[Rei]

I know how to do this problem, but need confirmation regarding precision of calculation involving significant figures.

Information given: 0.010 M morphine solution, pH = 10.10, calculate Kb and pKb, morphine is a weak base

Calculating the [OH-] from the pH given yields an unrounded 1.258E-04 M, but the value accurate to the number of significant figures given from a pH of 10.10 is 1.2E-04 M.

My question is, after going through the necessary ICE table and writing the expression for Kb, is it correct to use the less precise value of [OH-] above, or is it also correct to use the more precise value? Each value yields a different value of Kb: 1.5E-06 and 1.6E-06, respectively to the less precise and more precise value.

[Borek]

yields an unrounded 1.258E-04 M, but the value accurate to the number of significant figures given from a pH of 10.10 is 1.2E-04 M.

That's not the correct way of rounding the result.

My question is, after going through the necessary ICE table and writing the expression for Kb, is it correct to use the less precise value of [OH-] above, or is it also correct to use the more precise value? Each value yields a different value of Kb: 1.5E-06 and 1.6E-06, respectively to the less precise and more precise value.

No, in general you should never use rounded down numbers in your calculations, that's asking for rounding errors (you see, this kind of error even has its own name).

[Rei]

1) Don't I retain the 2 in 1.25, and round down, because it's even?

2) I see, but could you give an explanation why, because we only know the concentration of [OH-] to be accurate to 2 significant figures, because there are two decimal places in the given pH?

[Corribus]

1) Don't I retain the 2 in 1.25, and round down, because it's even?

This rule most frequently applies when it is the last digit that is 5.

[Borek]

I see, but could you give an explanation why, because we only know the concentration of [OH-] to be accurate to 2 significant figures, because there are two decimal places in the given pH?

Report rounded down, but calculate with full digits (or at least several so called guard digits). Otherwise rounding errors will accumulate and your final result can be quite off, and can depend on the way you calculated it (ie what were the intermediate results).

See http://mathworld.wolfram.com/RoundoffError.html