Model Graph For First Derivative Plot Biology Essay

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Visual method involves the use of pH indicators. There are number of organic substances available which show different colour at different pH values. Several companies have manufactured proprietary mixtures of indicators under the trade name Universal Indicator, which reduces the labour work involved in the choice of appropriate indicator. One can easily fix the pH of the solution by comparing the colour developed by the solution with the standard. To obtain more accurate pH selective indicators are to be choosed where the pH of the solution falls in the working range of the indicator.

e.g. (1): Phenolphthalein is the most commonly used Acid-Base indicator which is colour less below the pH 8.3 and distinctly pink above the pH 10

e.g. (2): Methyl Orange solution is distinct red colour below the pH 3.1 and a yellow colour above the pH 4.4.

Potentiometric method:

Potentiometric titration involves the detection of equivalence point by measuring the change in potential across the suitable electrode during the titration.

(or)

Potentiometric titration involves the direct measurement of electrode potential in which concentration of an active ion may be found and change in EMF of an electrolyte cell brought about by the addition of the titrant.

Wide variety of titrations such as Acid-Base titrations, Redox titration, precipitation titrations and Complexometric titrations use potentiometric method to determine the end point. Graphical representation of such data yields more accurate equivalence point. Few of such graphical representations include.

pH curve

First derivative plot

Second derivative plot

Gran plot (forward and backward)

pH Curve:

pH curve is typically a S-shaped curve. The plot of pH versus volume of titrant gives the pH curve. When alkali is run into acid pH raise slowly and increases fast as more alkali is added and when acid is run into alkali pH of the solution slowly falls and the rate of fall in pH of the solution increases as more acid is added into the solution. When alkali is added into diprotic acid pH curve shows two steps of increase in pH indicating that reaction completes in two steps which possess two end points.

Example of different pH graphs

When alkali is added into the acid following curve is obtained.

C:\Users\manish\Desktop\pH curve 1.gif

Graph 1: Model pH curve

When acid is added into alkali obtains following curve.

C:\Users\manish\Desktop\pH curve 2.gif

Graph 2: Model pH curve

When alkali is added into diprotic acid following curve is obtained.

C:\Users\manish\Desktop\pH curve 3.gif

Graph 3: Model pH curve

First derivative plot:

Determination of equivalence point of Acid-Base titration is maximum done from its first derivative plot. This is because the rapid change in pH at the equivalence point can be easily determined by this plot. Here the end points are sharply determined. This graph is obtained by plotting dpH/dV versus volume of titrant.

C:\Users\kathi\Downloads\titration-derivative.gif

Graph 4: Model graph for first derivative plot

The advantage of this method is that it does not require the care full calibration of pH meter.

But there are two reasons which make the first derivative plot inefficient. They are

Titration curve theory shows that equivalence point of a practical titration does not coincide with the value of titrant where dpH/dV is maximal.

Experimental noises greatly affect the derivative graph of titration, where the filtration of data is often required.

Second derivative plot:

Derivative of derivative is the second derivative.

Second derivative plot is used to determine the end point which is done by observing the line where it crosses the X-axis with the largest slope. This graph is obtained by plotting d2pH/dV2 verses volume of titrant.

Graph 5: Model graph for second derivative plot

The problem for using this technique is that the data should be always ideal which is rarely possible.

Gran plot:

Gran plot is the linearization method of determining the end point for the titration data. Gran plot estimates two parameters essentially,

The slope of the line which estimates the dissociation constant.

The intersection of the line with X-axis, which estimates the equivalence point volume (which is mainly considered in this project).

Gran plot is obtained by plotting gran function on Y-axis and volume of titrant on X-axis. Gran plot is of two types Gran forward plot and Gran backward plot.

Gran function mainly depends on the following equation

Kw = [H+] * [OH-] (Kw = ionic constant of water)

Gran forward function is given by:

[H+] * (Vb/Va)

[H+] = 10-pH

Gran backward function is given by:

[OH-] * (Vb+Va)

[OH-] = 1014-[H+]

The graph obtained is a curve with the linear section. Trend line was added to the linear section of the graph which gives the equation Y = MX+C

Value of X is the endpoint volume for which Y=0

Advantages of using Gran plot are:

Simplicity of measurement: Gran plot do not require large number of readings to calculate the end point i.e. readings are taken until the linear section of the plot is obtained from which the end point is derived where as the differential plots require large number of measurements before and after the end point.

Simple calculations: calculation for Gran plot is simple and easy; sometimes software is used to calculate the end point.

Precision: End point obtained by the extrapolation of linear section of Gran plot is more precise than the end point values obtained by the differential plots.

Materials and methods:

Apparatus:

Beakers, Conical flasks, Burettes, Burette stand, Magnetic stirrer, Pipette, Accurate Weighing machine, Burette stand, Watt-man filter paper, pH meter.

Chemicals and solutions:

0.1M NaOH, 0.01M NaOH

0.1M Ethanoic Acid, 0.01M Ethanoic Acid

0.1M Maleic Acid, 0.01M Maleic Acid

0.1M Ammonia

Buffer 4 and Buffer 7

Distilled water.

Calibration of pH meter:

To get precise results in an experimental work calibration of an instrument is most important. pH meter used for the experiment is "JENWAY pH METER 3305" which is a digital pH meter. It was calibrated by using two buffer solutions of pH 4 & pH 7. These solutions are taken in two different beakers. Now the glass probe of pH was checked for the deposition of only salt and was washed thoroughly. pH meter was switched on, the probe was washed with distilled water and wiped off with soft tissue and immersed into a beaker containing solution of pH 7 and pH meter was allowed to settle down for the reading. Now the pH screw was adjusted to the reading 7. Then the probe washed again washed with distilled water and wiped off with tissue and then immersed in the beaker containing buffer solution of pH 4 and allowed for the reading to settle down. Now the pH screw was adjusted until the reading shows 4.

pH meter was calibrated before starting each titration to obtain precise results.

C:\Users\kathi\Desktop\3505_unit.jpg

Figure 1: JENWAY pH meter

Method:

25cm3 of 0.1 M ethanoic acid (Titrate) was transferred into a clean and dry conical flask by the use of graduated pipette. Initially burette was rinsed with 0.1M NaOH (Titrant) and then filled with it up to the zero mark. pH meter was calibrated with buffers of pH 7 and pH 4 and kept ready to start the experiment.

Titrant was allowed to rundown into the conical flask in 2ml aliquots, between 20-30ml of titrant aliquot volume was reduced to 1 ml and added into the conical flask.

pH of the solution was measured using pH meter.

This procedure was continued until 50ml of titrant was added to the conical flask and pH was measured using pH meter.

The above procedure was repeated with different titrate solutions of 0.01M Ethanoic Acid with titrant 0.01M NaOH, 0.1M Maleic Acid with 0.1M NaOH, 0.01M Maleic Acid with 0.01M NaOH and 0.1M Ammonia with 0.1M NaOH and pH was measured.

Each titration was repeated twice, these readings were recorded on excel and analyzed by various plots.

C:\Users\kathi\Desktop\titration.gif

Figure 2: Set up for titration

After recording the readings on Excel for analysis of titration data, four types of graphs are plotted. pH curve is plotted by taking volume of titrant o X-axis and pH on Y-axis which determines the approximate end point. To obtain the accurate end point first derivative graph is plotted from which second derivative graph is obtained.

Finally Gran plot is obtained by plotting volume of titrant on X-axis and Gran function on Y-axis. Later linear section of the Gran plot is identified manually and trend line is derived for the linear section from which endpoint volume is obtained.

Table 1: Titration Of 0.1M Ethanoic Acid With 0.1M NaOH

Vol of titrant

pH

dV

dpH

dpH/dV

Vb/Va

H ion conc

H*Vb/Va

Vavg

d2pH/dV2

[OH-]

[OH-]*(Va+Vb)

2

3.24

0.08

0.0005754

4.60352E-05

1.7378E-11

4.69206E-10

4

3.58

2

0.34

0.17

0.16

0.000263

4.20843E-05

3

3.8019E-11

1.10255E-09

6

3.83

2

0.25

0.125

0.24

0.0001479

3.54986E-05

5

0.165

6.7608E-11

2.09586E-09

8

4.06

2

0.23

0.115

0.32

8.71E-05

2.78708E-05

7

0.1675

1.1482E-10

3.78891E-09

10

4.25

2

0.19

0.095

0.4

5.623E-05

2.24937E-05

9

0.1325

1.7783E-10

6.22398E-09

12

4.43

2

0.18

0.09

0.48

3.715E-05

1.78337E-05

11

0.1325

2.6915E-10

9.95868E-09

14

4.6

2

0.17

0.085

0.56

2.512E-05

1.40666E-05

13

0.125

3.9811E-10

1.55262E-08

16

4.78

2

0.18

0.09

0.64

1.66E-05

1.06214E-05

15

0.1375

6.0256E-10

2.47049E-08

18

4.98

2

0.2

0.1

0.72

1.047E-05

7.53933E-06

17

0.155

9.5499E-10

4.10647E-08

20

5.33

2

0.35

0.175

0.8

4.677E-06

3.74188E-06

19

0.3

2.138E-09

9.62083E-08

22

5.91

2

0.58

0.29

0.88

1.23E-06

1.08264E-06

21

0.4925

8.1283E-09

3.8203E-07

24

11.69

2

5.78

2.89

0.96

2.042E-12

1.96007E-12

23

5.635

0.00489779

0.239991621

26

12.12

2

0.43

0.215

1.04

7.586E-13

7.88921E-13

25

-1.015

0.01318257

0.672310937

28

12.37

2

0.25

0.125

1.12

4.266E-13

4.77769E-13

27

0.1425

0.02344229

1.242441272

30

12.46

2

0.09

0.045

1.2

3.467E-13

4.16084E-13

29

0.0275

0.02884032

1.586217327

32

12.58

2

0.12

0.06

1.28

2.63E-13

3.36674E-13

31

0.0975

0.03801894

2.167079559

34

12.62

2

0.04

0.02

1.36

2.399E-13

3.26241E-13

33

0.01

0.04168694

2.459529362

36

12.68

2

0.06

0.03

1.44

2.089E-13

3.00859E-13

35

0.05

0.04786301

2.919643563

38

12.72

2

0.04

0.02

1.52

1.905E-13

2.8963E-13

37

0.025

0.05248075

3.306287

40

12.78

2

0.06

0.03

1.6

1.66E-13

2.65534E-13

39

0.05

0.06025596

3.916637309

42

12.81

2

0.03

0.015

1.68

1.549E-13

2.60201E-13

41

0.015

0.06456542

4.325883335

44

12.82

2

0.01

0.005

1.76

1.514E-13

2.66387E-13

43

0.0025

0.06606934

4.558784791

46

12.82

2

0

0

1.84

1.514E-13

2.78495E-13

45

-0.0025

0.06606934

4.690923481

48

12.84

2

0.02

0.01

1.92

1.445E-13

2.77524E-13

47

0.02

0.0691831

5.050366088

50

12.86

2

0.02

0.01

2

1.38E-13

2.76077E-13

49

0.015

0.0724436

5.433269701

For table 1, all the graphs plotted above suggest different end points like, pH curve shows 23ml as end point volume, first derivative plot shows 24ml where as second derivative plot shows 22.75ml as end point volume. While Gran plot suggest two different end point volumes one for Gran forward plot and the other for Gran backward plot include 21.78ml and 22.94ml respectively.

Difference between end point volumes of Gran forward plot and the second derivative plot (which is considered to be most accurate of all the first three graphs) is 0.97ml which is 1.94% more accurate then the second derivative plot.

End point volume shown by Gran plot is lower when compared to any other graphs. It indicates that titration may have been completed before the end points indicated by other graphs probably at the volume indicated by the Gran plot.

From the above observations Gran plot can be considered as the most accurate plot than any other plots for determining the equivalence point for Acid-Base titration data for higher concentrations.

The titration was repeated for the second time and analysed similarly to confirm the accuracy of the Gran plot.

Table2: Titration of 0.1M Ethanoic Acid with 0.1M NaoH

Vol of titrant

pH

dV

dpH

dpH/dV

Vb/Va

H ion conc

H*Vb/Va

Vavg

d2pH/dV2

[OH-]

[OH-]*(Va+Vb)

2

3.3

0.08

0.000501187

4.0095E-05

1.99526E-11

5.38721E-10

4

3.68

2

0.38

0.19

0.16

0.00020893

3.34287E-05

3

4.7863E-11

1.38803E-09

6

3.93

2

0.25

0.125

0.24

0.00011749

2.81975E-05

5

0.155

8.51138E-11

2.63853E-09

8

4.14

2

0.21

0.105

0.32

7.24436E-05

2.3182E-05

7

0.1475

1.38038E-10

4.55527E-09

10

4.33

2

0.19

0.095

0.4

4.67735E-05

1.87094E-05

9

0.1375

2.13796E-10

7.48287E-09

12

4.51

2

0.18

0.09

0.48

3.0903E-05

1.48334E-05

11

0.1325

3.23594E-10

1.1973E-08

14

4.69

2

0.18

0.09

0.56

2.04174E-05

1.14337E-05

13

0.135

4.89779E-10

1.91014E-08

16

4.86

2

0.17

0.085

0.64

1.38038E-05

8.83446E-06

15

0.125

7.24436E-10

2.97019E-08

18

5.01

2

0.15

0.075

0.72

9.77237E-06

7.03611E-06

17

0.1075

1.02329E-09

4.40016E-08

20

5.27

2

0.26

0.13

0.8

5.37032E-06

4.29625E-06

19

0.2225

1.86209E-09

8.37939E-08

21

5.5

1

0.23

0.23

0.84

3.16228E-06

2.65631E-06

20.5

0.165

3.16228E-09

1.45465E-07

22

5.83

1

0.33

0.33

0.88

1.47911E-06

1.30162E-06

21.5

0.2725

6.76083E-09

3.17759E-07

23

8.73

1

2.9

2.9

0.92

1.86209E-09

1.71312E-09

22.5

2.8175

5.37032E-06

0.000257775

24

11.44

1

2.71

2.71

0.96

3.63078E-12

3.48555E-12

23.5

1.985

0.002754229

0.134957206

25

11.79

1

0.35

0.35

1

1.62181E-12

1.62181E-12

24.5

-0.3275

0.00616595

0.308297501

26

11.92

1

0.13

0.13

1.04

1.20226E-12

1.25036E-12

25.5

0.0425

0.008317638

0.424199523

27

12

1

0.08

0.08

1.08

1E-12

1.08E-12

26.5

0.0475

0.01

0.52

28

12.08

1

0.08

0.08

1.12

8.31764E-13

9.31575E-13

27.5

0.06

0.012022644

0.63720015

29

12.18

1

0.1

0.1

1.16

6.60693E-13

7.66404E-13

28.5

0.08

0.015135612

0.817323074

30

12.2

1

0.02

0.02

1.2

6.30957E-13

7.57149E-13

29.5

-0.005

0.015848932

0.871691256

32

12.25

2

0.05

0.025

1.28

5.62341E-13

7.19797E-13

31

0.45

0.017782794

1.013619264

34

12.38

2

0.13

0.065

1.36

4.16869E-13

5.66942E-13

33

0.1175

0.023988329

1.415311422

36

12.48

2

0.1

0.05

1.44

3.31131E-13

4.76829E-13

35

0.0675

0.030199517

1.842170549

38

12.59

2

0.11

0.055

1.52

2.5704E-13

3.907E-13

37

0.085

0.038904514

2.450984413

40

12.64

2

0.05

0.025

1.6

2.29087E-13

3.66539E-13

39

0.225

0.043651583

2.83735291

42

12.68

2

0.04

0.02

1.68

2.089E-13

3.51E-13

41

0.0275

0.047863009

3.206821619

44

12.7

2

0.02

0.01

1.76

1.995E-13

3.5117E-13

43

0.01

0.050118723

3.458191912

46

12.74

2

0.04

0.02

1.84

1.82E-13

3.3482E-13

45

0.035

0.054954087

3.901740204

48

12.78

2

0.04

0.02

1.92

1.66E-13

3.1864E-13

47

0.03

0.060255959

4.398684978

50

12.79

2

0.01

0.005

2

1.622E-13

3.2436E-13

49

0

0.0616595

4.624462514

Table 2 shows the second set of titration data and analysis of 0.1M Ethanoic Acid with 0.1M NaOH. Apart from Gran plot equivalence point shown by pH curve, first derivative plot and second derivative plot are 23ml, 23ml and 24.8ml respectively. Whereas the end point values by Gran forward and Gran backward are 22.89ml and 22.78ml.

The difference between the end point volume of second derivative plot and the Gran forward plot is 1.91ml which is 3.82 %.

From the above discussion it can be said that Gran plot is more accurate in determining the end point for monoprotic acid for higher concentration but there is no much accuracy difference between other three plots and the Gran forward plot.

Table 3: Titration Of 0.01M Ethanoic Acid With 0.01M NaOH

Vol of titrant

pH

dV

dpH

dpH/dV

Vb/Va

H ion conc

H*Vb/Va

Vavg

d2pH/dV2

[OH-]

[OH-]*(Va+Vb)

2

3.52

0.08

0.000301995

2.41596E-05

3.31131E-11

8.94054E-10

4

3.83

2

0.31

0.155

0.16

0.000147911

2.36657E-05

3

6.76083E-11

1.96064E-09

6

4.06

2

0.23

0.115

0.24

8.70964E-05

2.09031E-05

5

0.1525

1.14815E-10

3.55928E-09

8

4.24

2

0.18

0.09

0.32

5.7544E-05

1.84141E-05

7

0.1225

1.7378E-10

5.73474E-09

10

4.42

2

0.18

0.09

0.4

3.80189E-05

1.52076E-05

9

0.135

2.63027E-10

9.20594E-09

12

4.59

2

0.17

0.085

0.48

2.5704E-05

1.23379E-05

11

0.125

3.89045E-10

1.43947E-08

14

4.75

2

0.16

0.08

0.56

1.77828E-05

9.95836E-06

13

0.1175

5.62341E-10

2.19313E-08

16

4.95

2

0.2

0.1

0.64

1.12202E-05

7.18092E-06

15

0.16

8.91251E-10

3.65413E-08

18

5.16

2

0.21

0.105

0.72

6.91831E-06

4.98118E-06

17

0.16

1.44544E-09

6.21539E-08

20

5.4

2

0.24

0.12

0.8

3.98107E-06

3.18486E-06

19

0.1875

2.51189E-09

1.13035E-07

22

6.21

2

0.81

0.405

0.88

6.16595E-07

5.42604E-07

21

0.75

1.62181E-08

7.62251E-07

24

10.58

2

4.37

2.185

0.96

2.63027E-11

2.52506E-11

23

4.1675

0.000380189

0.01862928

26

10.99

2

0.41

0.205

1.04

1.02329E-11

1.06422E-11

25

-0.6825

0.000977237

0.049839098

28

11.16

2

0.17

0.085

1.12

6.91831E-12

7.74851E-12

27

0.0675

0.00144544

0.076608308

30

11.27

2

0.11

0.055

1.2

5.37032E-12

6.44438E-12

29

0.0675

0.001862087

0.102414793

32

11.36

2

0.09

0.045

1.28

4.36516E-12

5.5874E-12

31

0.0625

0.002290868

0.130579456

34

11.42

2

0.06

0.03

1.36

3.80189E-12

5.17058E-12

33

0.0375

0.002630268

0.155185812

36

11.48

2

0.06

0.03

1.44

3.31131E-12

4.76829E-12

35

0.045

0.003019952

0.184217055

38

11.5

2

0.02

0.01

1.52

3.16228E-12

4.80666E-12

37

0.005

0.003162278

0.199223493

40

11.53

2

0.03

0.015

1.6

2.95121E-12

4.72193E-12

39

0.025

0.003388442

0.220248701

42

11.56

2

0.03

0.015

1.68

2.75423E-12

4.6271E-12

41

0.0225

0.003630781

0.243262297

44

11.6

2

0.04

0.02

1.76

2.51189E-12

4.42092E-12

43

0.0325

0.003981072

0.274693948

46

11.61

2

0.01

0.005

1.84

2.45471E-12

4.51666E-12

45

0

0.004073803

0.289239997

48

11.63

2

0.02

0.01

1.92

2.34423E-12

4.50092E-12

47

0.0175

0.004265795

0.311403049

50

11.66

2

0.03

0.015

2

2.18776E-12

4.37552E-12

49

0.025

0.004570882

0.342816142

For table 3, all the graphs plotted above shows the end point results for the titration between 0.01M Ethanoic Acid and 0.01M NaOH which include 23ml by pH curve, 24ml by first derivative plot and 25.8ml by second derivative plot where as two different end point volumes for Gran forward and Gran backward plots include 21.94ml and 22.22ml respectively.

Difference between end point volume of Gran forward plot and the second derivative plot (which is considered to be most accurate of all the first three graphs) is 3.86ml which is 7.72% more accurate then the second derivative plot.

From the above observations it can be said that, even for the lower concentrations of Acid-Base titration for monoprotic acid Gran plot has given the accurate end point when compared to the other graphs. Accuracy is higher for the titration of acid with base at lower concentrations than that with higher concentration.

The titration was repeated for the second time and analysed similarly to confirm the accuracy of the Gran plot.

Table 4: Titration of 0.01M Ethanoic Acid with 0.01M NaOH

Vol of titrant

pH

dV

dpH

dpH/dV

Vb/Va

H ion conc

H*Vb/Va

Vavg

d2pH/dV2

[OH-]

[OH-]*(Va+Vb)

2

3.82

0.08

0.0001514

1.21085E-05

6.60693E-11

1.78387E-09

4

4.11

2

0.29

0.145

0.16

7.762E-05

1.242E-05

3

1.28825E-10

3.73592E-09

6

4.29

2

0.18

0.09

0.24

5.129E-05

1.23087E-05

5

0.1075

1.94984E-10

6.04452E-09

8

4.46

2

0.17

0.085

0.32

3.467E-05

1.10956E-05

7

0.125

2.88403E-10

9.5173E-09

10

4.62

2

0.16

0.08

0.4

2.399E-05

9.59533E-06

9

0.1175

4.16869E-10

1.45904E-08

12

4.78

2

0.16

0.08

0.48

1.66E-05

7.96602E-06

11

0.12

6.0256E-10

2.22947E-08

14

4.94

2

0.16

0.08

0.56

1.148E-05

6.42966E-06

13

0.12

8.70964E-10

3.39676E-08

16

5.14

2

0.2

0.1

0.64

7.244E-06

4.63639E-06

15

0.16

1.38038E-09

5.65958E-08

18

5.38

2

0.24

0.12

0.72

4.169E-06

3.00146E-06

17

0.19

2.39883E-09

1.0315E-07

20

5.81

2

0.43

0.215

0.8

1.549E-06

1.23905E-06

19

0.37

6.45654E-09

2.90544E-07

22

9.74

2

3.93

1.965

0.88

1.82E-10

1.60134E-10

21

3.8225

5.49541E-05

0.002582842

24

10.74

2

1

0.5

0.96

1.82E-11

1.74691E-11

23

0.0175

0.000549541

0.026927503

26

10.97

2

0.23

0.115

1.04

1.072E-11

1.11438E-11

25

-0.02

0.000933254

0.047595969

28

11.18

2

0.21

0.105

1.12

6.607E-12

7.39977E-12

27

0.1525

0.001513561

0.080218746

30

11.28

2

0.1

0.05

1.2

5.248E-12

6.29769E-12

29

0.0475

0.001905461

0.104800339

32

11.33

2

0.05

0.025

1.28

4.677E-12

5.98701E-12

31

0.025

0.002137962

0.121863839

34

11.41

2

0.08

0.04

1.36

3.89E-12

5.29101E-12

33

0.0675

0.002570396

0.151653351

36

11.47

2

0.06

0.03

1.44

3.388E-12

4.87936E-12

35

0.04

0.002951209

0.180023763

38

11.51

2

0.04

0.02

1.52

3.09E-12

4.69725E-12

37

0.025

0.003235937

0.203864004

40

11.52

2

0.01

0.005

1.6

3.02E-12

4.83192E-12

39

0

0.003311311

0.215235229

42

11.54

2

0.02

0.01

1.68

2.884E-12

4.84517E-12

41

0.0175

0.003467369

0.23231369

44

11.58

2

0.04

0.02

1.76

2.63E-12

4.62927E-12

43

0.035

0.003801894

0.262330683

46

11.61

2

0.03

0.015

1.84

2.455E-12

4.51666E-12

45

0.02

0.004073803

0.289239997

48

11.64

2

0.03

0.015

1.92

2.291E-12

4.39847E-12

47

0.0225

0.004365158

0.318656558

50

11.67

2

0.03

0.015

2

2.138E-12

4.27592E-12

49

0.0225

0.004677351

0.350801356

Table 4 indicates the second set of titration data and analysis for 0.01M Ethanoic Acid with 0.01M NaOH. pH curve, first derivative plot and second derivative plot shows 21ml, 22ml and 24ml respectively as their end point volumes. Whereas Gran forward plot and Gran backward plot shows 21.44ml and 21.89ml respectively.

Difference between the end point volumes of second derivative plot and Gran forward plot is 2.56ml, which is 5.12%. When compared to the first set of data this difference is less, but individually the difference between the end points of second derivative plot and Gran forward plot is higher indicating that Gran forward plot determines accurate end point.

From the above results it can be said that Gran plot gives accurate end point volume for the titration of a monoprotic acid with a base for lower concentration. Accuracy of Gran forward plot over second derivative plot is more for the titration of monoprotic acid with a base at lower concentration than at higher concentration

Table 5: Titration of 0.1M Maleic Acid with 0.1M NaOH

Vol of titrant

pH

dV

dpH

dpH/dV

Vb/Va

H ion conc

H*Vb/Va

Vavg

d2pH/dV2

[OH-]

[OH]*(Va+Vb)

1

1.46

0.04

0.034673685

0.001386947

2.88403E-13

7.49848E-12

2

1.48

1

0.02

0.02

0.08

0.033113112

0.002649049

1.5

3.01995E-13

8.15387E-12

3

1.5

1

0.02

0.02

0.12

0.031622777

0.003794733

2.5

0

3.16228E-13

8.85438E-12

4

1.52

1

0.02

0.02

0.16

0.030199517

0.004831923

3.5

0

3.31131E-13

9.6028E-12

5

1.53

1

0.01

0.01

0.2

0.029512092

0.005902418

4.5

-0.01

3.38844E-13

1.01653E-11

6

1.55

1

0.02

0.02

0.24

0.028183829

0.006764119

5.5

0.01

3.54813E-13

1.09992E-11

7

1.57

1

0.02

0.02

0.28

0.026915348

0.007536297

6.5

0

3.71535E-13

1.18891E-11

8

1.59

1

0.02

0.02

0.32

0.025703958

0.008225267

7.5

0

3.89045E-13

1.28385E-11

9

1.62

1

0.03

0.03

0.36

0.023988329

0.008635799

8.5

0.01

4.16869E-13

1.41736E-11

10

1.66

1

0.04

0.04

0.4

0.021877616

0.008751046

9.5

0.01

4.57088E-13

1.59981E-11

11

1.74

1

0.08

0.08

0.44

0.018197009

0.008006684

10.5

0.04

5.49541E-13

1.97835E-11

12

1.8

1

0.06

0.06

0.48

0.015848932

0.007607487

11.5

-0.02

6.30957E-13

2.33454E-11

13

1.84

1

0.04

0.04

0.52

0.014454398

0.007516287

12.5

-0.02

6.91831E-13

2.62896E-11

14

1.89

1

0.05

0.05

0.56

0.012882496

0.007214197

13.5

0.01

7.76247E-13

3.02736E-11

15

1.94

1

0.05

0.05

0.6

0.011481536

0.006888922

14.5

2.22E-16

8.70964E-13

3.48385E-11

16

2

1

0.06

0.06

0.64

0.01

0.0064

15.5

0.01

1E-12

4.1E-11

17

2.08

1

0.08

0.08

0.68

0.008317638

0.005655994

16.5

0.02

1.20226E-12

5.04951E-11

18

2.17

1

0.09

0.09

0.72

0.00676083

0.004867797

17.5

0.01

1.47911E-12

6.36017E-11

19

2.3

1

0.13

0.13

0.76

0.005011872

0.003809023

18.5

0.04

1.99526E-12

8.77915E-11

20

2.43

1

0.13

0.13

0.8

0.003715352

0.002972282

19.5

4.44E-16

2.69153E-12

1.21119E-10

21

2.64

1

0.21

0.21

0.84

0.002290868

0.001924329

20.5

0.08

4.36516E-12

2.00797E-10

22

3.03

1

0.39

0.39

0.88

0.000933254

0.000821264

21.5

0.18

1.07152E-11

5.03614E-10

23

4.02

1

0.99

0.99

0.92

9.54993E-05

8.78593E-05

22.5

0.6

1.04713E-10

5.02622E-09

24

4.68

1

0.66

0.66

0.96

2.0893E-05

2.00572E-05

23.5

-0.33

4.7863E-10

2.34529E-08

25

4.98

1

0.3

0.3

1

1.04713E-05

1.04713E-05

24.5

-0.36

9.54993E-10

4.77496E-08

26

5.2

1

0.22

0.22

1.04

6.30957E-06

6.56196E-06

25.5

-0.08

1.58489E-09

8.08296E-08

27

5.36

1

0.16

0.16

1.08

4.36516E-06

4.71437E-06

26.5

-0.06

2.29087E-09

1.19125E-07

28

5.5

1

0.14

0.14

1.12

3.16228E-06

3.54175E-06

27.5

-0.02

3.16228E-09

1.67601E-07

29

5.63

1

0.13

0.13

1.16

2.34423E-06

2.71931E-06

28.5

-0.01

4.2658E-09

2.30353E-07

30

5.72

1

0.09

0.09

1.2

1.90546E-06

2.28655E-06

29.5

-0.04

5.24807E-09

2.88644E-07

31

5.93

1

0.21

0.21

1.24

1.1749E-06

1.45687E-06

30.5

0.12

8.51138E-09

4.76637E-07

32

6.02

1

0.09

0.09

1.28

9.54993E-07

1.22239E-06

31.5

-0.12

1.04713E-08

5.96863E-07

33

6.12

1

0.1

0.1

1.32

7.58578E-07

1.00132E-06

32.5

0.01

1.31826E-08

7.64589E-07

34

6.2

1

0.08

0.08

1.36

6.30957E-07

8.58102E-07

33.5

-0.02

1.58489E-08

9.35087E-07

35

6.27

1

0.07

0.07

1.4

5.37032E-07

7.51845E-07

34.5

-0.01

1.86209E-08

1.11725E-06

36

6.34

1

0.07

0.07

1.44

4.57088E-07

6.58207E-07

35.5

8.88E-16

2.18776E-08

1.33453E-06

37

6.47

1

0.13

0.13

1.48

3.38844E-07

5.01489E-07

36.5

0.06

2.95121E-08

1.82975E-06

38

6.61

1

0.14

0.14

1.52

2.45471E-07

3.73116E-07

37.5

0.01

4.0738E-08

2.5665E-06

39

6.77

1

0.16

0.16

1.56

1.69824E-07

2.64926E-07

38.5

0.02

5.88844E-08

3.7686E-06

40

6.97

1

0.2

0.2

1.6

1.07152E-07

1.71443E-07

39.5

0.04

9.33254E-08

6.06615E-06

41

7.3

1

0.33

0.33

1.64

5.01187E-08

8.21947E-08

40.5

0.13

1.99526E-07

1.31687E-05

42

7.84

1

0.54

0.54

1.68

1.44544E-08

2.42834E-08

41.5

0.21

6.91831E-07

4.63527E-05

43

11.3

1

3.46

3.46

1.72

5.01187E-12

8.62042E-12

42.5

2.92

0.001995262

0.135677837

44

11.83

1

0.53

0.53

1.76

1.47911E-12

2.60323E-12

43.5

-2.93

0.00676083

0.466497253

45

12.06

1

0.23

0.23

1.8

8.70964E-13

1.56773E-12

44.5

-0.3

0.011481536

0.803707535

46

12.18

1

0.12

0.12

1.84

6.60693E-13

1.21568E-12

45.5

-0.11

0.015135612

1.074628486

47

12.26

1

0.08

0.08

1.88

5.49541E-13

1.03314E-12

46.5

-0.04

0.018197009

1.310184618

48

12.34

1

0.08

0.08

1.92

4.57088E-13

8.77609E-13

47.5

0

0.021877616

1.597065985

49

12.39

1

0.05

0.05

1.96

4.0738E-13

7.98465E-13

48.5

-0.03

0.024547089

1.816484598

50

12.44

1

0.05

0.05

2

3.63078E-13

7.26156E-13

49.5

-1.8E-15

0.027542287

2.065671528

For table 5, all the graphs plotted above shows the end point results for the titration between 0.1M Maleic Acid (a diprotic acid) and 0.1M NaOH. As Maleic acid is a diprotic acid it completes its reaction in two steps i.e. it consist of two equivalence points for one titration. Hence analysis of twod2pH/dV2 end points by four different plots is done to test the accuracy of the Gran plot.

Various end point volumes shown by different plots include 23ml and 42.5ml by pH curve, 23ml and 43ml by first derivative plot and 23.5ml and 43.5ml by second derivative plot While Gran plot suggest four different end point volumes two for Gran forward plot and the other two for Gran backward plot include 22.99ml, 41.84 and 23.38ml, 42.54ml respectively.

End point volumes shown by Gran plot are lower when compared to any other graphs. It indicates that titration may have been completed before the end points indicated by other graphs probably at the volume indicated by the Gran plot.

Difference between end point volumes of Gran forward plot and the second derivative plot (which is considered to be most accurate of all the first three graphs) are 0.51ml for first end point and 1.66ml which is more accurate i.e.3.32% than the second derivative plot (in determining the accuracy percentage for diprotic acid second end point is considered since reaction completes at the second end point).

From the above observations Gran plot is also proved to give the accurate results than the remaining three plots for titration of diprotic acids with an alkali of higher concentrations i.e. 0.1M of both the solutions.

The titration was repeated for the second time and analysed similarly to confirm the accuracy of the Gran plot.

Table 6: Titaration of 0.1M Maleic Acid with 0.1M NaOH

Vol of titrant

pH

dV

dpH

dpH/dV

Vb/Va

H ion conc

H*Vb/Va

Vavg

d2pH/dV2

[OH-]

[OH-]*(Va+Vb)

1

1.66

0.04

0.0218776

0.0008751

4.57088E-13

1.18843E-11

2

1.69

1

0.03

0.03

0.08

0.0204174

0.0016334

1.5

4.89779E-13

1.3224E-11

3

1.69

1

0

0

0.12

0.0204174

0.0024501

2.5

-0.03

4.89779E-13

1.37138E-11

4

1.7

1

0.01

0.01

0.16

0.0199526

0.0031924

3.5

0.01

5.01187E-13

1.45344E-11

5

1.71

1

0.01

0.01

0.2

0.0194984

0.0038997

4.5

0

5.12861E-13

1.53858E-11

6

1.74

1

0.03

0.03

0.24

0.018197

0.0043673

5.5

0.02

5.49541E-13

1.70358E-11

7

1.77

1

0.03

0.03

0.28

0.0169824

0.0047551

6.5

0

5.88844E-13

1.8843E-11

8

1.8

1

0.03

0.03

0.32

0.0158489

0.0050717

7.5

0

6.30957E-13

2.08216E-11

9

1.85

1

0.05

0.05

0.36

0.0141254

0.0050851

8.5

0.02

7.07946E-13

2.40702E-11

10

1.89

1

0.04

0.04

0.4

0.0128825

0.005153

9.5

-0.01

7.76247E-13

2.71686E-11

11

1.96

1

0.07

0.07

0.44

0.0109648

0.0048245

10.5

0.03

9.12011E-13

3.28324E-11

12

2.02

1

0.06

0.06

0.48

0.0095499

0.004584

11.5

-0.01

1.04713E-12

3.87438E-11

13

2.09

1

0.07

0.07

0.52

0.0081283

0.0042267

12.5

0.01

1.23027E-12

4.67502E-11

14

2.16

1

0.07

0.07

0.56

0.0069183

0.0038743

13.5

4.44E-16

1.44544E-12

5.63722E-11

15

2.21

1

0.05

0.05

0.6

0.006166

0.0036996

14.5

-0.02

1.62181E-12

6.48724E-11

16

2.3

1

0.09

0.09

0.64

0.0050119

0.0032076

15.5

0.04

1.99526E-12

8.18058E-11

17

2.37

1

0.07

0.07

0.68

0.0042658

0.0029007

16.5

-0.02

2.34423E-12

9.84576E-11

18

2.47

1

0.1

0.1

0.72

0.0033884

0.0024397

17.5

0.03

2.95121E-12

1.26902E-10

19

2.59

1

0.12

0.12

0.76

0.0025704

0.0019535

18.5

0.02

3.89045E-12

1.7118E-10

20

2.74

1

0.15

0.15

0.8

0.0018197

0.0014558

19.5

0.03

5.49541E-12

2.47293E-10

21

2.92

1

0.18

0.18

0.84

0.0012023

0.0010099

20.5

0.03

8.31764E-12

3.82611E-10

22

3.21

1

0.29

0.29

0.88

0.0006166

0.0005426

21.5

0.11

1.62181E-11

7.62251E-10

23

3.9

1

0.69

0.69

0.92

0.0001259

0.0001158

22.5

0.4

7.94328E-11

3.81278E-09

24

4.67

1

0.77

0.77

0.96

2.138E-05

2.052E-05

23.5

0.08

4.67735E-10

2.2919E-08

25

5

1

0.33

0.33

1

0.00001

0.00001

24.5

-0.44

0.000000001

0.00000005

26

5.19

1

0.19

0.19

1.04

6.457E-06

6.715E-06

25.5

-0.14

1.54882E-09

7.89896E-08

27

5.35

1

0.16

0.16

1.08

4.467E-06

4.824E-06

26.5

-0.03

2.23872E-09

1.16413E-07

28

5.48

1

0.13

0.13

1.12

3.311E-06

3.709E-06

27.5

-0.03

3.01995E-09

1.60057E-07

29

5.6

1

0.12

0.12

1.16

2.512E-06

2.914E-06

28.5

-0.01

3.98107E-09

2.14978E-07

30

5.69

1

0.09

0.09

1.2

2.042E-06

2.45E-06

29.5

-0.03

4.89779E-09

2.69378E-07

31

5.78

1

0.09

0.09

1.24

1.66E-06

2.058E-06

30.5

-8.9E-16

6.0256E-09

3.37433E-07

32

5.87

1

0.09

0.09

1.28

1.349E-06

1.727E-06

31.5

0

7.4131E-09

4.22547E-07

33

5.95

1

0.08

0.08

1.32

1.122E-06

1.481E-06

32.5

-0.01

8.91251E-09

5.16926E-07

34

6.03

1

0.08

0.08

1.36

9.333E-07

1.269E-06

33.5

0

1.07152E-08

6.32196E-07

35

6.11

1

0.08

0.08

1.4

7.762E-07

1.087E-06

34.5

0

1.28825E-08

7.7295E-07

36

6.21

1

0.1

0.1

1.44

6.166E-07

8.879E-07

35.5

0.02

1.62181E-08

9.89304E-07

37

6.28

1

0.07

0.07

1.48

5.248E-07

7.767E-07

36.5

-0.03

1.90546E-08

1.18139E-06

38

6.35

1

0.07

0.07

1.52

4.467E-07

6.79E-07

37.5

-8.9E-16

2.23872E-08

1.41039E-06

39

6.46

1

0.11

0.11

1.56

3.467E-07

5.409E-07

38.5

0.04

2.88403E-08

1.84578E-06

40

6.59

1

0.13

0.13

1.6

2.57E-07

4.113E-07

39.5

0.02

3.89045E-08

2.52879E-06

41

6.72

1

0.13

0.13

1.64

1.905E-07

3.125E-07

40.5

0

5.24807E-08

3.46373E-06

42

6.9

1

0.18

0.18

1.68

1.259E-07

2.115E-07

41.5

0.05

7.94328E-08

5.322E-06

43

7.14

1

0.24

0.24

1.72

7.244E-08

1.246E-07

42.5

0.06

1.38038E-07

9.38661E-06

44

7.69

1

0.55

0.55

1.76

2.042E-08

3.593E-08

43.5

0.31

4.89779E-07

3.37947E-05

45

10.8

1

3.11

3.11

1.8

1.585E-11

2.853E-11

44.5

2.56

0.000630957

0.044167014

46

11.5

1

0.7

0.7

1.84

3.162E-12

5.819E-12

45.5

-2.41

0.003162278

0.224521714

47

11.75

1

0.25

0.25

1.88

1.778E-12

3.343E-12

46.5

-0.45

0.005623413

0.404885754

48

11.91

1

0.16

0.16

1.92

1.23E-12

2.362E-12

47.5

-0.09

0.008128305

0.593366277

49

12.02

1

0.11

0.11

1.96

9.55E-13

1.872E-12

48.5

-0.05

0.010471285

0.774875126

50

12.06

1

0.04

0.04

2

8.71E-13

1.742E-12

49.5

-0.07

0.011481536

0.861115216

Table 6 shows the second set of titration data and analysis for 0.01M Maleic Acid with 0.01M NaOH. Each graph except Gran plot show two different end points as Maleic Acid is a diprotic acid which include 23ml and 44.5ml by pH curve, 24ml and 45ml by first derivative plot, 24.2ml and 45.5ml by second derivative plot. Whereas Gran forward plot gives 23.13ml and 44.25ml and Gran backward plot gives 23.73ml and 44.79ml.

Difference between the end point values given by second derivative plot and the Gran plot are 1.07ml and 1.25ml which is 2.14% more accurate than the second derivative plot which is considered to be the more accurate plot of all the first three graphs.

It is evident from the analysis of table 1 and 2 that Gran plot determines the end point accurately for the titration of monoprotic acid with the base at higher concentrations, which is also been proved true for the titration of diprotic acid with base at higher concentrations. But the percentage of accuracy is higher for the titration of diprotic acid with the base when compared to the titration of monoprotic acid with the base.

Table 7: Titration of 0.01M Maleic Acid with 0.01M NaOH

Vol of titrant

pH

dV

dpH

dpH/dV

Vb/Va

H ion conc

H*Vb/Va

Vavg

d2pH/dV2

[OH-]

[OH-]*(Va+Vb)

1

2.28

0.04

0.005248075

0.000209923

1.90546E-12

4.9542E-11

2

2.31

1

0.03

0.03

0.08

0.004897788

0.000391823

1.5

2.04174E-12

5.51269E-11

3

2.36

1

0.05

0.05

0.12

0.004365158

0.000523819

2.5

0.02

2.29087E-12

6.41443E-11

4

2.4

1

0.04

0.04

0.16

0.003981072

0.000636971

3.5

-0.01

2.51189E-12

7.28447E-11

5

2.44

1

0.04

0.04

0.2

0.003630781

0.000726156

4.5

0

2.75423E-12

8.26269E-11

6

2.46

1

0.02

0.02

0.24

0.003467369

0.000832168

5.5

-0.02

2.88403E-12

8.9405E-11

7

2.5

1

0.04

0.04

0.28

0.003162278

0.000885438

6.5

0.02

3.16228E-12

1.01193E-10

8

2.53

1

0.03

0.03

0.32

0.002951209

0.000944387

7.5

-0.01

3.38844E-12

1.11819E-10

9

2.56

1

0.03

0.03

0.36

0.002754229

0.000991522

8.5

4.441E-16

3.63078E-12

1.23447E-10

10

2.58

1

0.02

0.02

0.4

0.002630268

0.001052107

9.5

-0.01

3.80189E-12

1.33066E-10

11

2.62

1

0.04

0.04

0.44

0.002398833

0.001055486

10.5

0.02

4.16869E-12

1.50073E-10

12

2.66

1

0.04

0.04

0.48

0.002187762

0.001050126

11.5

0

4.57088E-12

1.69123E-10

13

2.7

1

0.04

0.04

0.52

0.001995262

0.001037536

12.5

0

5.01187E-12

1.90451E-10

14

2.75

1

0.05

0.05

0.56

0.001778279

0.000995836

13.5

0.01

5.62341E-12

2.19313E-10

15

2.8

1

0.05

0.05

0.6

0.001584893

0.000950936

14.5

0

6.30957E-12

2.52383E-10

16

2.86

1

0.06

0.06

0.64

0.001380384

0.000883446

15.5

0.01

7.24436E-12

2.97019E-10

17

2.93

1

0.07

0.07

0.68

0.001174898

0.00079893

16.5

0.01

8.51138E-12

3.57478E-10

18

3

1

0.07

0.07

0.72

0.001

0.00072

17.5

-4.44E-16

1E-11

4.3E-10

19

3.12

1

0.12

0.12

0.76

0.000758578

0.000576519

18.5

0.05

1.31826E-11

5.80033E-10

20

3.26

1

0.14

0.14

0.8

0.000549541

0.000439633

19.5

0.02

1.8197E-11

8.18865E-10

21

3.47

1

0.21

0.21

0.84

0.000338844

0.000284629

20.5

0.07

2.95121E-11

1.35756E-09

22

3.9

1

0.43

0.43

0.88

0.000125893

0.000110785

21.5

0.22

7.94328E-11

3.73334E-09

23

4.54

1

0.64

0.64

0.92

2.88403E-05

2.65331E-05

22.5

0.21

3.46737E-10

1.66434E-08

24

4.94

1

0.4

0.4

0.96

1.14815E-05

1.10223E-05

23.5

-0.24

8.70964E-10

4.26772E-08

25

5.17

1

0.23

0.23

1

6.76083E-06

6.76083E-06

24.5

-0.17

1.47911E-09

7.39554E-08

26

5.35

1

0.18

0.18

1.04

4.46684E-06

4.64551E-06

25.5

-0.05

2.23872E-09

1.14175E-07

27

5.48

1

0.13

0.13

1.08

3.31131E-06

3.57622E-06

26.5

-0.05

3.01995E-09

1.57037E-07

28

5.6

1

0.12

0.12

1.12

2.51189E-06

2.81331E-06

27.5

-0.01

3.98107E-09

2.10997E-07

29

5.7

1

0.1

0.1

1.16

1.99526E-06

2.3145E-06

28.5

-0.02

5.01187E-09

2.70641E-07

30

5.8

1

0.1

0.1

1.2

1.58489E-06

1.90187E-06

29.5

-8.88E-16

6.30957E-09

3.47027E-07

31

5.89

1

0.09

0.09

1.24

1.28825E-06

1.59743E-06

30.5

-0.01

7.76247E-09

4.34698E-07

32

5.98

1

0.09

0.09

1.28

1.04713E-06

1.34032E-06

31.5

8.882E-16

9.54993E-09

5.44346E-07

33

6.05

1

0.07

0.07

1.32

8.91251E-07

1.17645E-06

32.5

-0.02

1.12202E-08

6.50771E-07

34

6.13

1

0.08

0.08

1.36

7.4131E-07

1.00818E-06

33.5

0.01

1.34896E-08

7.95888E-07

35

6.22

1

0.09

0.09

1.4

6.0256E-07

8.43583E-07

34.5

0.01

1.65959E-08

9.95752E-07

36

6.31

1

0.09

0.09

1.44

4.89779E-07

7.05281E-07

35.5

0

2.04174E-08

1.24546E-06

37

6.39

1

0.08

0.08

1.48

4.0738E-07

6.02923E-07

36.5

-0.01

2.45471E-08

1.52192E-06

38

6.49

1

0.1

0.1

1.52

3.23594E-07

4.91862E-07

37.5

0.02

3.0903E-08

1.94689E-06

39

6.58

1

0.09

0.09

1.56

2.63027E-07

4.10322E-07

38.5

-0.01

3.80189E-08

2.43321E-06

40

6.71

1

0.13

0.13

1.6

1.94984E-07

3.11975E-07

39.5

0.04

5.12861E-08

3.3336E-06

41

6.86

1

0.15

0.15

1.64

1.38038E-07

2.26383E-07

40.5

0.02

7.24436E-08

4.78128E-06

42

7.03

1

0.17

0.17

1.68

9.33254E-08

1.56787E-07

41.5

0.02

1.07152E-07

7.17918E-06

43

7.3

1

0.27

0.27

1.72

5.01187E-08

8.62042E-08

42.5

0.1

1.99526E-07

1.35678E-05

44

7.79

1

0.49

0.49

1.76

1.62181E-08

2.85439E-08

43.5

0.22

6.16595E-07

4.25451E-05

45

9.17

1

1.38

1.38

1.8

6.76083E-10

1.21695E-09

44.5

0.89

1.47911E-05

0.001035376

46

9.88

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