this is for holding javascript data
Jason R. Green edited Second-order decay.tex
over 9 years ago
Commit id: 84686ec2e0d8354f49534ecefd91fcca61f7faa9
deletions | additions
diff --git a/Second-order decay.tex b/Second-order decay.tex
index 9576d2a..8710570 100644
--- a/Second-order decay.tex
+++ b/Second-order decay.tex
...
In first order irreversible decay, the inequality between the statistical length squared and Fisher divergence determines when a rate coefficient is constant, which is only when the inequality turns into an equality.[cite] A similar inequality is found in second order kinetics.
Putting in the time dependent rate coefficient for a second order irreversible decay, the inequality becomes
\begin{equation}
\omega^2[A_0]^2\Delta{t}^2-\left(\omega[A_0]\Delta{t}\right)^2\geq0 \omega^2 C_A(0)^2\Delta{t}^2-\left(\omega C_A(0)\Delta{t}\right)^2 \geq 0
\end{equation}
This result is very similar to that of first order irreversible decay($\omega^2\Delta{t}^2)-\left(\omega\Delta{t}\right)^2\geq0$, the only difference being a dependence on the initial concentration of the reactant. This initial concentration dependence serves to cancel the concentration units in the second order rate coefficient, making the statistical length and Fisher divergence dimensionless. When there is a time independent rate coefficient and there is no static disorder, the equality holds
$\omega^2[A_0]^2\Delta{t}^2=\left(\omega[A_0]\Delta{t}\right)^2$. $\omega^2 C_A(0)^2\Delta{t}^2 = \left(\omega C_A(0)\Delta{t}\right)^2$.