Titration

Titration of a Strong Acid by a Strong Base

Consider what happens to the pH of 25 mL of 0.2 M HCl as it is titrated with 25 mL of 0.2 M NaOH. This result is shown in the diagram to the right. The diagram is referred to as a ___________________ _____________. As you add base, [H+] ____________ and pH ___________ until what happens?

Ex #1: The following quantities of 0.100 M NaOH have been added to 50.0 mL of 0.100 M HCl. Calculate the pH of the

resulting solutions.

a. 49.00 mLb. 50.00 mLc. 50.10 mLd. 51.00 mL 

Titration of a Strong Acid by a Strong Base

a. 49.00 mLb. 50.00 mLc. 50.10 mLd. 51.00 mL 

Because the pH change for strong/strong titrations is large near the equivalence point, the indicator need not change color at exactly pH = 7. Phenolphthalein is often the choice for strong/strong titrations. Its color change occurs during a pH change of 8.3 to 10, but just a slight excess (a few drops) of the titrant will cause this change.

Titration of a Strong Acid by a Strong BaseEx #1: The following quantities of 0.100 M NaOH have

been added to 50.0 mL of 0.100 M HCl. Calculate the pH of the resulting solutions.

Titration of a Weak Acid with a Strong Base

Calculating the pH of the weak acid depends on where you are in the titration process.

HC2H3O2 + Na+ + OH- Na+ + C2H3O2- + H2O

Titration Process1) Before the titration starts2) Before the equivalence point is

reached3) At the equivalence point4) After the equivalence point has been

reached HC2H3O2

NaOH

Consider the titration of acetic acid with sodium hydroxide.

Titration of a Weak Acid with a Strong Base

Titration Process1) Before the titration starts

HC2H3O2

NaOH

Consider the titration of acetic acid with sodium hydroxide.

Initially, we just consider the acetic acid before any base is added. To calculate the pH, follow the same process as calculating the pH of a weak acid.

Calculating the pH of the weak acid depends on where you are in the titration process.

HC2H3O2 ↔ C2H3O2- + H2O

Titration of a Weak Acid with a Strong Base

Titration Process2) Before the equivalence point is reached

HC2H3O2

NaOH

Consider the titration of acetic acid with sodium hydroxide.

Think about what species are present so that we approach the problem from the correct perspective.

 The equation shows that since both HC2H3O2 and C2H3O2

-- are present, this becomes a _______ problem.

Calculating the pH of the weak acid depends on where you are in the titration process.

HC2H3O2 ↔ C2H3O2- + H2O

Titration of a Weak Acid with a Strong Base

Titration Process3) At the equivalence point

HC2H3O2

NaOH

Consider the titration of acetic acid with sodium hydroxide.

At the equivalence point, for a strong acid with a strong base, the pH = ______. This is not the case for a weak acid problem. Why?

Calculating the pH of the weak acid depends on where you are in the titration process.

HC2H3O2 + Na+ + OH- Na+ + C2H3O2- + H2O

Titration of a Weak Acid with a Strong Base

Titration Process4) After the equivalence point has

been reached

HC2H3O2

NaOH

Consider the titration of acetic acid with sodium hydroxide.

After the equivalence point has been reached, the additional OH-- has nothing left to react with so the pH is determined by __________________________________.

Calculating the pH of the weak acid depends on where you are in the titration process.

Titration of a Weak Acid with a Strong Base

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Since the molarities are equal and the acid is monoprotic, we will need _______ mL of NaOH to reach the equivalence point.

Why is it important to realize this before we begin the problem?

25

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

Initially, we just consider the acetic acid before any base is added. To calculate the pH, follow the same process as calculating the pH of a weak acid.

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

HC2H3O2 ↔ H+ + C2H3O2-

2 3 2

2 3 2

+

a

HK =

C H O

HC H O

 R [HC2H3O2] ↔ [H+] [C2H3O2

-]I 0.2 0 0C -x +x +xE 0.2-x x x

-5 ( )( )1.8x10 = (0.2 )x x

x2

-5 ( )1.8x10 = (0.2)x

-6

-3 +

3.6x10 = x

1.9x10 = x=[H ]

-3pH=-log(1.9x10 )pH=2.72

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

HC2H3O2 ↔ H+ + C2H3O2-

2 3 2

2 3 2

+

a

HK =

C H O

HC H O

 R [HC2H3O2] ↔ [H+] [C2H3O2-]

I 0.2 0 0C -x +x +xE 0.2-x x x

-5 ( )( )1.8x10 = (0.2 )x x

x2

-5 ( )1.8x10 = (0.2)x

-6

-3 +

3.6x10 = x

1.9x10 = x=[H ]

-3pH=-log(1.9x10 )pH=2.72

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

HC2H3O2 ↔ H+ + C2H3O2-

2 3 2

2 3 2

+

a

HK =

C H O

HC H O

 R [HC2H3O2] ↔ [H+] [C2H3O2-]

I 0.2 0 0C -x +x +xE 0.2-x x x

-5 ( )( )1.8x10 = (0.2 )x x

x2

-5 ( )1.8x10 = (0.2)x

-6

-3 +

3.6x10 = x

1.9x10 = x=[H ]

-3pH=-log(1.9x10 )pH=2.72

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

HC2H3O2 ↔ H+ + C2H3O2-

2 3 2

2 3 2

+

a

HK =

C H O

HC H O

 R [HC2H3O2] ↔ [H+] [C2H3O2-]

I 0.2 0 0C -x +x +xE 0.2-x x x

-5 ( )( )1.8x10 = (0.2 )x x

x2

-5 ( )1.8x10 = (0.2)x

-6

-3 +

3.6x10 = x

1.9x10 = x=[H ]

-3pH=-log(1.9x10 )pH=2.72

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

HC2H3O2 ↔ H+ + C2H3O2-

2 3 2

2 3 2

+

a

HK =

C H O

HC H O

 R [HC2H3O2] ↔ [H+] [C2H3O2-]

I 0.2 0 0C -x +x +xE 0.2-x x x

-5 ( )( )1.8x10 = (0.2 )x x

x2

-5 ( )1.8x10 = (0.2)x

-6

-3 +

3.6x10 = x

1.9x10 = x=[H ]

-3pH=-log(1.9x10 )pH=2.72

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

HC2H3O2 ↔ H+ + C2H3O2-

2 3 2

2 3 2

+

a

HK =

C H O

HC H O

 R [HC2H3O2] ↔ [H+] [C2H3O2-]

I 0.2 0 0C -x +x +xE 0.2-x x x

-5 ( )( )1.8x10 = (0.2 )x x

x2

-5 ( )1.8x10 = (0.2)x

-6

-3 +

3.6x10 = x

1.9x10 = x=[H ]

-3pH=-log(1.9x10 )pH=2.72

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

HC2H3O2 ↔ H+ + C2H3O2-

2 3 2

2 3 2

+

a

HK =

C H O

HC H O

 R [HC2H3O2] ↔ [H+] [C2H3O2-]

I 0.2 0 0C -x +x +xE 0.2-x x x

-5 ( )( )1.8x10 = (0.2 )x x

x2

-5 ( )1.8x10 = (0.2)x

-6

-3 +

3.6x10 = x

1.9x10 = x=[H ]

-3pH=-log(1.9x10 )pH=2.72

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

HC2H3O2 ↔ H+ + C2H3O2-

2 3 2

2 3 2

+

a

HK =

C H O

HC H O

 R [HC2H3O2] ↔ [H+] [C2H3O2-]

I 0.2 0 0C -x +x +xE 0.2-x x x

-5 ( )( )1.8x10 = (0.2 )x x

x2

-5 ( )1.8x10 = (0.2)x

-6

-3 +

3.6x10 = x

1.9x10 = x=[H ]

-3pH=-log(1.9x10 )pH=2.72

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

HC2H3O2 ↔ H+ + C2H3O2-

2 3 2

2 3 2

+

a

HK =

C H O

HC H O

 R [HC2H3O2] ↔ [H+] [C2H3O2-]

I 0.2 0 0C -x +x +xE 0.2-x x x

-5 ( )( )1.8x10 = (0.2 )x x

x2

-5 ( )1.8x10 = (0.2)x

-6

-3 +

3.6x10 = x

1.9x10 = x=[H ]

-3pH=-log(1.9x10 )pH=2.72

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

HC2H3O2 ↔ H+ + C2H3O2-

2 3 2

2 3 2

+

a

HK =

C H O

HC H O

 R [HC2H3O2] ↔ [H+] [C2H3O2-]

I 0.2 0 0C -x +x +xE 0.2-x x x

-5 ( )( )1.8x10 = (0.2 )x x

x2

-5 ( )1.8x10 = (0.2)x

-6

-3 +

3.6x10 = x

1.9x10 = x=[H ]

-3pH=-log(1.9x10 )pH=2.72

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

HC2H3O2 ↔ H+ + C2H3O2-

2 3 2

2 3 2

+

a

HK =

C H O

HC H O

 R [HC2H3O2] ↔ [H+] [C2H3O2-]

I 0.2 0 0C -x +x +xE 0.2-x x x

-5 ( )( )1.8x10 = (0.2 )x x

x2

-5 ( )1.8x10 = (0.2)x

-6

-3 +

3.6x10 = x

1.9x10 = x=[H ]

-3pH=-log(1.9x10 )pH=2.72

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

HC2H3O2 ↔ H+ + C2H3O2-

2 3 2

2 3 2

+

a

HK =

C H O

HC H O

 R [HC2H3O2] ↔ [H+] [C2H3O2-]

I 0.2 0 0C -x +x +xE 0.2-x x x

-5 ( )( )1.8x10 = (0.2 )x x

x2

-5 ( )1.8x10 = (0.2)x

-6

-3 +

3.6x10 = x

1.9x10 = x=[H ]

-3pH=-log(1.9x10 )pH=2.72

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

HC2H3O2 ↔ H+ + C2H3O2-

2 3 2

2 3 2

+

a

HK =

C H O

HC H O

 R [HC2H3O2] ↔ [H+] [C2H3O2-]

I 0.2 0 0C -x +x +xE 0.2-x x x

-5 ( )( )1.8x10 = (0.2 )x x

x2

-5 ( )1.8x10 = (0.2)x

-6

-3 +

3.6x10 = x

1.9x10 = x=[H ]

-3pH=-log(1.9x10 )pH=2.72

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

HC2H3O2 ↔ H+ + C2H3O2-

2 3 2

2 3 2

+

a

HK =

C H O

HC H O

 R [HC2H3O2] ↔ [H+] [C2H3O2-]

I 0.2 0 0C -x +x +xE 0.2-x x x

-5 ( )( )1.8x10 = (0.2 )x x

x2

-5 ( )1.8x10 = (0.2)x

-6

-3 +

3.6x10 = x

1.9x10 = x=[H ]

-3pH=-log(1.9x10 )pH=2.72

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

HC2H3O2 ↔ H+ + C2H3O2-

2 3 2

2 3 2

+

a

HK =

C H O

HC H O

 R [HC2H3O2] ↔ [H+] [C2H3O2-]

I 0.2 0 0C -x +x +xE 0.2-x x x

-5 ( )( )1.8x10 = (0.2 )x x

x2

-5 ( )1.8x10 = (0.2)x

-6

-3 +

3.6x10 = x

1.9x10 = x=[H ]

-3pH=-log(1.9x10 )pH=2.72

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

HC2H3O2 ↔ H+ + C2H3O2-

2 3 2

2 3 2

+

a

HK =

C H O

HC H O

 R [HC2H3O2] ↔ [H+] [C2H3O2-]

I 0.2 0 0C -x +x +xE 0.2-x x x

-5 ( )( )1.8x10 = (0.2 )x x

x2

-5 ( )1.8x10 = (0.2)x

-6

-3 +

3.6x10 = x

1.9x10 = x=[H ]

-3pH=-log(1.9x10 )pH=2.72

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Titration of a Weak Acid with a Strong Base

1) What is the pH before titration?

HC2H3O2 ↔ H+ + C2H3O2-

2 3 2

2 3 2

+

a

HK =

C H O

HC H O

 R [HC2H3O2] ↔ [H+] [C2H3O2-]

I 0.2 0 0C -x +x +xE 0.2-x x x

-5 ( )( )1.8x10 = (0.2 )x x

x2

-5 ( )1.8x10 = (0.2)x

-6

-3 +

3.6x10 = x

1.9x10 = x=[H ]

-3pH=-log(1.9x10 )pH=2.72

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

2) What is the pH after 10.00 mL of the base has been added?

Titration of a Weak Acid with a Strong Base

Think about what species are present so that we approach the problem from the correct perspective.

 The equation shows that since both HC2H3O2 and C2H3O2

-- are present, this becomes a _______ problem.

HC2H3O2 ↔ C2H3O2- + H2O

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

2) What is the pH after 10.00 mL of the base has been added?

Titration of a Weak Acid with a Strong Base

HC2H3O2 ↔ C2H3O2- +

H2O

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

 R HC2H3O2 OH- H2O C2H3O2-

I (0.2M)(25x10-3L)=0.005

(0.2M)(10x10-3L)=0.002 0

C - 0.002 - 0.002 + 0.002

Final 0.003 0 0.002

HC2H3O2 + OH- C2H3O2- +

H2O

 R [HC2H3O2] ↔ [H+] [C2H3O2-]

I 0.003mol/35x10-3L=0.0857 M 0 0.002mol/35x10-3L

=0.057 MC -x +x +x

E 0.2-x x x

Convert to M (divide by 35 x 10-3L)

2 3 2

2 3 2

+

a

HK =

C H O

HC H O

+ 2-5

2

+ -5

H (5.71 10 )1.8x10 =

(8.57 10 )

H 2.7x10

4.57

x

x

M

pH

Use moles in this chart!

3) What is the pH when 25 mL of the base is added?

Titration of a Weak Acid with a Strong Base

At the equivalence point, for a strong acid with a strong base, the pH = ______. This is not the case for a weak acid problem. Why?

HC2H3O2 + Na+ + OH- Na+ + C2H3O2- + H2O

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

4) What is the pH after 26 mL of NaOH has been added?

Titration of a Weak Acid with a Strong Base

After the equivalence point has been reached, the additional OH-- has nothing left to react with so the pH is determined by ______________________________.

25mL reacts, 1mL of NaOH left

3 4

43

3

3

0.2? 1 10 2 101

2 10 3.92 1051 10

log(3.92 10 )2.4

11.59

molmolOH x L x molL

x mol x MOHx L

pOH xpOHpH

Ex. 25.0mL of 0.200 M HC2H3O2 is titrated with 0.200 M NaOH.

Conclusions for Titrations of Weak Acids

1. The pH of a weak acid is ___________ initially than a strong acid of the same concentration because

 

2. The pH rises rapidly in the early part of a titration, but more slowly near the _____________ ________ because

 

3. The pH at the equivalence point is not _________ because

Titration of a Weak Acid with a Strong Base

HC2H3O2

NaOH

The titration curve for a weak acid with a strong base is similar to the curve for a strong acid with a strong base. Construct a titration curve for this problem and compare it to the curve for a strong/strong titration.