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DETERMINATION OF THE K A OF A WEAK ACID 

Introduction:

Acids and bases are often described as being “weak” or “strong”. While this

classification seems somewhat arbitrary, other more quantitative descriptors exist. For acids, Ka

values are commonly used. The ionization of an acid can be shown by the following equation:

HA(aq)   H+

(aq) + A-(aq)  (Eq. 1)

Since an equilibrium exists, an equilibrium constant, Ka, can be written:

K a  = [H+] [A

-] (Eq. 2)

[HA]

The K a value is an indication of acid strength. The larger the value of the Ka, the

stronger the acid. This value is characteristic of the acid and can be used to help identify an

unknown acid. A similar system exists for bases (K  b).

Two methods may be used to determine the K a value. Both methods require the use of a

 pH meter. In the first method, a sample of acid is titrated with base. The pH values are plotted

vs. the volume of base added. The equivalence point is determined from the graph. Next, the

volume of base halfway to the equivalence point is found, and the pH at this volume is noted.

The [H+] corresponding to this pH is equal to the K a for the acid. At a point halfway to the

equivalence point, [H+] = [HA] = [A

-] for a monoprotic acid. Canceling out [A

-] and [HA] in

Equation 2 gives K a = [H+].

The second method for determining K a values involves a “half volume” method. A

solution of the acid is prepared and divided in half as accurately as possible. One portion is

titrated to its endpoint with phenolphthalein. The two portions are then recombined, and the pH

of the resulting solution is measured. Since half of the acid has been titrated, [H+] = [HA] = [A

-].

Again, if [A-] and [HA] are canceled in Equation 2,

K a = [H+]. The pH value of the combined solutions can be converted to [H

+] to give a K a value.

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Aim/Objective

To determine the acid ionization constant, Ka, of a weak acid by titration with sodium hydroxide

and by measuring the pH of the weak acid.

Theory

There are two methods to determine the Ka value of a weak acid, that is:

  Titrating the weak acid with sodium hydroxide

  Measuring the pH of the weak acid

Weak acid titrated with NaOH

A titration curve is produce by plotting the pH of the acid solution versus the volume of NaOH

added. The equivalence point of the titration is reached when all of the weak acid (HA) hascompletely reacted with NaOH. On the titration curve, the equivalence point is read at the center

of the region where pH increases sharply. The half-equivalence point for the titration is reached

when exactly one half of the based required to completely neutralized the acid has been added.

At this point of concentration of the acid in the solution, [HA] is equal to the concentration of its

conjugate base, [A

].

][][  

  A HA  ( equation 4-3)

Equation 4-2 can be simplified to yield equation 4-4,

  O H  Ka3   (equation 4-4)

Taking the negative of the algorithm of each side of equation 4-4, equation 4-5 can be deriving.

]log[~)log( 3

  O H  Ka 

 pKa = pH (equation 4-5)

equation 4-5 indicates that the pKa for the acid is equal to the pH of the solution at half

equivalence point. The Ka of the acid is determined from the pKa value as follows.

 pKa Ka  

10  (equation 4-6)

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Sample calculation using 1 st 

method

A weak acid is titrated with 0.10 M NaOH.

Equivalence point = 11.62mL, determine the titration curve.

Half equivalence point = 11.62/2 = 5.81mL

The pH value corresponding to 5.81 mL is 4.2, determine the titration curve. pKa= pH = 4.2 at the half equivalence point

Ka = pKa

10 = 10  20.4

= 6.3 × 10  5

 

Knowing the pH of the weak acid and initial weak acid concentration

From the pH of the acid solution (HA), we can determine the H

 and A

 ion concentration isrelated to the pH of a solution by equation 4-7

 pH O H 

 

103   (equation 4-7)

By substituting [HA], [H3O

] and [A

] at equilibrium in to equation 4-2, value of Ka can becalculated.

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Sample calculation using 2nd 

method

The pH of 0.10 M weak acid solutions 2.52 at 25   C  . Calculate the Ka of the weak acid at 25   C  .

Initially, only the weak acid HA molecules ionize, forming H3O

and H3O

. The initial HA

concentration decreases while the concentration of H3O

  and A

  increase until equilibrium

attained. The equilibrium concentration of HA, H3O

  and A

 are calculated as follows.

 pH = 2.52

 M O H   pH    352.2

3  100.31010

 

 

HA + H 2 O  H3O

 + A

 

Initial 0.10M 0 0

Change -3.0×10ˉ³ +3.0×10ˉ³M +3.0×10ˉ³M 

Equilibrium (0.10-3.0×10ˉ³)M 3.0×10ˉ³M 3.0×10ˉ³M 

Ka=    HA

 AO H  

3

 

5

3

33

103.9100.310.0

100.3100.3  

 Ka

 

The calculated Ka value of the unknown acid is closest to that of benzoic acid, 6.3×10  5

 

Table1: Ionization constant (K a) for some weak acids at

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Procedures:

Determination of Ka value of a weak acid by titration with NaOH

  Approximately 40mL of unknown acid solution was obtained. Data was recorded.

 

10.0mL of the unknown acid solution was added to dry 250mL beaker.

  The solution was titrated with NaOH  The reaction mixture was poured into lab sink, and was flushed with continuous water.

  Step 2-4 was repeated to perform 2nd 

titration of the weak acid with 0.1M NaOH solution  The titration curve was draw

  From the titration curve, the volume of NaOH required to neutralizing the weak acidsolution in each titration was determined. Data was recorded.

  The Ka value for titration 1 and 2 was calculated.

  The average Ka value for the weak acid was calculated.

  Using the Ka value calculated in step 10; the unknown weak acid from table 1 wasidentified.

 

The molarity of the unknown acid solution for each titration was calculated.

Determination of Ka from the initial concentration and pH of a weak acid solution

  20mL of the unknown weak acid solution (same unknown used in Part A) was added to a

dry beaker.

  The pH electrode was removed from the pH 7 buffer solution. The electrode was rinsed

with distilled water and the tip of the probe was dried.

  The electrode was inserted into the beaker containing the acid solution from step 1. Thesolution was stirred. After the pH reading was stabilized, the pH of the solution was

recorded.

  The weak acid solution was decanted into waste container.  Step 1-4 was repeated to perform second pH measurement

  The pH probe was rinsed with distilled water

  Using initial concentration (molarity calculated in step12, part A) the pH of the unknownacid solution, the Ka for each trial was calculated.

  Using the Ka value calculated in step 8, the weak acid was identified from table 1