Titration Curves

1
UNIT IV

• Titration Curves

2
FINDING THE PH OF MIXTURES OF ACIDS AND BASES

• Mixing an acid and a base produces a solution
  which can be acidic, basic, or neutral depending
  on the relative amounts of reactants.
• NOTE In acid base reactions, if one or both of
  the reactants are strong then the reaction will
  go to completion.
• Only when both reactants are weak, will you get
  an equilibrium situation.
• Titrations always require reactions which go to
  completion (single arrow), so acid/base
  titrations will always have either a strong acid,
  a strong base, or both.

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FINDING THE PH OF MIXTURES OF ACIDS AND BASES

• Example
• If 3 moles of NaOH are mixed with 1 mole of HCl,
  what will happen?
• NaOH HCl ? H2O NaCl

4
FINDING THE PH OF MIXTURES OF ACIDS AND BASES

• Example
• 10.00 mL of 0.100M NaOH is mixed with 25.00 mL
  of 0.100 M HCl. Find the pH of the final
  (resulting) mixture.
• Balanced equation
• Initial moles of NaOH
• Initial moles of HCl

5
FINDING THE PH OF MIXTURES OF ACIDS AND BASES

• Excess moles
• H3O HCl in the final mixture
• pH
• Note Moles of acid or base may be determined
  from solids samples as well using molar mass.

6
FINDING THE PH OF MIXTURES OF ACIDS AND BASES

• Example40.00 mL of 0.100 M NaOH is mixed with
  25.00 mL of 0.100 M HCl. Calculate the pH of the
  resulting solution.

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FINDING THE PH OF MIXTURES OF ACIDS AND BASES

• Think of a diprotic acid as releasing 2 protons
  (Hs) to the base.
• (NOTE even though we learned that diprotic
  acids like H2SO4, donate only 1 proton
  completely, that was to WATER, not to a STRONG
  BASE. A STRONG BASE will take both the protons
  from H2SO4!)
• Dissociate bases to find out the number of OH-
  ions they provide.

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FINDING THE PH OF MIXTURES OF ACIDS AND BASES

• Example
• 15.00 mL of 0.100 M H2SO4 is mixed with 12.50 mL
  of 0.200 M NaOH. Calculate the pH of the
  resulting solution.
• Balanced equation
• Dissociations

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FINDING THE PH OF MIXTURES OF ACIDS AND BASES

• Initial moles of NaOH
• Initial moles of HCl
• Excess moles
• H3O
• pH
• Hebden Textbook page 143 Questions 58-68

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TITRATION CURVES

• Titration Curves a plot of pH as a function of
  volume of added titrant.

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STRONG ACID STRONG BASETITRATION CURVES

• We can calculate the pH of the mixture in the
  beaker throughout the titration. First, we
  separate the process into 3 stages
• INITIAL POINT Acid before any base is added
• EQUIVALENCE POINT Equivalence (Stoichiometric)
  Point
• FINAL POINT Base in excess

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STRONG ACID STRONG BASETITRATION CURVES

• 1. INITIAL POINT
• The beaker contains 25.00 mL of 0.100 M HCl.
  Calculate the pH.

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STRONG ACID STRONG BASETITRATION CURVES

• 2. EQUIVALENCE POINT
• 0.100 M NaOH is added to 25.00 mL of 0.100 M HCl.
  Find the volume of base added and calculate the
  pH.

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STRONG ACID STRONG BASETITRATION CURVES

• THE SALT FORMED FROM A SA-SB TITRATION IS ALWAYS
  NEUTRAL.
• Since there is no SA, no SB, and just H2O and a
  NEUTRAL salt, the pH of the solution formed will
  be 7.00.
• At the Equivalence (Stoichiometric)Point of
• a SASB Titration, the pH is always 7.00

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STRONG ACID STRONG BASETITRATION CURVES

• 3. FINAL POINT
• 26.00 mL of 0.100 M NaOH is added to 25.00 mL of
  0.100 M HCl. Find the pH of the resulting
  solution.

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STRONG ACID STRONG BASETITRATION CURVES
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WEAK ACID STRONG BASETITRATION CURVES

• Again, this type of titration has the 3 stages
• INITIAL POINT Acid before any base is added
• EQUIVALENCE POINT Equivalence (Stoichiometric)
  Point
• FINAL POINT Base in excess

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WEAK ACID STRONG BASETITRATION CURVES

• 1. INITIAL POINT
• Find the pH of 25.00 mL of 0.10 M CH3COOH before
  any base is added to it.

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WEAK ACID STRONG BASETITRATION CURVES

• We see that for a WEAK ACID STRONG BASE
  titration, the pH before the base is added is
  higher (ex. 2.87) than it was for a SA-SB
  titration (where the pH before the base is added
  is 1.00).
• For the same concentration, the weaker the acid,
  the HIGHER the pH will start out!

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WEAK ACID STRONG BASETITRATION CURVES

• A note about the BUFFER REGION
• 10.00 mL of 0.100 M NaOH is added to 25.00 mL of
  0.10 M CH3COOH.

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WEAK ACID STRONG BASETITRATION CURVES

• What we are left with is a mixture of a weak acid
  (CH3COOH) and the salt of its conjugate base
  (NaCH3COO).
• A mixture of a weak acid and a weak base (the
  salt of its conjugate base) is called a BUFFER
  SOLUTION.
•  
• As we will see later, a buffer solution is a
  solution which maintains the pH at a fairly
  constant value.
• This causes the titration curve to decrease in
  slope during this stage. The area on the curve
  is called the Buffer Region.
• (In Chem12, we will not need to be able to
  calculate the pH in a buffer solution.)

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WEAK ACID STRONG BASETITRATION CURVES

• 2. EQUIVALENCE POINT
• 0.100 M NaOH is added to 25.00 mL of 0.100 M
  CH3COOH.

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WEAK ACID STRONG BASETITRATION CURVES

• But, this time we must consider the salt
  (NaCH3COO) that is produced ? because it is NOT
  neutral!
• NaOH CH3COOH ? H2O NaCH3COO
• This salt that is produced (NaCH3COO) dissociates
  to form Na (spectator) and CH3COO- which
  undergoes base hydrolysis in water.

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WEAK ACID STRONG BASETITRATION CURVES

• We can now use the hydrolysis equation and an ICE
  table to calculate the OH- and then pOH and
  then pH

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WEAK ACID STRONG BASETITRATION CURVES

• For a WEAK ACID STRONG BASE Titration,
• the pH at Equivalence Point is ALWAYS gt 7
• This is because, when a weak acid reacts with a
  strong base, you always produce the conjugate
  base of the weak acid, which is BASIC.

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WEAK ACID STRONG BASETITRATION CURVES

• 3. FINAL POINT
• Looking at the Balanced equation
• NaOH CH3COOH ? H2O NaCH3COO
• Once NaOH is in excess, you will have some STRONG
  BASE (NaOH) and some WEAK BASE (CH3COO-) in the
  resulting mixture.
• The OH- contributed by the weak base (
  CH3COO-)was significant when there was no other
  base present (EP), but once a strong base (NaOH)
  is present, the OH- contributed by the weak base
  is insignificant compared to that produced by
  the NaOH.
• So, the titration curve past the EP for a WA/SB
  Titration is the same as it is for a SA/SB
  Titration (where NaOH is in excess).

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WEAK ACID STRONG BASETITRATION CURVE
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WEAK BASE STRONG ACIDTITRATION CURVE

• An example of a WB/SA Titration could be done
  with the strong acid HCl and the weak base NH3.  
• HCl NH3 ? NH4 Cl-
• The pH will start out high (base), but not too
  high (weak).

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WEAK BASE STRONG ACIDTITRATION CURVE

• When HCl is added but the NH3 is still in excess,
  we will have a mixture of NH3 (a weak base) and
  NH4 (a weak acid) which is a buffer.
• So again, we will have a buffer region as the pH
  goes down.

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WEAK BASE STRONG ACIDTITRATION CURVE

• At the equivalence point in this titration, all
  of the HCl and NH3 will be gone and only NH4 (a
  weak acid) and Cl- (a neutral spectator) will
  remain.
• Because there is a WEAK ACID (NH4) present,
  
  
  the pH will be LESS THAN 7. (but not
  
  
  really low). 

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WEAK BASE STRONG ACIDTITRATION CURVE
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SUMMARY
Reactants Salt Formed Is... pH at EP
Strong Acid Strong Base Neutral (conjugate base of SA) 7.00
Weak Acid Strong Base Basic (conjugate base of WA) gt 7.00
Strong Acid Weak Base Acidic (conjugate acid of WB) lt 7.00
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INDICATORS FOR TITRATIONS

• Indicators can be used to tell you when you have
  reached the equivalence (stoichiometric) point in
  a titration.
• However, different indicators must be used for
  different types of titrations.
• Ideally, the pH at the transition point (pKa) of
  the indicator will be the same as the pH at the
  equivalence point of the titration.
• pKa (indicator) pH at EP of Titration

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SELECTING A SUITABLE INDICATOR

• STRONG ACID-STRONG BASE TITRATION
• The best indicators would be Bromthymol Blue (6.0
  7.6), Phenol Red (6.6 8.0) or Neutral Red
  (6.8 8.0) as these all have pH 7 within their
  transition ranges.
• However, looking at the graph, there is an almost
  vertical line from pH 3 to pH 11 on the
  graph.
• (This means that VERY LITTLE volume change of
  base would give a huge change in pH. Any of the
  indicators from Bromcresol Green to
  Thymolphthalein would change colour in this pH
  range, so they would all work.)

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SELECTING A SUITABLE INDICATOR

• WEAK ACID-STRONG BASE TITRATION
• For a WA-SB Titration Curve, the vertical section
  is shorter than that of a SA-SB curve.
• This means that you have a more narrow range of
  suitable indicators. For this particular
  titration, any indicator which has pH 9 (8 -
  10) within its transition range is suitable.
• List all indicators suitable for a WA-SB
  Titration

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SELECTING A SUITABLE INDICATOR

• WEAK BASE-STRONG ACID TITRATION
• For a WB-SA Titration Curve, the vertical section
  is shorter than that of a SA-SB curve.
• For this particular titration, any indicator
  which has pH 5 (4 - 6) within its transition
  range is suitable.
• List all indicators suitable for a WB-SA
  Titration

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CALCULATIONS INVOLVING TITRATION CURVES

• I. Draw a Titration Curve Using THREE Points
• Example
• 0.10 M HNO3 is added to 25.0 mL of 0.10 M NaOH.
  Draw the titration curve you would expect would
  result from the following titration. Get the
  shape and the important points (IP, EP, FP) as
  close as you can.

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CALCULATIONS INVOLVING TITRATION CURVES

• Name an indicator which would be suitable for
  this titration. _________________________
• As you pass through the equivalence
  (stoichiometric) point in this titration, the
  colour of your indicator would change from
  _____________ to ____________ (to ____________)

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CALCULATIONS INVOLVING TITRATION CURVES

• II. Identify a Sample as Strong or Weak
• If we have a strong base (ex. NaOH or KOH) in the
  burette (Volume of base is on x axis), we can
  tell by the shape and by the pH at the beginning
  (Volume of Base 0) whether the acid is strong
  or weak (given the acid).

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CALCULATIONS INVOLVING TITRATION CURVES

• Example
• If we have a 0.10 M acid in the beaker and 0.10 M
  KOH in the burette and the titration curve looks
  like

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CALCULATIONS INVOLVING TITRATION CURVES

• Then we know that our acid must be a STRONG acid
  because the pH with no base added (Volume of Base
  0 ) is 1.0.
• This means
• H3O antilog (-pH) antilog (-1.0) 0.1 M
• So, since H3O acid we can see that this is
  a Strong Acid.
• Also the pH at EP 7, which also signifies that
  we have a strong acid.
• Note You could also calculate the initial
  concentration of the acid in this example from
  the volume of base added at the equivalence
  point.

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CALCULATIONS INVOLVING TITRATION CURVES

• III. Calculate the Ka of a Weak Acid (or Kb of a
  Weak Base)
• By using the pH at Volume of Base 0, we can
  calculate the Ka for a weak acid we are
  titrating.
• Look at the following example in which a 0.10 M
  weak acid is being titrated with 0.10 M NaOH.

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CALCULATIONS INVOLVING TITRATION CURVES

• Since pH 2.5, H3O antilog (-2.5)
• 3.16 x 10-3 M

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CALCULATIONS INVOLVING TITRATION CURVES

• Solve for Ka.

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CALCULATIONS INVOLVING TITRATION CURVES

• IV. Calculate the Concentration of Strong Base
  (or SA) Added
• When titrating a 25.0 mL sample of 0.10 M HCl
  with a solution of NaOH, the following titration
  curve was obtained. Calculate the NaOH in the
  burette
• 
  
  
• 
  
  
• 
  
  
  32 mL

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CALCULATIONS INVOLVING TITRATION CURVES

• We know that this is a SA-SB titration, so at the
  EP, pH 7.
• Also, the EP is always in the center of the
  almost vertical region.
• We mark the EP and draw a straight line down to
  see where it hits the Volume of Base axis.
• This will give us the Volume of NaOH needed to
  reach the equivalence point.

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CALCULATIONS INVOLVING TITRATION CURVES

• We see that the volume of NaOH needed to reach
  the equivalence point is approximately 32 mL.  
• Given this and the information at the beginning
  of the question, calculate the NaOH in the
  burette

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CALCULATIONS INVOLVING TITRATION CURVES

• Example
• The following titration curve results from
  titrating 25.0 mL of a 0.10 M weak acid HA with a
  strong base KOH
• 17 mL

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CALCULATIONS INVOLVING TITRATION CURVES

• a. Use this graph to estimate the Ka of the acid
  HA.
• b. Use this graph to calculate the KOH.

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SELECTING SOLUTIONS FOR ACID-BASE TITRATIONS

• If you are titrating an acid, make sure you use a
  base so that your titration reaction is a
  neutralization. It should have at least one
  STRONG reactant so it will go to completion.
• Also, the concentration of your standard should
  be relatively close to the concentration of the
  solution you are titrating so that the volumes
  used are comparable. (So you dont need buckets
  or a fraction of a drop).

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ASSIGNMENT

• 1. A 25.00 mL sample of H2SO4 was neutralized by
  67.82 mL of 0.125 M NaOH solution. Determine the
  concentration of H2SO4.

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ASSIGNMENT

• 2. A 35.0 mL sample of 0.500 M NaOH was titrated
  with 0.350 M unknown acid, HxA. It took 49.4 mL
  of the acid to reach the equivalence point.
  Determine the proton number of the acid.

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ASSIGNMENT

• 3. Hebden Textbook Page 167 Question 124

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ASSIGNMENT

• 4. A 15.00 mL sample of HBr was titrated with
  NaOH. A volume of 34.87 mL of 0.1250 M NaOH was
  required to reach the equivalence point.
• Determine the concentration of HBr.
• Sketch the titration curve.
• Name a good indicator to use.

55
ASSIGNMENT

• 5. A 20.00 mL sample of sulfuric acid was
  titrated with NaOH. A volume of 23.55 mL of
  0.1500 M NaOH was required to reach the
  equivalence point.
• Determine the concentration of sulfuric acid.
• Sketch the titration curve.
• Name a good indicator to use.

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ASSIGNMENT

• 6. 25.00 mL of acetic acid of unknown
  concentration was titrated with 0.10 M NaOH. The
  following data was obtained. Use EXCEL to plot
  the data with pH on the y-axis and volume of NaOH
  on the x-axis.
• Calculate the concentration of acetic acid.
• Calculate the Ka of acetic acid.

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Volume of NaOH (mL) pH
0.00 2.87
5.00 4.14
10.00 4.57
15.00 4.92
20.00 5.35
22.00 5.61
24.00 6.12
24.50 6.43
24.80 6.84
24.90 7.14
24.95 7.44
24.99 8.14
25.00 8.72
25.01 9.30
25.05 10.00
25.10 10.30
25.20 10.60
25.50 11.00
26.00 11.29
28.00 11.75
30.00 11.96
40.00 12.36
50.00 12.52
58
ASSIGNMENT

• 7. A 15.00 mL sample of hydrofluoric acid, HF,
  was titrated with 28.13 mL of 0.100 M KOH.
• Determine the concentration of hydrofluoric acid.
• Sketch the titration curve.
• Is the pH at the equivalence point neutral,
  basic, or acidic? Explain your answer with
  equations. (Calculate pH at EP?!!)
• List 2 indicators which would be good for this
  titration.

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ASSIGNMENT

• 8. Draw the titration curve (IP, EP, FP) when
  40.0 mL of 1.00 M sodium hydroxide is added to
  10.0 mL of 1.50 M acetic acid.

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ASSIGNMENT

• 9. Data
• 25.00 mL of weak base A-1 with an unknown
  concentration
• 19.22 mL of 0.113 M HCl was used to reach the
  equivalence point
• initial pH 11.855
• Determine the concentration of A-1 .
• Determine the Kb of A-1 from the data given.

61
ASSIGNMENT

• 10. What colour is a solution of chlorophenol red
  in 1.0 x 10-4 M HCl?

62
ASSIGNMENT

• 11. Determine the Ka of phenol red indicator.

63
ASSIGNMENT

• 12. The indicator Hin is clear in acids and pink
  in bases. What colour is the anion In-1?

64
ASSIGNMENT

• 13. 3.000 g of the diprotic acid oxalic acid
  dihydrate (126.07 g/mol) was used to make a 100.0
  mL solution. 20.00 mL of the oxalic acid
  solution was used to titrate an unknown NaOH
  solution. It took 48.21 mL of NaOH solution to
  neutralize the oxalic acid solution. Determine
  the concentration of the NaOH.

65
ASSIGNMENT

• 14. Which indicator could be used in a titration
  of HF and KOH?
• Bromcresol green?
• Bromthymol blue?
• Thymolphthalein?