Acid base equilibria

Starter 44.0g of ethyl ethanoate was mixed with 36.0g of water containing HCl as a catalyst and allowed to reach equilibrium over several days. The equilibrium mixture was then made up to 250cm3 with pure water. A 25.0 cm3 sample of diluted mixture was titrated with 1.00mol dm-3 NaOH. After allowing for the acid catalyst present, the ethanoic acid in the equilibrium mixture was found to require 29.5 cm3 of NaOH for neutralisation. Find the Kc for the reaction: CH3COOC2H5(l)+ H2O(l) CH3COOH(l) + C2H5OH(l) The equation of for the neutralisation reaction is: CH3COOH + NaOH  CH3COONa + H2O

Starter 44.0g of ethyl ethanoate was mixed with 36.0g of water containing HCl as a catalyst and allowed to reach equilibrium over several days. The equilibrium mixture was then made up to 250cm3 with pure water. A 25.0 cm3 sample of diluted mixture was titrated with 1.00mol dm-3 NaOH. After allowing for the acid catalyst present, the ethanoic acid in the equilibrium mixture was found to require 29.5 cm3 of NaOH for neutralisation. Find the Kc for the reaction: CH3COOC2H5(l)+ H2O(l) CH3COOH(l) + C2H5OH(l) The equation of for the neutralisation reaction is: CH3COOH + NaOH  CH3COONa + H2O = 0.249 (no units)

Learning Objectives Define pH Calculate pH and H+ ion concentration for strong acids Define the ionic product for water Calculate the pH and the OH- ion concentration for strong bases

Defining pH pH = -log10[H+] 100 is 102 the logarithm to base 10 of 100 is 2 1000 is 103 the logarithm to base 10 of 1000 is 3 2 is 100.3010 the logarithm to base 10 of 2 is 0.3010 The logarithm to base 10 of a number is the power you have to raise 10 to in order to equal that number

Using your calculator To find log102: [2] [log][=] [0.301029995] OR To unlog use the 10x often found above the log button and using the shift key.

Calculating pH from hydrogen ion concentration What is the pH if [H+] = 0.1 mol dm-3 Find log10(0.1) = -1 NB: pH = -log10[H+] “-(-1) is 1” pH = 1

Calculating hydrogen ion concentration from pH NB: hydrogen ion concentrations will almost always be less than 1 mol dm-3 pH is 2.80 what is the hydrogen ion concentration? pH = -log10[H+] Rearranging this: log10[H+] = -pH log10[H+] = -2.80 [shift][log][-][2.8][=][1.58 x 10-3] = 1.58 x 10-3 mol dm-3

Questions Convert the following hydrogen ion concentrations (all in mol dm-3) into pHs 0.0100 0.0250 3.00 x 10-4 1.00 x 10-7 7.50 x 10-10

Convert the following pHs into hydrogen ion concentrations in mol dm-3 3.42 1.20 5.65 8.40 13.0

The pH of strong acids What is the pH of 0.1 mol dm-3 HCl? Because HCl is a strong acid every 1 mole of HCl is entirely split up into 1 mole of H+(aq) and 1 mole of Cl-(aq). The concentration of hydrogen ions is therefore exactly the same as the concentration of the acid [H+] = 0.1 pH = log10[H+] pH = -log10(0.1) pH = 1

What is the pH of 0.00100mol dm-3 H2SO4? H2SO4  2H+(aq) + SO42-(aq) [H+] = 2 x 0.0100 pH = – log10(0.0200) pH = 1.70

Finding the concentration of a strong acid from its pH Simply the reverse the process Convert pH into [H+] Use [H+] to find the concentration of the acid

What is the concentration of HCl whose pH is 1.60? “Unlogging” the pH gives [H+] = 0.0251 mol dm-3 If you got an answer of 39.8107 you forgot to make the pH ‘-’ before you unlogged it. As HCl is a monoprotic acid the concentration of the acid is the same as the concentration of the H+ ions.

What is the concentration of H2SO4, if its pH is 1.00? Sulfuric acid is diprotic. Unlogging th pH gives [H+] = 0.1 mol dm-3 Now stop and think: H2SO4(aq)  2H+(aq) + SO42-(aq) Each mole af acid gives 2 moles of H+(aq). There are only half the number of moles of acid as of H+ ions. The concentration of the acid is therefore 0.0500mol dm-3.

Calculate the pHs of the following strong acids 0.0300 mol dm-3 HCl 0.00500 mol dm-3 H2SO4 0.120 mol dm-3 HNO3

Calculate the pHs of the following strong acids 0.0300 mol dm-3 HCl 1.52 0.00500 mol dm-3 H2SO4 2.00 0.120 mol dm-3 HNO3 0.92

Calculate the concentrations of the following strong acids from their pHs HCl of pH 0.70 H2SO4 of pH 1.5 HNO3 of pH 2.0

Calculate the concentrations of the following strong acids from their pHs HCl of pH 0.70 0.2 mol dm-3 H2SO4 of pH 1.5 0.0016 mol dm-3 HNO3 of pH 2.0 0.010 mol dm-3

Ionic product of water Whenever liquid water is present, this equilibrium is established H2O(l) H+(aq)+ OH-(aq) Just like any other equilibrium, you can write an expression for the equilibrium constant Kc. You might expect it to look like this: Kc = [H+] [OH-] [H2O]

But it doesn’t! such a tiny amount of water ionises that the concentration of the water is effectively constant. You need to go to 9 significant figures before you noticed any change in the concentration of the wtare following ionisation!

Ionic product of water Kw = [H+][OH-] Kw is usually 1.00 x 10-14 The units are [concentration]2

Calculating the pH of pure water pH varies with temperature, The ionisation process is endothermic If the water is pure the concentrations of [H+] and [OH-] will be equal H2O(l) H+(aq) + OH-(aq)

If Kw is 1.00 x 10-14 mol2dm-6 (at 24oC) Kw = [H+][OH-] And [OH-] = [H+] because the water is pure So Kw = [H+]2 [H+]2 = 1.00x 10-14 [H+] = 1.00 x 10-7 pH = -log10 [H+] pH = 7.00

If Kw is 5.3 x 10-13 mol2dm-6 (at 100oC) pH = 6.14 The neutral point has moved from the more familiar value.

Calculate the pH of pure water at: 15oC Kw = 4.52 x 10-15 mol2dm-6 50oC Kw = 5.48 x 10-14 mol2dm-6

Calculate the pH of pure water at: 15oC Kw = 4.52 x 10-15 mol2dm-6 7.17 50oC Kw = 5.48 x 10-14 mol2dm-6 6.63

The pH of strong bases When most bases dissolve in water, the solution consist of free hydrated metal ions and hydroxide ions E.g NaOH(s) + aq  Na+(aq) + OH- (aq) Ca(OH)2(s) + aq  Ca2+(aq) + 2OH-(aq) Typical pHs are 13 or 14 This means [H+] is 10-13 or 10-14

Calculating the pH of a strong base Use the concentration of the base to find [OH-] Use Kw to find [H+] Convert [H+] into pH In the next examples I will take Kw to be 1.00 x 10-14 mol2dm-6

What is the pH of 0.10mol dm-3 NaOH? Each mole of NaOH gives 1 mole of OH- in solution, so the concentration of OH- is also 0.1 mol dm-3 Now use Kw and substitute in the value for [OH-] [H+][OH-] = 1.00 x 10-14 [H+] x 0.1 = 1.00 x 10-14 [H+] = 1.00 x 10-14/0.10 [H+]= 1.0 x 10-13 Convert [H+] into pH = 13

Finding the concentration of a strong base from its pH Again you reverse the process Convert pH into [H+] Use Kw to find [OH-] Use the [OH-] to find the concentration of the base.

What is the concentration of KOH solution if its pH is 12.8? “Unlog” the pH to give the [H+] pH =-log10[H+] 12.8 = -log10[H+] Log10[H+] = -12.8 [H+] = 1.585 x 10-13

Now use Kw to find [OH-] [H+][OH-] = 1.00 x 10-14 1.585 x 10-13 x [OH-] = 1.00 x 10-14 [OH-] = 1.00 x 10-14/1.585 x 10-13 [OH-] = 0.0631 mol dm-3 Because each mole of KOH produces 1 mole of OH-, the concentration of KOH = 0.0631 mol dm-3

What is the concentration of Ba(OH)2 if its pH is 12.0? “Unlogging” the pH gives [H+] = 1.00 x 10-12 Now use Kw to find [OH-]: [H+][OH-] = 1.00 x 10-14 1.00 x 10-12 x [OH-] = 1.00 x 10-14 [OH-] = 1.00 x 10-14/ 1.00 x 10 -12 [OH-] = 0.0100 mol dm-3 Each mole of Ba(OH)2 gives 2 moles of OH- this means the concentration will only be half = 0.00500mol dm-3

Calculate the pHs of the following strong bases 0.250 mol dm-3 NaOH 0.100 mol dm-3 Ba(OH)2 0.00500 mol dm-3 KOH

Calculate the pHs of the following strong bases 0.250 mol dm-3 NaOH 13.4 0.100 mol dm-3 Ba(OH)2 13.3 0.00500 mol dm-3 KOH 11.7

Calculate the concentrations of the following strong bases from their pHs NaOH of pH 13.2 Sr(OH)2 of pH 11.3

Calculate the concentrations of the following strong bases from their pHs NaOH of pH 13.2 0.158 mol dm-3 Sr(OH)2 of pH 11.3 1.00 x 10-3 mol dm-3

Summarise pH [OH-] log10 10x [H+] strong acids diprotic acids monoprotic acids Kw Strong bases

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