pH measurement and determination of pKa value

Objectives:

• To measure the pH of various solutions using pH indicators and meter.
• To determine the value of \(K_{a}\) of acetic acid in three different ways.
• To create and study the properties of buffer solutions.

Part A: Using Indicators to Measure pH

In this part of the experiment you will use five indicators to determine the pH of four solutions to within one pH unit. An acid-base indicator is a chemical species that changes color at a specific pH as the pH (acidity) of the solution is varied. Acid-base indicators are themselves weak acids where the color of the aqueous acid is different than the color of the corresponding conjugate base. We can represent the dissociation of an acid-base indicator in an aqueous solution with the following equation.

\[\underbrace{\ce{HIn (aq)}}_{\text{yellow}}+\ce{H2O (l) <=> } \underbrace{\ce{In^{-} (aq)}}_{\text{blue}} + \ce{H3O^{+} (aq) } \label{1}\]

In this hypothetical example \(\ce{In}\) stands for the indicator. As you can see from Equation \ref{1}, the protonated form of the acid-base indicator, \(\ce{HIn}\) (aq), will be one color (color I, yellow in this example) and the deprotonated form, \(\ce{In^{-}}\) (aq), will be another color (color II, blue in this example). The equilibrium-constant expression for Equation \ref{1} is:

\[K_{a} =\dfrac{[\ce{H3O^{+}}][\ce{In^{-}}]}{[\ce{HIn}]} \label{2}\]

This equation can also be written as:

\[ \dfrac{K_{a}}{ [\ce{H3O^{+}}]} = \dfrac{[\ce{In^{-}}]}{[\ce{HIn}]} \label{3}\]

Generally only one or two drops of indicator are added to the solution of interest and therefore the amount of \(\ce{H3O^{+}}\) due to the indicator itself can be considered negligible. The total amount of \(\ce{H3O^{+}}\) in the solution is therefore controlled by the concentrations of the other acids and/or bases present in the solution. Note that when \([\ce{H3O^{+}}] >> K_{ai}\), \([\ce{HIn}] >> [\ce{In^{–}}]\) and the color of the solution will be essentially the same as color I. Similarly, when \([\ce{H3O^{+}}] << K_{a}, [\ce{HIn}] << [\ce{In^{–}}]\) and the color of the solution will be essentially the same as color II.

As an example consider a very acidic solution (say pH = 0) containing the indicator \(\ce{HIn}\) where \([\ce{H3O^{+}}] >> K_{a}\), and therefore, \([\ce{HIn}] >> [\ce{In^{–}}]\). Under these conditions the solution will be yellow. Suppose we add base to the solution resulting in a decrease of \([\ce{H3O^{+}}]\). As \([\ce{H3O^{+}}]\) decreases the reaction indicated by Equation \ref{1} will go net forward and \([\ce{HIn}]\) will decrease while \([\ce{In^{–}}]\) increases. When \([\ce{In^{–}}]\) becomes significant compared to \([\ce{HIn}]\) the color of the solution will begin to change. Eventually as \([\ce{H3O^{+}}]\) decreases still further we will have, \([\ce{H3O^{+}}] << K_{ai}\), and the color of the solution will have turned to blue. Depending on the indicator, this could happen while the solution is still acidic, only less so. In other words the solution will change color when \([\ce{HIn}] ≈ [\ce{In^{–}}]\), and so \(K_{a} = [\ce{H3O^{+}}]\), or \(pK_{a} = pH\). In general we can say that an acid-base indicator changes color at a pH determined by the value of \(K_{a}\) or pK_a for that particular indicator.

The five indicators you will use in this experiment, their color transitions, and their respective values of \(\text{p}K_{ai}\) are given in Table 1.

The actual colors in solution vary somewhat from those shown here depending on the concentration. *Thymol blue is a polyprotic acid with two pK_a values. The second pK_a is around 8.8. Adding too much NaOH, to a pH beyond its second pK_a results in a colorless solution.

We can use the values in Table 1 to determine the approximate pH of a solution. For example, suppose we have a solution in which methyl violet is violet. This tells us that the pH of our unknown solution is greater than or equal to 2 because methyl violet turns violet at pH values of 2 or greater. Now suppose we add some congo red to a fresh sample of our solution and find that the color is violet. This tells us that the pH of our solution is less than or equal to 3 because congo red turns violet at pH values of 3 or less. From these two tests we know that the pH range our solution is between 2 and 3. Thus, we have determined the pH of our solution to within one pH unit. Proceeding in a similar manner, you will use the acid-base indicators in Table 1 to determine the pH range of four solutions to within one pH unit.

Part B: Using pH meters

In this part of the experiment you will learn to use a pH meter to measure pH. Your instructor will demonstrate how to use the pH meter appropriately at the beginning of your laboratory session, explaining why the pH probe should always be submerged in a solution, and how to avoid contamination of a sample with the one measured previously.

Part C: Using pH to determine the value of \(K_{a}\) for acetic acid, \(\ce{CH3COOH}\)(aq)

In this part of the experiment you will use your pH meter to measure the pH of an acetic acid solution of known concentration, and an acetate solution (the conjugate base) of known concentration. From the measured pH and concentration you can determine the value of \(K_{a}\) for the acid. The general equation for the dissociation of a weak acid, \(\ce{HA}\) (aq), in water is:

\[\ce{HA (aq) + H2O (l) <=> A(aq) + H3O^{+} (aq)} \label{4}\]

For which

\[K_{a}=\dfrac{[\ce{A}] [\ce{H3O^{+}}]}{[\ce{HA}]} \label{5}\]

When we construct an ICE table for this reaction we can see that at equilibrium

\[[\ce{A^{-}}] = [\ce{H3O^{+}}] \label{6}\]

and

\[[\ce{HA}] = [\ce{HA}]_{0} - [\ce{H3O^{+}}] \label{7}\]

where \([\ce{HA}]_{0}\) is the initial (nominal) concentration of \(\ce{HA}\) (aq) before equilibrium is established.

Using Equations \ref{6} and \ref{7} , we may express Equation \ref{5} as

\[K_{a}=\dfrac{[\ce{H3O^{+}}]^{2} }{[\ce{HA}]_{0} - [\ce{H3O^{+}}]} \label{8}\]

Because \([\ce{H3O^{+}}]\) can be determined by measuring the pH of the weak acid and \([\ce{HA}]_{0}\) is known you can determine the value of \(K_{a}\) using Equation \ref{8}.

For the pH measurement of the acetate, hydroxide rather than hydronium is a major species, so it makes sense to use a different version of the acid/base reaction for the ICE table:

\[\ce{AH(aq) + OH^{-} (aq) <=> A- (aq) + H2O (l) } \label{9}\]

So the ICE table starting with the conjugate base is similar but should include hydroxide instead of hydronium. Once you figure out the equilibrium concentrations of acetic acid and acetate, you can plug in those as well as the hydronium concentration to calculate the \(K_{a}\) using Equation \ref{5}.

Part D: Buffer Solutions

In this part of the experiment you will prepare a buffer solution with a certain pH from solutions of 0.1 M acetic acid and of 0.1 M acetate (sodium as counter ion).

Recall that the pH of a buffer solution is given by the Henderson-Hasselbach approximation:

\[\mathrm{pH}=\mathrm{pKa}+  \log{\dfrac{[A^{-}]}{[HA]} \label{10}}\]

This can be accomplished using Equation \ref{10} to determine the ratio, \(\frac{[\ce{A^{-}}]} {[\ce{HA}]}\), that will produce the specified pH of the buffer solution. You will confirm the pH of this solution using your pH meter.

Finally, you will compare the buffering capacity of the buffer you prepare with that of deionized water.

Procedure

All experiments will be done in pairs. This way, you can compare your calculations before you do the next step. One way to organize group work is having one student to the experiment and another writing down results. It might make sense to do calculations outside of the lab after taking off gloves and goggles.

Materials and Equipment:

You will need the following additional items for this experiment: pH meter. There will be one shared one at every bench (so 3 pairs will share a pH meter).

Safety

Students must wear safety goggles when in the lab. Do not leave the lab with gloves on.

GLOVES: Gloves are needed when handling:

• zinc sulfate
• sodium carbonate
• sodium bisulfate
• methyl yellow
• congo red
• bromocresol green

WASTE DISPOSAL: All chemicals used must go in the proper waste container for disposal.

Part A: Determination of pH using Acid-Base Indicators

1. Rinse five small test tubes using deionized water (there is no need to dry these). To each of these test tubes add about 1 mL of 0.1 M \(\ce{HCl}\) (aq). (Estimate these volumes). To each of these test tubes add one of the five indicators listed in Table 1. Be sure to arrange or label your test tubes so that you know which indicator was added to which tube.
2. By comparing the colors you observe in each tube you should be able to determine the pH of the 0.1 M \(\ce{HCl}\) solution to within one pH unit (see background discussion). Record your color observations and your determination of the pH range of the 0.1 M \(\ce{HCl}\) solution on your data sheet.
3. Repeat the same procedure using each of the following solutions:

0.1 M sodium hydrogen phosphate, \(\ce{NaH2PO4}\) (aq)

0.1 M acetic acid, \(\ce{CH3COOH}\) (aq)

0.1 M zinc sulfate, \(\ce{ZnSO4}\) (aq)

4. Record your results for each on your data sheet.

Part B: Using pH Meters

Your instructor will demonstrate the proper use of the pH meters. 

1. Rinse four small 100 or 150-mL beakers several times using deionized water. Do not use any soap as the residue may affect your pH measurements.
2. Into each of your four clean beakers collect about 30 mL of one of the following:

0.1 M sodium chloride, \(\ce{NaCl}\) (aq)

0.1 M sodium carbonate, \(\ce{Na2CO3}\) (aq)

0.1 M sodium acetate, \(\ce{NaCH3COO}\) (aq)

0.1 M sodium hydrogen sulfate, \(\ce{NaHSO4}\) (aq)

3. Use your pH meter to determine the pH of each of these four solutions. Record the results on your data sheet. Add a drop or two or bromcresol green indicator to each of these solutions. Record the color of the indicator in each solution on your data sheet.

Part C: Using pH to Determine the Value of \(K_{a}\) for Acetic Acid, \(\ce{CH3COOH}\) (aq)

1. Rinse two small 100 or 150-mL beakers as before. Put 30 mL of 0.1 M acetic acid solution into the first beaker and 30 mL of 0.10 M sodium acetate solution into the second.
2. Use your pH meter to determine the pH of each solution. Record the results on your data sheet. You will use these values to calculate \(K_{a}\).

Part D: Buffer Solutions

First, verify the pKa measured in part C by combining 10 mL each of 0.1 M acetic acid solution and of 0.1 M acetate, and measuring the pH of this "1:1 buffer". 

Each student pair will try to get a slightly different pH value for their buffer: The pair closest to the windows will try to set the pH to be 0.1 units higher (more basic) than the pKa, the pair closest to the white board will try the set the pH 0.2 units lower (more acidic) than the pKa, and the remaining pair at a given bench will try to set the pH 0.3 units higher (more basic) than the pKa.Then, change the pH to the desired pH by adding the appropriate volume of one of the stock solutions.

You have to figure out which one, and how much you have to add. Make the new buffer solution and use your pH meter to measure the pH of your buffer solution and see how much it deviates from the assigned value.

Now we will test the buffer solution you prepared against changes in pH.

1. Rinse and fill another 150-mL beaker with a volume of deionized water equal to that of your buffer solution. Using your pH meter measure the pH of the deionized water. Do not be alarmed if this pH is less than neutral. It should be between 5.2 and 7.0. Do you know why? What species from the atmosphere dissolves in water that is left standing?
2. Add 1 drop of 0.1 M \(\ce{HCl}\) solution to both the beaker containing your buffer solution and that containing the deionized water. Measure the pH of each of these solutions following this addition and determine the change in pH of each. Record these values on your data sheet.
3. Clean up. Discard all chemicals in the proper chemical waste container. Clean and then return all borrowed equipment.