How to Interpret Titration Curves• find the equivalence point

– it is the steepest part of the curve where the pH rises the fastest

– the equivalence point can be used to determine the equivalent weight (molar mass) of the acid

• find the mid point– located in the center of the buffer region– geometrically halfway between the equivalence

point and the beginning of the titration– sometimes it is a little more complicated than this

- see the example– the midpoint determines the pKa of the acid

How to Interpret Titration Curves• things to do first

– graph your data as seen in the next slide– make sure you turn on the major and minor tick

marks on both axes• right click on the axis, choose Format Axis…, change

Major/Minor Tick Mark settings

– Is there enough precision in the tick marks?• you should have at least 1 mL or smaller for the minor

tick mark on the x-axis

• you should have at least 0.2 pH units or smaller for the minor tick mark on the y-axis

• Format Axis…, change Major/Minor Units

Two Different Methods• there are two methods of analysis that will be

shown– geometric method

• requires a ruler, a pencil, and the titration graph

– 1st derivative method• requires a spreadsheet and some formula entries

• gives you cool graphs with the 1st derivative pointing to the equivalence and mid points

• scores you brownie points with the instructors

• pick your method (either will work)

Weak Acid Titration Curve

2

4

6

8

10

12

0 10 20 30 40 50

Buret Volume (mL)

pH

equivalence point

mid point

A Typical Titration Curve

Weak Acid Titration Curve

2

4

6

8

10

12

0 10 20 30 40 50

Buret Volume (mL)

pH

equivalence point

Find the Equivalence Point (Geometric method)

1) using a ruler, draw lines that follow the flat, more horizontal part of the curve

2) draw a line that follows the flat, more vertical part of the curve

Weak Acid Titration Curve

2

4

6

8

10

12

0 10 20 30 40 50

Buret Volume (mL)

pH

equivalence point

Find the Equivalence Point (Geometric method)

3) using a ruler, measure the distance between the top intersection and the bottom intersection

4) the geometric center of this line segment is the equivalence point

Weak Acid Titration Curve

2

4

6

8

10

12

0 10 20 30 40 50

Buret Volume (mL)

pH

equivalence point

Find the Equivalence Point (Geometric method)

5) draw a vertical line from the equivalence point to the x-axis

6) where the line crosses the x-axis is the volume at the equivalence point

(28.7 mL in this case)

Weak Acid Titration Curve

2

4

6

8

10

12

0 10 20 30 40 50

Buret Volume (mL)

pH

mid point

Find the Mid Point (Geometric method)

1) if there is a steep rise in the pH at the beginning of the graph, draw a line that follows the steep part of the curve

Weak Acid Titration Curve

2

4

6

8

10

12

0 10 20 30 40 50

Buret Volume (mL)

pH

equivalence point

Find the Mid Point (Geometric method)

2) using a ruler, measure the distance between the far left and right intersections

3) the geometric center between these points is the mid point

mid point

Weak Acid Titration Curve

2

4

6

8

10

12

0 10 20 30 40 50

Buret Volume (mL)

pH

equivalence point

Find the Mid Point (Geometric method)

4) draw a horizontal line from the mid point to the y-axis

5) where the line crosses the y-axis is the pH at the equivalence point

(pH = 7.2 in this case)mid point

How to Interpret Titration Curves• find the equivalence point

– make sure you subtract the initial buret volume!– in this case, the initial buret volume was 1.07 mL

– true equiv. pt. = 28.7 mL - 1.07 mL = 27.63 mL

– the 3 is the indicate the limit of the significant figures

• calculate the equivalent weight (molar mass)– equiv. wt. = (acid mass)/[(NaOH conc)(equiv. pt.)]

– equiv. wt. = (430.2 mg)/[(0.1139 M)(27.63mL)]

– equiv. wt. = 136.699 = 137 g/mol

How to Interpret Titration Curves• find the mid point

– mid pt = 7.2 = pKa of the acid

For you Excel Aficionados• equivalence point

– use the first derivative d pH / d Vol– plot volume as x and 1st derivative as y in a 2nd series on graph– the spike in the graph points to the equiv. pt.

• mid point– make a new graph and reverse the axes for the pH curve

• x axis = pH values; y-axis = Vol values

– use the first derivative d Vol / d pH– plot pH as x and 1st derivative as y in a 2nd series on graph– the spike in the graph points to the mid point

• use extra columns in the spreadsheet to make these calcs– equiv. pt. deriv. (d pH / d Vol) = (pH2 - pH1)/(Vol2 - Vol1)– midpoint deriv. (d Vol / d pH) = (Vol2 - Vol1)/ (pH2 - pH1)

• or just the reciprocal of the equiv. pt. derivative

Weak Acid Titration Curve

2

4

6

8

10

12

0 10 20 30 40 50

Buret Volume (mL)

pH

0

1

2

3

4

5

6

7

1st

Der

ivat

ive

(mL

-1)

pH

1st deriv.

Find the Equivalence Point (derivative method)

1) identify volume value at the peak

1) identify volume value at the peak

(28.5 mL in this case)

Weak Acid Titration Curve

05

101520253035404550

2 4 6 8 10 12

pH

Bu

ret

Vo

lum

e (m

L)

0

5

10

15

20

25

30

35

40

1st

Der

ivat

ive

(mL

)mL

1st deriv.

Find the Mid Point (derivative method)

1) identify pH value at the peak

(pH = 7.3 in this case)