A weak base is a base that, upon dissolution in water, does not dissociate completely, so that the resulting aqueous solution contains only a small proportion of hydroxide ions and the concerned basic radical, and a large proportion of undissociated molecules of the base.
Bases yield solutions in which the hydrogen ion activity is lower than it is in pure water, i.e., the solution is said to have a pH greater than 7.0 at standard conditions, potentially as high as 14 (and even greater than 14 for some bases). The formula for pH is:
Bases are proton acceptors; a base will receive a hydrogen ion from water, H_{2}O, and the remaining H^{+} concentration in the solution determines pH. A weak base will have a higher H^{+} concentration than a stronger base because it is less completely protonated than a stronger base and, therefore, more hydrogen ions remain in its solution. Given its greater H^{+} concentration, the formula yields a lower pH value for the weak base. However, pH of bases is usually calculated in terms of the OH^{−} concentration. This is done because the H^{+} concentration is not a part of the reaction, whereas the OH^{−} concentration is. The pOH is defined as:
If we multiply the equilibrium constants of a conjugate acid (such as NH_{4}^{+}) and a conjugate base (such as NH_{3}) we obtain:
As is just the self-ionization constant of water, we have
Taking the logarithm of both sides of the equation yields:
Finally, multiplying both sides by -1, we obtain:
With pOH obtained from the pOH formula given above, the pH of the base can then be calculated from , where pK_{w} = 14.00.
A weak base persists in chemical equilibrium in much the same way as a weak acid does, with a base dissociation constant (K_{b}) indicating the strength of the base. For example, when ammonia is put in water, the following equilibrium is set up:
A base that has a large K_{b} will ionize more completely and is thus a stronger base. As shown above, the pH of the solution, which depends on the H^{+} concentration, increases with increasing OH^{−} concentration; a greater OH^{−} concentration means a smaller H^{+} concentration, therefore a greater pH. Strong bases have smaller H^{+} concentrations because they are more fully protonated, leaving fewer hydrogen ions in the solution. A smaller H^{+} concentration means a greater OH^{−} concentration and, therefore, a greater K_{b} and a greater pH.
NaOH (s) (sodium hydroxide) is a stronger base than (CH_{3}CH_{2})_{2}NH (l) (diethylamine) which is a stronger base than NH_{3} (g) (ammonia). As the bases get weaker, the smaller the K_{b} values become.^{[1]}
As seen above, the strength of a base depends primarily on pH. To help describe the strengths of weak bases, it is helpful to know the percentage protonated-the percentage of base molecules that have been protonated. A lower percentage will correspond with a lower pH because both numbers result from the amount of protonation. A weak base is less protonated, leading to a lower pH and a lower percentage protonated.^{[2]}
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, C_{5}H_{5}N. The K_{b} for C_{5}H_{5}N is 1.8 x 10^{−9}.^{[3]}
First, write the proton transfer equilibrium:
The equilibrium table, with all concentrations in moles per liter, is
C_{5}H_{5}N | C_{5}H_{6}N^{+} | OH^{−} | |
---|---|---|---|
initial normality | .20 | 0 | 0 |
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 = pK_{w} - 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 C_{5}H_{5}NH^{+}.