By multiplying a conjugate acid (such as NH4+) and a conjugate base (such as NH3) the following is given:
By taking logarithms of both sides of the equation, the following is reached:
Finally, multipying throughout the equation by -1, the equation turns into:
After acquiring pOH from the previous pOH formula, pH can be calculated using the formula pH = pKw - pOH where pKw = 14.00.
Weak bases exist in chemical equilibrium much in the same way as weak acids do, with a Base Ionization Constant (Kb) (or the Base Dissociation Constant) indicating the strength of the base. For example, when ammonia is put in water, the following equilibrium is set up:
Bases that have a large Kb will ionize more completely and are thus stronger bases. As stated above, the pH of the solution depends on the H+ concentration, which is related to the OH- concentration by the Ionic Constant of water (Kw = 1.0x10-14) (See article Self-ionization of water.) A strong base has a lower H+ concentration because they are fully protonated and less hydrogen ions remain in the solution. A lower H+ concentration also means a higher OH- concentration and therefore, a larger Kb.
NaOH (s) (sodium hydroxide) is a stronger base than (CH3CH2)2NH (l) (diethylamine) which is a stronger base than NH3 (g) (ammonia). As the bases get weaker, the smaller the Kb values become. The pie-chart representation is as follows:
The typical proton transfer equilibrium appears as such:
B represents the base.
In this formula, [B]initial is the initial molar concentration of the base, assuming that no protonation has occurred.
Calculate the pH and percentage protonation of a .20 M aqueous solution of pyridine, C5H5N. The Kb for C5H5N is 1.8 x 10-9.
First, write the proton transfer equilibrium:
The equilibrium table, with all concentrations in moles per liter, is
|change in normality||-x||+x||+x|
|equilibrium normality||.20 -x||x||x|
|Substitute the equilibrium molarities into the basicity constant|
|We can assume that x is so small that it will be meaningless by the time we use significant figures.|
|Solve for x.|
|Check the assumption that x << .20||; so the approximation is valid|
|Find pOH from pOH = -log [OH-] with [OH-]=x|
|From pH = pKw - pOH,|
|From the equation for percentage protonated with [HB+] = x and [B]initial = .20,|
This means .0095% of the pyridine is in the protonated form of C5H6N+.
Other weak bases are essentially any bases not on the list of strong bases.
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