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The textbook says that the weaker the acid, the smaller the value of Ka and the greater the value of pKa. If I'm interpreting this correctly, it makes sense that a weak acid would have a greater number on the pH scale because the lower the number the more acidic and the greater the number the more basic. However, the textbook also says that the weaker the base, the smaller the value of Kb and the greater the value of pKb. I'm confused because I thought that a weak base would have a lower value on the pH scale. How do pKa/pKb relate to pH?
The pKa/pKb have no direct relation to the actual pH of a solution, however you use the values pKa and pKb to determine the hydronium and hydroxide ions of their respective reaction and use those values to determine the pH.
With regards to Kb, one is looking at the pOH scale instead of the pH scale because OH- ions are produced, not H3O+ during the dissociation/reaction of a base. Therefore, on the pOH scale, having a greater value means that the base is weak.
The pKa gives you the acidity value of a substance and the Ka value indicates that the amount of acid that actually dissociates. While the pkb gives you the basicity value of a substance and the Kb value determines the level of dissociation of a base. For example, if given the pKa, you can use 10^-pKA to get the Ka. Essentially to solve for the [H+] or x value, you set the Ka equal to [products]/[reactants]. To find the pH, you then take the -log of [H+]. The pKa gives you the acidity value of a substance and the Ka value indicates that the amount of acid that actually dissociates. The same is for pkb and Kb, except they're used to find the pOH.
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