Even More Obvious Tricks in Acid Base Equilibrium

Iterative Numerical Approximation is often used instead of analytic solutions because the application of such algorithms is much more general than symbolic solutions. For example, consider the solution of a weak acid HA an approximate solution is of the form

If we ignore the [H3O+] in the denominator we have the concentrated weak acid approximation.

If the initial ionization of water can be ignored, this is the standard setup for dissociation that we see in the text and very similar to the dimerization equilibrium we solved using the quadratic formula.

A more accurate solution may be obtained from the simultaneous solution of the water autoinionization equilibrium:

To solve for four unknowns we need two more equations. Defining nHA0/V = [HA]0

But the solution must be electrically neutral

And of course the acid equilibrium gives us the four equations we need

So, solving for the [H3O+] in terms of constants and initial conditions

Yields the final, although cumberson result:





Numerical Example (Iteration): Calculate the pH of 0.100M NaHSO4

Sodium ions are the conjugate acid of a strong base

Bisulfate is the conjugate base of a strong acid but the conjugate acid of a weak base!

Determine Ka of (HSO4)- from a Table (1.1 x 10-2)

Make series of 'iterated guesses' for the value of y

Iteration trial y [HA]0 - y LHS
1 0 M 0.10 M 0.033166
2 0.0331166 0.066834 0.027114
3 0.027114 0.072886 0.028315
4 0.028315 0.071685 0.028081




Result [H3O+]e = 0.028M (2 sig figs); pH = 1.55 (2 sig figs)



A Review of General Equilibrium Concepts
Remember that the Numerical Value Equilibrium Constants depends on Choice opf the Standard State. We can forget about this in Acid / Base calculations if we choose only to use one Standard State.
But Gases had two standard states which could be interrelated...

The equilibrium constant, taken as a dimensionless number that is a function of temperature only, has to be referenced to a definition of the standard state for the molecular number density. If that standard is 1 mol/L, we say the equilibrium constant is KC, if the standard is atm pressure, the equilibrium constant is labeled Kp

Recall the expression for KC:

The proper quotient of equilibrium partial pressures, assuming the ideal gas equation of state (pV=nRT) is

Therefore the relationship relating the equilibrium constants references to the different standard states is temperature dependent

This distinction is particularly important in systems where the volume is changed. Then, the partial pressure divided by the total pressure yields the mole fraction of the particular constituent

Only when the sum of the generalized stoichiometric coefficients in the reaction is non-zero will a change in pressure or volume affect the equilibrium mole fractions, concentrations of course all scale with total volume for a closed system.

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