Is the equation pH + pOH = 14 valid at different temperatures?
$\mathrm{pH + pOH = 14}$


This equation only holds true at around $25~^\circ\mathrm{C}$, where the water autodissociation constant $K_\mathrm{w} = 10^{-14}$.

Mathematically, you can write

$$\begin{align}
K_\mathrm{w} = [\ce{H+}][\ce{OH-}] &amp;= 10^{-14} &amp; &amp;\\
\log([\ce{H+}][\ce{OH-}]) &amp;= \log(10^{-14}) &amp; &amp;\text{(logarithms of both sides)} \\
\log[\ce{H+}] + \log[\ce{OH-}] &amp;= -14 &amp; &amp;(\log(ab) = \log a + \log b) \\
-\log[\ce{H+}] - \log[\ce{OH-}] &amp;= 14 &amp; &amp; \\
\mathrm{pH + pOH} &amp;= 14 &amp; &amp; \text{(definitions of pH and pOH)}
\end{align}$$

It's fairly clear from this that if $K_\mathrm{w}$ is $10^{-x}$ at some other temperature, then you will obtain $\mathrm{pH + pOH} = x$.