1

Determining the Concentration of a Mixture of HCl and H3PO4 by

Potentiometric Titration

Michelle Arsjad

Purpose

The purpose of this experiment was to determine the respective concentrations of HCl and H3PO4 in

a concentration of their mixture. The respective concentrations of HCL and H3PO4 will be

determined through a potentiometric titration against NaOH. Using first and second derivative

graphs of the data obtained, the endpoints of the titration will be determined and used to accurately

calculate the concentrations of the acids.

Data and Observations

Qualitative:

No color change observed, as no indicator was used.

Quantitative:

Table 1: Titration 1 (Not used for calculations)

Buret Reading (ml) pH

1 0.7 1.64

2 1.6 1.69

3 2.5 1.72

4 3.7 1.74

5 4.7 1.79

6 5.7 1.83

7 6.8 1.89

8 8 1.96

9 9.1 2.08

10 10.2 2.11

11 11.2 2.19

12 12.15 2.28

13 13.45 2.43

14 14.6 2.61

15 15.3 2.75

16 16.5 3.11

17 17.4 4.55

18 18 6.11

19 20.05 7.18

20 22 7.79

21 24 10.81

22 24.9 11.19

23 25.9 11.39

24 26.95 11.52

Table 2: Titration 2

Buret Reading (ml) pH

1 14.2 1.77

2 15.25 1.79

3 16.2 1.81

4 17.2 1.84

5 18.3 1.87

6 19.15 1.9

7 20.2 1.96

8 21.25 2.02

9 22.2 2.07

10 2.3 2.14

11 25.2 2.31

12 27 2.54

13 27.7 2.7

14 28.1 2.78

15 28.7 2.98

16 29.1 3.17

17 29.3 3.28

18 29.4 3.35

19 29.5 3.48

20 29.6 3.6

21 29.75 3.8

22 29.8 3.91

23 29.9 4.36

24 30 5.18

2

25 30.1 5.54

26 30.2 5.82

27 30.3 5.96

28 30.4 6.09

29 30.5 6.27

30 31 6.58

31 31.5 6.83

32 32 7.03

33 33 7.34

34 33.5 7.52

35 34.1 7.74

36 34.9 8.21

37 35 8.29

38 35.1 8.55

39 35.2 8.76

40 35.3 9.22

41 35.4 9.78

42 35.5 10.1

43 35.6 10.39

44 35.7 10.5

45 35.8 10.67

46 35.9 10.67

47 36.5 11.02

48 37.55 11.22

49 38.85 11.5

50 39.9 11.62

51 41 11.69

52 42.1 11.77

53 44 11.88

Table 3: Titration 3

Buret Reading (ml) pH

1 12.2 1.79

2 14.2 1.81

3 15.3 1.83

4 17.2 1.88

5 19 1.95

6 20.55 2.06

7 22 2.14

8 23.05 2.22

9 24.1 2.33

10 25.6 2.54

11 26.5 2.72

12 27.3 2.94

13 27.4 2.99

14 27.55 3.08

15 27.6 3.09

16 27.7 3.2

17 27.75 3.24

18 27.8 3.28

19 28 3.3

20 28.2 3.47

21 28.5 3.97

22 28.6 4.36

23 28.7 5.06

24 28.8 5.55

25 28.9 5.85

26 29.15 6.15

27 30.5 6.91

28 31.5 7.28

29 32.55 7.53

30 33.6 7.98

31 34 8.58

32 34.1 8.62

33 34.2 9.08

34 34.3 9.61

35 34.4 9.94

36 34.5 10.32

37 34.65 10.45

38 35 10.84

39 35.5 11.08

40 36.5 11.32

41 37.5 11.49

42 38 11.54

43 40 11.68

44 42.1 11.82

3

Data Analysis

Step 1: Calculating 1st Derivative

pH2 − pH1

Vol2 − Vol1=

(1.79 − 1.77)

(1.05 − 0)= 0.019048

Vol2 + Vol12

=1.05 + 0

2= 0.525 ml

Step 2: Calculating 2nd Derivative

∆pH/∆vol2 − ∆pH/∆vol1𝑉𝑜𝑙2 − 𝑉𝑜𝑙1

=(0.021053 − 0.019048)

(1.525 − 0.525)= 0.00200501

𝑉𝑜𝑙2 + 𝑉𝑜𝑙1

2=

1.525 + 0.525

2= 1.025 𝑚𝑙

Table 4: Calculations for Titration 2

*yellow highlighted cells below refer to the smaller volume ranges for the two areas of interests

Buret Reading pH

Total Vol. NaOH Added

∆pH/∆vol

Average Volume

∆2pH/∆2vol

Average Volume

14.2 1.77 0

15.25 1.79 1.05 0.019048 0.525

16.2 1.81 2 0.021053 1.525 0.00200501 1.025

17.2 1.84 3 0.03 2.5 0.00917679 2.0125

18.3 1.87 4.1 0.027273 3.55 -0.0025974 3.025

19.15 1.9 4.95 0.035294 4.525 0.00822707 4.0375

20.2 1.96 6 0.057143 5.475 0.02299867 5

21.25 2.02 7.05 0.057143 6.525 0 6

22.2 2.07 8 0.052632 7.525 -0.0045113 7.025

23.3 2.14 9.1 0.063636 8.55 0.01073638 8.0375

25.2 2.31 11 0.089474 10.05 0.01722488 9.3

27 2.54 12.8 0.127778 11.9 0.02070492 10.975

27.7 2.7 13.5 0.228571 13.15 0.08063492 12.525

28.1 2.78 13.9 0.2 13.7 -0.0519481 13.425

28.7 2.98 14.5 0.333333 14.2 0.26666667 13.95

29.1 3.17 14.9 0.475 14.7 0.28333333 14.45

29.3 3.28 15.1 0.55 15 0.25 14.85

29.4 3.35 15.2 0.7 15.15 1 15.075

29.5 3.48 15.3 1.3 15.25 6 15.2

29.6 3.6 15.4 1.2 15.35 -1 15.3

29.75 3.8 15.55 1.333333 15.475 1.06666667 15.4125

29.8 3.91 15.6 2.2 15.575 8.66666667 15.525

29.9 4.36 15.7 4.5 15.65 30.6666667 15.6125

30 5.18 15.8 8.2 15.75 37 15.7

30.1 5.54 15.9 3.6 15.85 -46 15.8

30.2 5.82 16 2.8 15.95 -8 15.9

30.3 5.96 16.1 1.4 16.05 -14 16

4

30.4 6.09 16.2 1.3 16.15 -1 16.1

30.5 6.27 16.3 1.8 16.25 5 16.2

31 6.58 16.8 0.62 16.55 -3.9333333 16.4

31.5 6.83 17.3 0.5 17.05 -0.24 16.8

32 7.03 17.8 0.4 17.55 -0.2 17.3

33 7.34 18.8 0.31 18.3 -0.12 17.925

33.5 7.52 19.3 0.36 19.05 0.06666667 18.675

34.1 7.74 19.9 0.366667 19.6 0.01212121 19.325

34.9 8.21 20.7 0.5875 20.3 0.31547619 19.95

35 8.29 20.8 0.8 20.75 0.47222222 20.525

35.1 8.55 20.9 2.6 20.85 18 20.8

35.2 8.76 21 2.1 20.95 -5 20.9

35.3 9.22 21.1 4.6 21.05 25 21

35.4 9.78 21.2 5.6 21.15 10 21.1

35.5 10.1 21.3 3.2 21.25 -24 21.2

35.6 10.39 21.4 2.9 21.35 -3 21.3

35.7 10.5 21.5 1.1 21.45 -18 21.4

35.8 10.67 21.6 1.7 21.55 6 21.5

35.9 10.67 21.7 0 21.65 -17 21.6

36.5 11.02 22.3 0.583333 22 1.66666667 21.825

37.55 11.22 23.35 0.190476 22.825 -0.4761905 22.4125

38.85 11.5 24.65 0.215385 24 0.02119866 23.4125

39.9 11.62 25.7 0.114286 25.175 -0.0860416 24.5875

41 11.69 26.8 0.063636 26.25 -0.0471157 25.7125

42.1 11.77 27.9 0.072727 27.35 0.00826446 26.8

44 11.88 29.8 0.057895 28.85 -0.0098884 28.1

Graph 1: Titration Curve for Titration 2

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30

pH

Volume of NaOH Added (ml)

Titration Curve

5

Graph 2: Titration Curve for Titration 2/End Point 1

Graph 3: Titration Curve for Titration 2/End Point 2

0

1

2

3

4

5

6

7

8

14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5

pH

Volume of NaOH Added (ml)

Titration 2- End Point 1

15.75 ml

0

2

4

6

8

10

12

14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5

pH

Volume of NaOH Added (ml)

Titration 2- End Point 2

21.1 ml

6

Graph 4: 1ST Derivative Curve for Titration 2

Graph 5: 1ST Derivative Curve for Titration 2/End Point 1

0

1

2

3

4

5

6

7

8

9

0 5 10 15 20 25 30

∆p

H/∆

vol

Volume of NaOH Added (ml)

∆pH/∆vol vs. Average Volume- Titration 2

15.75 ml

0

1

2

3

4

5

6

7

8

9

14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5

∆p

H/∆

vol

Volume of NaOH Added (ml)

∆pH/∆vol vs. Average Volume- Titration 2/End Point 1

7

Graph 6: 1ST Derivative Curve for Titration 2/End Point 2

Graph 7: 2nd Derivative Curve for Titration 2

21.15 mL,

0

1

2

3

4

5

6

14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5

∆p

H/∆

vol

Volume of NaOH Added (ml)

∆pH/∆vol vs. Average Volume- Titration 2/End Point 2

-60

-50

-40

-30

-20

-10

0

10

20

30

40

50

0 5 10 15 20 25 30

∆2

pH

/∆2

vol

Volume of NaOH Added (ml)

∆2pH/∆2vol vs. Average Volume- Titration 2

8

Graph 8: 2nd Derivative Curve for Titration 2/End Point 1

Graph 9: 2nd Derivative Curve for Titration 2/End Point 2

-60

-50

-40

-30

-20

-10

0

10

20

30

40

50

14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5

∆2

pH

/∆2

vol

Volume of NaOH Added (ml)

∆2pH/∆2vol vs. Average Volume- Titration 2/End Point 1

15.8 ml

-30

-20

-10

0

10

20

30

14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5

∆2

pH

/∆2

vol

Volume of NaOH Added (ml)

∆2pH/∆2vol vs. Average Volume- Titration 2/End Point 2

21.15 ml

9

Table 5: Calculations for Titration 3

Buret Reading pH

Total Vol. NaOH Added ∆pH/∆vol

Average Volume ∆2pH/∆2vol

Average Volume

12.2 1.79 0

14.2 1.81 2 0.01 1

15.3 1.83 3.1 0.018182 2.55 0.00527859 1.775

17.2 1.88 5 0.026316 4.05 0.00542265 3.3

19 1.95 6.8 0.038889 5.9 0.00679627 4.975

20.55 2.06 8.35 0.070968 7.575 0.01915155 6.7375

22 2.14 9.8 0.055172 9.075 -0.0105302 8.325

23.05 2.22 10.85 0.07619 10.325 0.01681445 9.7

24.1 2.33 11.9 0.104762 11.375 0.02721088 10.85

25.6 2.54 13.4 0.14 12.65 0.02763772 12.0125

26.5 2.72 14.3 0.2 13.85 0.05 13.25

27.3 2.94 15.1 0.275 14.7 0.08823529 14.275

27.4 2.99 15.2 0.5 15.15 0.5 14.925

27.55 3.08 15.35 0.6 15.275 0.8 15.2125

27.6 3.09 15.4 0.2 15.375 -4 15.325

27.7 3.2 15.5 1.1 15.45 12 15.4125

27.75 3.24 15.55 0.8 15.525 -4 15.4875

27.8 3.28 15.6 0.8 15.575 -1.776E-13 15.55

28 3.3 15.8 0.1 15.7 -5.6 15.6375

28.2 3.47 16 0.85 15.9 3.75 15.8

28.5 3.97 16.3 1.666667 16.15 3.26666667 16.025

28.6 4.36 16.4 3.9 16.35 11.1666667 16.25

28.7 5.06 16.5 7 16.45 31 16.4

28.8 5.55 16.6 4.9 16.55 -21 16.5

28.9 5.85 16.7 3 16.65 -19 16.6

29.15 6.15 16.95 1.2 16.825 -10.285714 16.7375

30.5 6.91 18.3 0.562963 17.625 -0.7962963 17.225

31.5 7.28 19.3 0.37 18.8 -0.1642238 18.2125

32.55 7.53 20.35 0.238095 19.825 -0.1286876 19.3125

33.6 7.98 21.4 0.428571 20.875 0.1814059 20.35

34 8.58 21.8 1.5 21.6 1.47783251 21.2375

34.1 8.62 21.9 0.4 21.85 -4.4 21.725

34.2 9.08 22 4.6 21.95 42 21.9

34.3 9.61 22.1 5.3 22.05 7 22

34.4 9.94 22.2 3.3 22.15 -20 22.1

34.5 10.32 22.3 3.8 22.25 5 22.2

34.65 10.45 22.45 0.866667 22.375 -23.466667 22.3125

35 10.84 22.8 1.114286 22.625 0.99047619 22.5

35.5 11.08 23.3 0.48 23.05 -1.492437 22.8375

36.5 11.32 24.3 0.24 23.8 -0.32 23.425

37.5 11.49 25.3 0.17 24.8 -0.07 24.3

10

38 11.54 25.8 0.1 25.55 -0.0933333 25.175

40 11.68 27.8 0.07 26.8 -0.024 26.175

42.1 11.82 29.9 0.066667 28.85 -0.001626 27.825

Graph 10: Titration Curve for Titration 3

Graph 11: Titration Curve for Titration 3/End Point 1

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30

pH

Volume of NaOH Added (ml)

Titration Curve

16.4 ml

0

1

2

3

4

5

6

7

14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5

pH

Volume of NaOH Added (ml)

Titration 3- Endpoint 1

11

Graph 12: Titration Curve for Titration 3/End Point 2

Graph 13: 1ST Derivative Curve for Titration 3

22.1 ml

0

2

4

6

8

10

12

14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5

Axi

s Ti

tle

Volume of NaOH Added (ml)

Titration 3- Endpoint 2

0

1

2

3

4

5

6

7

8

0 5 10 15 20 25 30

∆p

H/∆

vol

Volume of NaOH Added (ml)

∆pH/∆vol vs. Average Volume- Titration 3

12

Graph 14: 1ST Derivative Curve for Titration 3/End Point 1

Graph 15: 1ST Derivative Curve for Titration 3/End Point 2

16.45 ml

0

1

2

3

4

5

6

7

8

14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5

∆p

H/∆

vol

Volume of NaOH Added (ml)

∆pH/∆vol vs. Average Volume- Titration 3/End Point 1

22.05 ml

0

1

2

3

4

5

6

14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5

∆p

H/∆

vol

Volume of NaOH Added (ml)

∆pH/∆vol vs. Average Volume- Titration 3/End Point 1

13

Graph 16: 2nd Derivative Curve for Titration 3

Graph 17: 2nd Derivative Curve for Titration 3/End Point 1

-30

-20

-10

0

10

20

30

40

50

0 5 10 15 20 25 30

∆2

pH

/∆2

vol

Volume of NaOH Added (ml)

∆2pH/∆2vol vs. Average Volume- Titration 3

-30

-20

-10

0

10

20

30

40

14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5∆2

pH

/∆2

vol

Volume of NaOH Added (ml)

∆2pH/∆2vol vs. Average Volume- Titration 3/End Point 1

16.5 ml

14

Graph 18: 2nd Derivative Curve for Titration 3/End Point 2

Table 6: Summary of Identified End-Points from Graphs 1-18

End Points

Titration

1 2

Titration Curve

1st Derivative

2nd Derivative

Titration Curve

1st Derivative

2nd Derivative

1 15.75 15.75 15.8 16.4 16.45 16.5

2 21.1 21.15 21.15 22.1 22.05 22.05

Step 3: Determining end point volumes

Taking the average, for End Point 1

Vol2 + Vol1 + Vol3 + Vol4 + Vol5 + Vol6

6=

15.75 + 15.75 + 15.8 + 16.4 + 16.45 + 16.5

6= 16.10833 ml

Repeat the same for End Point 2

Step 4: Determining no. of moles of NaOH reacted with both acids in the mixture:

Let’s take End Point 1,

16. 10833 ml = 0.016108333 L

Concentration of NaOH = 0.100

Moles of NaOH = 0.01610833 × 0.100 = 0.001610833

Step 5: Determining no. of moles of NaOH that reacted with only the H2PO4

Let’s take End Point 2,

5.4916667 ml = 0.005491667 L

Concentration of NaOH = 0.100

-30

-20

-10

0

10

20

30

40

50

14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5

∆2

pH

/∆2

vol

Volume of NaOH Added (ml)

∆2pH/∆2vol vs. Average Volume- Titration 3/End Point 2

22.05 ml

15

Moles of NaOH = = 0.005491667 × 0.100 = 0.000549167

End Points

Average Volume Added (ml)

Average Volume Added (L)

Moles of NaOH reacted

1 16.10833333 0.016108333 0.001610833

2 5.491666667 0.005491667 0.000549167

Step 6: Calculating the no. of moles of HCl and H2PO4 in the 25 ml sample

Moles of HCl = Moles of reacted NaOH – Moles of NaOH that reacted with H2PO4

= 0.001610833 – 0.000549167 = 0.001061667 mol

Moles of H2PO4 = Moles of NaOH in Step 5 = 0.000549167

Step 7: Calculating the molarity of each acid in the 25 ml.

𝑀𝑜𝑙𝑎𝑟𝑖𝑡𝑦 𝑜𝑓 𝐻3𝑃𝑂4 = 0.001061667 mol

25 ml1𝐿

1000𝑚𝑙

= 0.02196667 𝑀

𝑀𝑜𝑙𝑎𝑟𝑖𝑡𝑦 𝑜𝑓 𝐻𝐶𝑙 = 0.000549167 mol

25 ml1𝐿

1000𝑚𝑙

= 0.04246667 𝑀

Results

The results are tabulated below:

Molarity of H3PO4 0.021966667

Molarity of HCl 0.042466667

References

Harris, D.C. Quantitative Chemical Analysis, W.H. Freeman, NY, 2010.