Question

When a general base associates in water, with `K_b` `"<<"` `10^(-5)`, what is the algebraic expression for `x` as a function of `K_b` and the equilibrium concentration of the base?

Answer 1

As usual, write out the reaction.

`"B"(aq) + "H"_2"O"(l) rightleftharpoons "OH"^(-)(aq) + "BH"^(+)(aq)`

By constructing an ICE table, you would obtain:

`K_b = (["OH"^(-)]["BH"^(+)])/(["B"]) = x^2/(["B"] - x)`

As `K_b` `"<<"` `10^(-5)`, we can of course use the small `x` approximation, and thus, `["B"] - x ~~ ["B"]`. Thus:

`color(blue)(x ~~ sqrt(K_b["B"]))`

And you can always use this expression for a weak base equilibrium in which `K_b` is on the order of `10^(-5)` or less. What does `x` represent, and what is the answer?

Did you check your answer by trying to see if the `"pH"` was more than `7`?