Chemistry 2710 Spring 2000 Quiz 9 Solution

The Boltzmann equation is

$$\frac{N_2}{N_1} = e^{-\Delta E/(kT)}.$$

We want to solve this equation for T:

$$\begin{eqnarray*}% latex2html id marker 12 \ln\left(\frac{N_2}{N_1}\right) & = &... ...fore T & = & -\frac{\Delta E}{k\ln\left(\frac{N_2}{N_1}\right)}. \end{eqnarray*}$$

We want $N_2/N_1 = \frac{1}{10}$. The results are (to one significant figure)

$\Delta E$ (J)	T (K)
10-18	30000
10-20	300
10-22	3