Final answer:
pKa and pKb are measures of the strengths of acids and bases, respectively, where pKa+pKb=pKw, the ionization constant of water, which is typically 14. Thus, knowing either pKa or pKb allows you to calculate the other, helping to determine the acid or base strength.
Step-by-step explanation:
The pKa and pKb values are related to the strength of acids and bases, respectively. The pKa is a measure of how easily an acid donates a proton, and the pKb measures how readily a base accepts a proton. The smaller the pKa, the stronger the acid, and conversely, the smaller the pKb, the stronger the base. In an aqueous solution, the relationship between pKa and pKb can be given as:
pKa + pKb = pKw,
where pKw is the ionization constant of water, which is generally 14 at 25 degrees Celsius. This means that knowing either the pKa or pKb allows one to calculate the other. These relationships are derived from the fundamental definitions of pKa and pKb which are:
- pKa = -log(Ka), where Ka is the acid dissociation constant.
- pKb = -log(Kb), where Kb is the base dissociation constant.
For weak acids and bases, Ka and Kb are related by the equation:
Ka × Kb = 1.0 × 10-14
Therefore, if you know the pKa, you can find the pKb using:
pKb = 14 - pKa
This relationship helps in calculating one value from the other, essentially allowing the determination of all four quantities (Ka, Kb, pKa, pKb) if any one is known.