Power-Law Reaction Rate

The power-law rate expression, $r = k C_A^{\,n}$, is an empirical fit rather than a law of nature, and treating it as more than that causes most of the trouble it gets into. The order $n$ is a number found by measuring rates at different concentrations and fitting a straight line to $\ln r$ against $\ln C_A$. It is NOT read off the balanced equation. Only an elementary reaction — one that really does happen in a single molecular collision — has orders equal to its stoichiometric coefficients, and most industrially interesting reactions are multi-step sequences that do not.

Fractional orders are therefore ordinary rather than pathological. An order of 1.5 usually signals a chain mechanism; an order of 0.5 often means a dimer dissociating before the rate-determining step; an order that starts near 1 at low concentration and falls toward 0 at high is the signature of a catalyst surface saturating, which the Langmuir–Hinshelwood form describes properly. A NEGATIVE order is real too, and means a species inhibits its own reaction — typically a product competing for the same active sites.

Now the part this site cannot fix for you, and the reason this page carries a warning the others do not. The units of $k$ depend on $n$. At first order $k$ is s⁻¹. At second order it is m³/(mol·s). At an order of 1.5 it is (mol/m³)^−0.5·s⁻¹, which has no name and no entry in any unit converter, because its dimensions are not known until the reader supplies $n$. This calculator therefore takes $k$ as a plain SI number and converts nothing: whatever you type is used exactly as typed.

That makes one specific error very easy and very expensive. Kinetics tables almost universally publish second-order constants in L/(mol·s), and SI wants m³/(mol·s) — a factor of 1000. Third-order constants are out by a million. The concentration boxes on this page do convert, so entering 2 mol/L correctly becomes 2000 mol/m³ internally; the $k$ box cannot. Divide a tabulated second-order constant by 1000 before it goes in, and check the resulting rate against something you know — a half-life, a conversion you have measured — before it sizes a vessel. A silent factor of a thousand in a reactor volume is not a rounding error.