K b = 5 6 10 10 0400 x
gives:
with x = 15 10 = [OH ], and pH = 9180
Acidic/Basic Properties of Salts
The behavior of a salt will depend upon the acid base properties of the ions present in the salt The ions may lead to solutions of the salt being acidic, basic, or neutral The pH of a solution depends on hydrolysis, a generic term for a variety of reactions with water Some ions will undergo hydrolysis and this changes the pH The reaction of an acid and a base will produce a salt The salt will contain the cation from the base and the anion from the acid In principle, the cation of the base is the conjugate acid of the base, and the anion from the acid is the conjugate base of the acid Thus, the salt contains a conjugate acid and a conjugate base This is always true in principle In some cases, one or the other of these ions is not a true conjugate base or a conjugate acid Just because the ion is not a true conjugate acid or base does not mean that we cannot use the ion as if it were The conjugate base of any strong acid is so weak that it will not undergo any significant hydrolysis; the conjugate acid of any strong base is so weak that it, too, will not undergo any significant hydrolysis Ions that do not undergo any significant hydrolysis will have no effect upon the pH of a solution and will leave the solution neutral The presence of the following conjugate bases Cl , Br , I , NO3 , ClO3 , and ClO4 will leave the + + + + + 2+ 2+ solution neutral The cations from the strong bases, Li , Na , K , Rb , Cs Ca , Sr , and 2+ Ba , while not true conjugate acids, will also leave the solution neutral Salts containing a combination of only these cations and anions are neutral The conjugate base from any weak acid is a strong base and will undergo hydrolysis in aqueous solution to produce a basic solution If the conjugate base (anion) of a weak acid is in a salt with the conjugate of a strong base (cation), the solution will be basic, because only the anion will undergo any significant hydrolysis Salts of this type are basic salts All salts containing the cation of a strong base and the anion of a weak acid are basic salts The conjugate acid of a weak base is a strong acid and it will undergo hydrolysis in an aqueous solution to make the solution acidic If the conjugate acid (cation) of a weak base is in a salt with the conjugate base of a strong acid (anion), the solution will be acidic, because only the cation will undergo any significant hydrolysis Salts of this type are acidic salts All salts containing the cation of a weak base and the anion of a strong acid are acidic salts There is a fourth category, consisting of salts that contain the cation of a weak base with the anion of a weak acid Prediction of the acid base character of these salts is less obvious, because both ions undergo hydrolysis The two equilibria not only alter the pH of the solution, but also interfere with each other Predictions require a comparison of the K values for
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