= Temperature sensitivity of a catalytic ozone balance
{title2=$d\ln[\mathrm O_3]/d(T^{-1})$}
Suppose a reduced steady balance is $P=AX^2+BX$, where $X=[\mathrm O_3]$, and hold $P$ and all specified background <concentrations> fixed. With $u=1/T$, $d\ln A/du=-a$ and $d\ln B/du=-b$, implicit differentiation gives $d\ln X/du=(aAX^2+bBX)/(2AX^2+BX)$. The quadratic loss term includes temperature-dependent O/O3 partitioning as well as the direct reaction coefficient. Holding the loss ratio fixed over a finite change is an additional approximation; solving the new quadratic provides a check.
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