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Solutions that are Mixtures of Acids and Bases, Problem A

4. Calculate the pH of a solution that is prepared by mixing 45 mL of 0.224 M chlorobenzoic acid (3-) with 30 mL of 0.187 M ethylamine.

Is ethylamine an acid or a base? What is its chemical formula?

After a few minutes the groups should have identified the species as an acid or base. It may be helpful at this point to introduce abbreviations for the species (e.g., Hcba = chlorobenzoic acid) present that take into account their acidic or basic properties that will simplify writing the reaction and equilibrium constant expression.

What happens when we add an acid to a base?

Students usually realize that neutralization occurs.

What is the correct reaction to express the neutralization that occurs? Write the Kn expression for this reaction?

It should take the students no more than five minutes to correctly answer both of these questions.

Do we have a table of Kn values?

Since we do not, is there a way we could construct the Kn reaction by adding together a series of reactions for which we do know the K values? 

In general, if a reaction can be broken down into steps, how do we calculate the K value for a net equation based on the K values for the steps?

Most likely a few students will recall that K values are multiplied together to find a K value for the net equation.

Based on this relationship, write an expression for Kn in terms of values we know.

All of the groups realize that the Ka and Kb expressions are needed, but most ignore the H3O+, OH- and H2O in these reactions and initially believe that Kn = Ka x Kb.  If so, ask them to evaluate the value for Kn using this expression.  Finding that the value is small:

What does it mean if Kn is quite small and does this make sense based on your knowledge of neutralizations?

Some students may not be bothered by the small Kn because it came from the reaction of a weak acid with a weak base.

What about the reaction involving H2O that is also occurring in the solution?

After a few minutes students should identify the reaction as the opposite of the Kw reaction. They will probably need to be reminded that when the opposite of a reaction with a known K is occurring, you multiply by the inverse.

What is the expression for Kn and what is the actual value of Kn in the problem. In general, how can we predict the magnitude of Kn­?

Spend about ten minutes talking about Kn values in general. When will Kn ­be big? What would it take for Kn to be small?  Point out that Kn will always be large when either the acid or base is strong.

Groups can then be instructed to set up a table of values under the neutralization reaction that show the initial concentrations and to construct other appropriate rows under that (e.g., equilibrium concentration, etc.)

Most groups often subtract x from the initial amounts of both reactants.  If so, it helps to ask:

What should x be when K is large?

Groups soon realize that x would be large and that a large K means that the reaction will go to completion.  Indicate that the second line in the table should be the concentrations present in solution after the reaction has gone to zero. 

What are the concentrations of the four species once the reaction has gone to completion?

One of the values in this line will be 0 and it is useful to ask whether this value could actually be zero.  Groups will realize that it cannot and must be a finite number.  The concept of a back reaction occurring for a reaction that goes to completion can be introduced.

Is there any substantial back reaction?

Most groups realize that the back reaction must be small for a reaction with a large K.  They can now write the third line of the chart, which has terms for the concentrations of each species at equilibrium.

Groups are now asked to calculate the pH for the solution?

Most groups see that there is extra chlorobenzoic acid and use this extra amount with its Ka expression to calculate a pH.  Rarely do the students see that appreciable amounts of chlorobenzoic acid and the chlorobenzoate anion exist such that this constitutes a buffer with appreciable quantities of a conjugate pair.  At this point I usually like to go up to the board where I have written the reaction and say let’s circle all those species that we have appreciable amounts of.  Prompting that there are appreciable amounts of chlorobenzoic acid and its conjugate anion usually eventually triggers the realization that it is a buffer. It is worth mentioning that neutralization reactions frequently result in buffer solutions.

At this point, the groups can calculate the pH using the Henderson-Hasselbach expression for the chlorobenzoic acid.  They can also calculate the pH by substituting the amounts of aniline and anilinium obtained from the neutralization reaction into its corresponding Henderson-Hasselbach expression.  We then discuss why both values must be identical if we have done the problem correctly.