Michael ChoeBB611/30/07

Characterization of a Weak AcidAbstract

Weak acids are characterized by their equilibrium Ka, molar mass, and

protonation. These characteristics were determined through a weak acid-strong base

titration curve using standardized NaOH. The number of equivalence points determined

the protonation-whether it was monoprotic or diprotic. The first equivalence point

described the molar mass of the unknown. The Ka was determined through the ¼, ½, ¾

equivalence points using the Henderson-Hasselbach Equation. Laboratory techniques

such as weighing by difference, use of indicator, manual titrations, Vernier Lab Pro

interface, automatic titrations, volumetric pipetting, volume-drop counter calibration, pH

calibration, and dilutions were employed. Determination of the weak acid yielded a molar

mass of with a percent yield of and a pKa of

with a percent yield of . The titration curve displayed a single

equivalence point, indicating that Potassium Hydrogen Phthalate was the acid with a

literature molar mass of and pKa of 5.432.

Introduction

The objective of this experiment was to determine the identity of an unknown

weak acid through the characteristics of its corresponding titration curve such as the

number of equivalence points, ¼, ½, ¾ equivalence points, and the volume of the first

equivalence point. The weak acid-strong base titration curve gives insight into the

unknown weak acid’s molar mass, Ka, and protonation.

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For the purposes of this titration, the standardization of the NaOH solution was

required for precision and accuracy. Through manual titration of a known amount of

KHP, the concentration of the NaOH base was effectively determined.

The assumption that the moles of acid equal the moles of base is derived from the

sensitivity of the equivalence point. In the case of a titration, the equivalence point

determines the molar mass of the acid through the assumption that at that point, the moles

of acid added equals the moles of base added. Since the acid was the dominant source of

H+ ions and OH- is an extremely strong base, the titration reaction HA(aq) + OH-(aq)

H2O(l ) + A-(aq) occurs to near completion.

The reaction suggests that one mole of OH- ions react with one mole of HA

molecules. This is essentially valid since the HA is the major proton donor. If the acid

and base react in a one to one ratio, the equivalence point indicates where the moles of

acid are equal to the moles of base in solution. The determination of the molecular weight

simply requires the grams of acid added over the moles of acid.

Monoprotic acids remain in a state of equilibrium described by HA(aq) ⇌ H+(aq) +

A-(aq) with . Like the Keq of a general reaction, the Ka posses similar

properties such as temperature dependence. However, the auto ionization of water is

excluded from the acid reaction because it remains at a standard concentration. The

derivation of the Henderson-Hasselbach equation comes from the log of the Ka

equilibrium equation. Thus, Ka, pH, and the ratio of acid to base are described by

. Using the ½ equivalence point where the term

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equals 0, the pKa is determined by the pH. The pKa could also be calculated at varying

points provided that the ratio of is known.

In the case of a diprotic acid, two equations and two equilibrium points such as

H2A(aq) + OH-(aq) H2O(l ) + HA-

(aq) with and HA-(aq) + OH-

(aq) H2O(l )

+ A2-(aq) with would be required for the characterization. However, the

determination of diprotic acids is roughly similar to the determination of a monoprotic

acid.

Acid-base titration curves are not limited in the determination of unknown weak

acids. Titration curves were also required to determine the purity of single walled carbon

nanotubules. Simple acid base titrations were conducted to determine the amount of

carboxylic acid groups present in carbon nanotubles, a measurement of its purity. Acid

base titrations provide an accurate and inexpensive means for testing the purity of these

structurally important molecules (1).

Experimental

The procedure of this experiment was conducted following the procedure of “An

Introduction to Chemical Systems in the Laboratory” pages 50-53 (2).

Instead of creating a 0.1M NaOH solution, 5.1 mL of 19.1M NaOH was diluted in

1L of water to form 0.094M NaOH solution

Instead of weighing 0.3g of KHP, 0.3076g, 0.3145g, 0.3058g of KHP was

weighed.

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Three drops of phenolphthalein were added to each trial

Instead of automatic volume calibration, manual calibrations were made using

number of drops and volume.

Instead of weighing 0.30g of unknown acid, 0.3068g, 0.3038g, 0.3033g was

weighed. The second trial was weighed twice because of a failed titration, initially

0.2994g were weighed.

Acids were diluted in 75ml of water precisely using a 25ml volumetric pipette

Titration was stopped at a pH of12.51, 12.50, 12.01 in a range between 12 and 13

Files were saved as choetrial1.txt, choetrial2.txt, choetrial3.txt

Results

Derivation of Henderson-Hasselbach Equation:

General Acid Reaction – Monoprotic acid:

HA(aq) ⇌ H+(aq) + A-

(aq) with

General Titration ReactionHA(aq) + OH-

(aq) H2O(l ) + A-(aq)

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ObservationsProcedure ObservationAdd 2-3 drops of phenophtalein to each KHP solution

Solution was clear

Add NaOH drop wise Solutions turned a pale pinkWeigh approximately 0.3000g of unknown and dilute in a precise amount of water

Acid dissolved in 75ml of water, and was clear

Calibrate the volume and pH pH solution of 7 was yellow, and pH solution of 2 was clear. Calibrating volume yielded 80 drops for 4.5ml indicating 17.78 drops per ml.

Titrate the acid with the standardized NaOH solution

Curve showed a monoprotic acid

Titrate until pH is beyond 12 pHs were 12.51, 12.50, 12.01 for trial 1,2,3 respectively

NaOH and KHP standardizationTrial 1 Trial 2 Trial 3

Mass KHP 0.3076g 0.3143g 0.3058gInitial Volume NaOH 5.0 ml 5.0 ml 21.6 mlFinal Volume NaOH 20.0 ml 21.6 ml 36.7 mlTotal Volume NaOH 15.0 ml 16.6 ml 15.1 ml

Trial 1 Sample Calculation

Trial 1 Trial 2 Trial 3Concentration NaOH 0.100411M 0.092709M 0.099162MMean Concentration

0.097428 M

Weak Acid TitrationTrial 1 Trial 2 Trial 3

Grams of Acid 0.3068g 0.3038g 0.3033gVol Equivalence 17.26659 ml 16.25625 ml 18.4500 mlpH ½ Equivalence 5.18075 5.16603 5.292098

pH ¼ Equivalence 4.66901 4.683145 4.764033

pH ¾ Equivalence 5.732399 5.667934 5.858229

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Trial 1

Trial 2

Trial 3

Volume NaOH vs pH

0

2

4

6

8

10

12

14

0 10 20 30 40 50

Volume NaOH mL

pH Series1

Volume NaOH vs Second Derivative pH

-1

0

1

2

3

4

5

0 10 20 30 40 50

Volume NaOH mL

Fir

st D

eriv

ativ

e o

f p

H

Series 1

Volume NaOH vs pH

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30

Volume NaOH mL

pH Series1

Volume NaOH vs First Derivative pH

-1

0

1

2

3

4

5

6

7

0 5 10 15 20 25 30

Volume NaOH mL

Fir

st D

eriv

ativ

e p

H

Series1

Volume NaOH vs pH

0

2

4

6

8

10

12

14

0 10 20 30 40

Volume NaOH mL

pH Series1

Volume NaOH vs First Derivative pH

-1

0

1

2

3

4

5

6

0 10 20 30 40

Volume NaOH mL

Fir

st D

eriv

ativ

e p

H

Series1

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Weak Acid Molar Mass

Trial 1 Sample Calculation

Trial 1 Trial 2 Trial 3

Weak Acid pKa

Trial 1 Sample Calculation

Trial 1 Trial 2 Trial 3pKa ½ Equivalence 5.18074 5.16603 5.292098

pKa ¼ Equivalence 5.14613 5.16027 5.24115

pKa ¾ Equivalence 5.25528 5.19081 5.38111

Mean pKa5.223735

Molar mass seems rather high and does not match anything exactly – roughly matches the MW of Citric, sulfanilic, and potassium hydrogen phthalate acids. However, the pKa only resembles the value of potassium hydrogen phthalate.

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Weak acid is potassium hydrogen phthalate.Acid Equilibrium Reaction:

HC8H4O4-(aq) ⇌ H+

(aq) + C8H4O42-

(aq) = 5.974x10-6M

Titration Reaction:HC8H4O4

-(aq) + OH-

(aq) H2O(l ) + C8H4O42-

(aq)

Error Analysis

Standardization of NaOH

0.097428 M

[NaOH] = M

Molecular Weight of Unknown Weak Acid

%Yield =

Molar Mass =

pKa of Unknown Weak Acid

5.223735

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%Yield =

pKa =

Discussion

The primary objective was to characterize an unknown weak acid through acid-

base titration curves and relating the ½ equivalence points to the Ka and the equivalence

point to the molar mass. Basic laboratory techniques such as such as weighing by

difference, use of indicator, manual titrations, Vernier Lab Pro interface, automatic

titrations, volumetric pipetting, volume-drop counter calibration, pH calibration, and

dilutions were employed to produce a titration curve.

Understanding of the mechanism of the titration curve requires thorough analysis

of the equations of acid-base interactions. When dissolved, the monoprotic acid KHP

remains in a state of equilibrium HC8H4O4-(aq) ⇌ H+

(aq) + C8H4O42-

(aq) with,

= 5.974x10-6M. Like the Keq expression, the Ka has the same

properties such as temperature dependency. However, in the case of Ka water as a species

was excluded because it was standard to all acid equilibrium. The value of the Ka

constant suggests that the dissociation of the weak acid was near infinitesimal, otherwise

negligible.

Since the predominant species of acid in solution was HC8H4O4-(aq), the following

reaction occurred towards completion during titration: HC8H4O4-(aq) + OH-

(aq) H2O(l ) +

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C8H4O42-

(aq). This reaction indicated that HC8H4O4-(aq) acted as a buffer against the OH-

base. Once the HA capacity was depleted, a rapid pH change occurred. Since any minute

amount of base quickly increased the pH, the point where the pH rapidly changed

indicated that the moles of base added equaled the moles of acid added. Thus, the

equivalence points marked the point when all HA became depleted, and when the pH

changed sharply. The pH for an acid-base titration at the equivalence point should be in

theory 7. However, in weak acids the conjugate base contributes to a high pH due to their

proton affinity. In the case of the unknown KHP acid, the equivalence points were higher

than 7. Using the moles of acid acquired from the equivalence point and the grams of

unknown added, the molar mass was determined.

To complete the titration of a weak acid and a strong base, a standardize NaOH

solution was determined through a manual titration of KHP and NaOH. The equivalence

point signified the moles of NaOH added, and thus the exact concentration of NaOH was

calculated.

An additional characteristic of the weak unknown acid, the pKa was determined

using the Henderson-Hasselbach equation . For the purposes of

convenience, the ½ equivalence point was chosen because [A-] = [HA] and the term

equaled zero indicating that pKa = pH. Additional points such as the ¼ and ¾

equivalence where the ratio equal and 3 respectively were chosen for the sake

of accuracy.

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The determination of the monoprotic weak acid yielded a molar mass of

with a percent yield of 88.59% and a pKa of with a

percent yield of 96.17%. The data suggests that KHP was the closest fit. Although the

molar mass was off by a significant amount, the pKa value was near exact fit. The pKa

value likely has less variance than the molar mass because the pH of the ½ equivalence

point is considerable more stable than the pH of the equivalence point.

The determination of the molar mass and pKa yielded an artificially low value.

Several factors of errors may have contributed to the difference between these

experimental values and literature values. Such errors that may include determinant errors

that create artificially low values include spilling while weighing by difference,

undershooting the manual titration, inadequate mixture of the NaOH solution,

unhomogenized levels of NaOH maintained in the burette, and improper volume/pH

calibration. Determinate errors could have caused a high yield include overshooting the

manual titration, shooting a stream of NaOH instead consistent drops, poor rinsing of the

probe, and improper volume/pH calibration. Additional indeterminate errors that may

have contributed to the experimental value include static in the analytical balance,

inhomogenous stirring of acid solution while reading pH, and viscous NaOH sinking to

the bottom of the burette during titration. Although all errors may have contributed, the

primary cause of the difference in molecular weight may have been in the volume

calibration. Since the unknown acid was the same identity as the KHP acid titrated

manually, in theory their titration volumes at the equivalence point should be exact.

However, the volumes during titrations were noticeably different, indicating that the

volume calibration was improperly carried out.

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Although the experimental molecular weight was considerably inaccurate, the

identity of the unknown weak acid was chosen with confidence based off the acid’s

protonation, and pKa. In essence, this experiment successfully illustrated the

determination of weak acid properties through its titration curve using simple laboratory

techniques such as weighing by difference, use of indicator, manual titrations, Vernier

Lab Pro interface, automatic titrations, volumetric pipetting, volume-drop counter

calibration, pH calibration, and dilutions. This experiment also illustrated practical

applications of using acid base titrations as an efficient means of the determination of

purity in important molecules such as single walled carbon nanotubules.

References(1) Hu, H.; Bhowmik, P.; Zhao, B.; Hamon, M. A.; Itkis, M. E.; Haddon, R. C.  Chemical Physics Letters  (2001),  345(1,2),  25-28.  (2) Chemistry 203/205 “An Introduction to Chemical Systems in the Laboratory”, Stipes Publishing Company, Champaign, IL .2007-2009; 3-8 (3) CRC “Handbook of Chemistry and Physics 88st Ed.”, CRC Press, New York, NY. 2000-2007; pg 8-42 - pg 8-51

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