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Chemistry LibreTexts

Solutions of Polyprotic Acid/Base Systems, Problem D

4. Calculate the pH of a solution prepared by adding 55 mL of 0.098 M sodium phosphate to 65 mL of 0.136 M phosphoric acid.

If groups are having trouble getting started on this problem, encourage them to write all of the reactions corresponding to the phosphate species and identify (circle) the species that are initially present.  When groups have written the proper reactions, write them on the board and circle the two species that are present in the initial solution.

What type of reaction is going to occur? What type of species is phosphoric acid?  What type of species is phosphate?

Students should recognize very quickly that phosphoric acid is an acid and phosphate is a base (but not conjugate pairs) and that these two can neutralize each other leading to the formation of intermediate species.

Write the neutralization reaction that will occur.

            Write this reaction on the board once the groups have written it. 

What is the Kn for this reaction? Does it go to completion?

            Students should not have trouble with this question at this point.

What is present after the initial neutralization?

Students should have no trouble calculating the concentration (or moles) of all of the phosphate species present after neutralization, and should recognize that one of the reactants is in excess. Encourage them to rewrite the equations corresponding to this system and circle all of the species present.

What will happen next?

Students may struggle with the next step of this problem. They may be tempted to assess the extent of back-reaction. They may need help seeing that another neutralization reaction can occur. If they are tempted to treat this system as a buffer, ask them which one they would use to calculate the pH in order to get them thinking more about species present. Spend about five to ten minutes discussing this.

Write the neutralization reaction that will occur.

Write this reaction on the board once the groups have written it.   Remind groups to carry forward any amounts that were already produced in the first neutralization reaction as the initial concentrations for the second neutralization reaction.

What is the Kn for the neutralization reaction that will occur with the remaining species?

Students may have trouble knowing which Ka and which Kb to use when calculating the Kn. Encourage the students to take their time with this step.

What is present after the second neutralization reaction? Are there any further neutralization reactions that can occur with those species that are now in solution? What is the pH?

Remind students to keep the stoichiometric coefficients in mind when carrying out these calculations. It should take students about ten minutes to complete this problem.  Spend some time at the board to summarize the entire calculation and describe why it makes sense for the system to eventually get to the state where only one reaction is needed to calculate the pH.  It can also be helpful to have groups use the major species and calculated pH to calculate the concentration of the other species in solution.  Writing the final concentrations of everything in solution further demonstrates how the other reactions and other species are insignificant compared to the two major species.