Weak Acid: Titration with Strong Base

The titration curve will be calculated for a weak acid analyte, HA, that has an acid equilibrium constant of Ka, and an initial concentration of FHA. A strong base, NaOH, with concentration FNaOH, is used as the titrant.

Using the systematic approach to chemical equilibrium problems...

Chemistry:

Charge Balance:

Mass Balance:

Equilibrium Equations:

Solve for concentration of A- using mass balance and Ka...

Substitute [A-], [OH-]=Kw/[H3O+], and [Na+]=FNaOH into charge balance equation

Solve for [H3O+]

Calculation of Points Along the Weak Acid/Strong Base Titration Curve

Kw equilibrium may be neglected prior to the equivalence point when the acid concentration is high.

When Kw equilibrium can be ignored, the cubic equation reduces to...

This equation serves as the rule we can use to calculate the theoretical titration curve prior to the equivalence point. There are some important points.

Initial (Region 1), FNaOH=0 and…

The pH is found from [H3O+]. An approximation can be found for a weak acid, [H3O+]<FHA...

Note that when Ka is large...

1/2 way to the equivalence point (Region 2) FNaOH=½FHA, and ...

For Ka<<FNaOH (Weaker Acid)

For Ka>>FNaOH (Stronger Acid)

At the equivalence point (Region 3) FHA=FNaOH. At this point one cannot ignore Kw equilibrium when calculating [H3O+]. This is because the acid has been mostly converted to the conjugate base. The solution can still be found by reformulating the problem in terms of [OH-]. Using the systematic approach results in the governing equation for [OH-]

Kb is the conjugate base equilibrium constant for

Solving for [OH-]

Now since Kw is negligible relative to KbFNaOH

The solution to this quadratic equation is the root

Past the equivalence point (Region 4) all acid has been consumed. Although the above equation is valid, it is easier to calculate the through the excess added base

Resulting titration curve

The titration curve resulting from 40.0 mL of an acid with pKa=6.0, titrated with 0.1 F NaOH is shown here. The diamonds are points calculated using the methods above. The smooth black line is found by solving the cubic equation using iteration methods. Shown for reference, in pink, is the titration curve for 0.1 F strong acid.

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