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In my book it's a multiple choice question with only one correct answer.

There are two solutions of $\ce{NaOH}$ and $\ce{NH_3}$ that have similar concentrations and volumes.

These two are among the options:

  1. $\ce{NaOH}$ has a higher $\ce{pH}$ than $\ce{NH_3}$
  2. $\ce{NaOH}$ has a higher $\ce{OH^-}$ concentration than $\ce{NH_3}$

Wouldn't these both be correct?

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Given that the solutions have equal concentrations, a solution of $\ce{NaOH}$ (a strong base) will be more basic than one of $\ce{NH3}$ (a weak base), since $\ce{NH3}$ only dissociates partially:

$$\ce{NH3 + H2O <<=> NH4+ + OH-}$$

Loosely speaking, the pH of a solution is defined to be

$$\mathrm{pH} = -\log_{10}[\ce{H+}]$$

and from the ionic product of water, we know that $[\ce{H+}][\ce{OH-}]$ is always a constant (equal to $10^{-14}\ \mathrm{M^2}$ at $25\ ^\circ\mathrm{C}$).

Therefore, a higher pH implies a lower concentration of $\ce{H+}$, and therefore a higher concentration of $\ce{OH-}$. This means that the truth of option 1 implies the truth of option 2, and vice versa, i.e. option 1 is logically equivalent to option 2.

My first suspicion would therefore be a typo in your book. In any case, your reasoning is correct.

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  • $\begingroup$ Great answer, thank you! I didn't know what the units for $K_w$ were, either. :) $\endgroup$ – Skeleton Bow Oct 6 '16 at 18:41
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    $\begingroup$ $[\ce{H+}][\ce{OH-}]$ is a product of two concentrations, so the units are simply concentration squared. $\endgroup$ – orthocresol Oct 6 '16 at 18:49
  • $\begingroup$ Correct me if I’m wrong, I’m new to these, but doesn’t it kind of matter based on what you mean by “higher pH”. Bc a higher pH on the Number scale would mean the solution is basic. However isn’t pH the measure of hydrogen ions in a solution? So by saying “higher pH” you could mean “higher measurement of hydrogen ions” which would then mean the solution is acidic. Someone just posted about this tonight on this question but it was deleted before I could reply. I can kinda see what they were saying tho. @orthocresol (Also how do you tag people in here) $\endgroup$ – Helloooo Feb 23 '18 at 2:48
  • $\begingroup$ @Hellooo no, a higher pH means less hydrogen ions not more. Please just read about this in any book/the Internet. $\endgroup$ – orthocresol Feb 23 '18 at 8:50

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