Concentrated Weak Acid: If the conditions (Ka and initial concentration) of the acid leads to little dissociation of the acid, then the denominator of the equilibrium relationship may be simplified (alleviating the need to solve a quadratic)
or, in a more familiar relation
In many cases (particularly for those where the system volume does not change) we
are free to assume a hypothetical system with a volume of 1 [liter], effectively
replacing mole numbers with concentrations and ignoring the volume.
Buffers are the solution which contain high concentrations of a weak acid and its conjugate base. If both HA and A- are present initially, the equilibrium relation looks like:
If both initial concentrations of HA and A- are large compared to the extent of the advancement, the [H+(aq)]e can be approximated as
The Dynamic Range of the human ear is supposedly 13 orders of magnitude. This means that the slightest noise perceptible to the ear is 1013 times smaller than the highest level of sound that we still can hear without damage. The dynamic range of the acidic strengths of molecules or ions in water slightly surpasses even this impressive value. The range of Ka's goes from 1 for H+(aq) to 10-14 for H2O itself, i.e.
Just like with sound levels, it is convenient to 'compress' the range of possible
values. In electronics, we use the Decibel, in Chemistry we use pH.
pH = -log10([H+(aq)] / 1M)
pOH = -log10([OH-(aq)] / 1M)
pKa =
-log10(Ka)
This convenient shorthand is ubiquitous in Acid/Base terminology. For instance, the pH of a buffer solution is often written (the 'Henderson-Hasselbalch' equation)
A note on significant figures: The number of significant figures of a pH value is the number of significant places to the right of the decimal. The whole number to the left of the decimal is an exponent and is taken as exact
i.e. pH = 2.88 implies [H+(aq)] = 1.3 x 10-3 M NOT 1.32 x 10-3 M
Conceptual Problems in Equilibrium
Consider the addition of a pressure of pA0 of gaseous monomer to a vessel of
volume V. Dimerization occurs and the total pressure of the system
decreases by 10% at equilibrium. What is the extent of the reaction, the
equilibrium mole fractions of the constituents and the equilibrium constant for
the reaction at this temperature? Is the volume of the system relevant? What
would be the pressure change upon equilibration if the initial pressure of
monomer, pA0 , was doubled?
Within what range of pH units is the 'Henderson-Hasselbalch' equation accurate to +/- 0.1 pH units? In other words, how close to the pKa of the acid does the pH have to be for the approximate buffer equation to be valid?