Question

Determine the pH of a 0.0003 M NaOH solution. Your answer must be within ± 0.1%?

Answer 1

If you really want to do this properly, just don't round until the end...

This is a strong base, so `["OH"^(-)] = ["NaOH"]`. Therefore:

`"pOH" = -log["OH"^(-)] = -log(0.0003) = 3.52_(287875)`

where subscripts indicate digits past a reasonable final digit of uncertainty.

Hence, the `"pH"` at `25^@ "C"` is:

`color(blue)("pH") = 14 - "pOH" = color(blue)(10.48)`

while the exact solution to `8` decimal places is `10.47_(712125)`. This is obviously within `0.1%`:

`(10.48 - 10.47712125)/(10.47712125) xx 100% ~~ 0.03%`