The base imidazole has a `K_(b)` of `8.1 xx 10^(-8)`.
a. In what amounts should `0.02 M HCI` and `0.02M` imidazole be mixted to make `100mL` of a buffer at `pH 7`?
b. If the resulting solution is diluted to `1L`, what is the `pH` of the diluted solution?

Explanation

a. `pOH = pK_(b) +log ("salt/base")`
`7 = 8 - 0.90848 + log ("salt/base")` and `("base/salt") = 1.234458`.
Let `xmL` of `HCI` and `ymL` of imisazole are mixed (since molarity is same)
`{:(,,HCI+,Baserarr,"Salt"),("Initial",,x,(y),0),("Final",,0,(y-x),x):}`
`x +y = 100mL, y = 100 - x`
`("Base")/("Salt") = (y-x)/(x) = (100-2x)/(x) = 1.2358`
`x = 30.9 mL ("volume of acid")`
Volume of imidanzole `= 100 - 30.9 = 69.1`
b. `pH remains same (since on dilution the concentration of salt and base changes in the same proportions).