Answer to Question #164571 in Molecular Physics | Thermodynamics for ziad

Question

consider two state system in thermal equilibrium, where the upper state has an energy 3.09 kj/mol higher than the lower state. if we have total population of thousand molecules distributed between these states, at what temperature (in c) will 15.6% of the molecules be in the upper state?

Answer 1

Answer

Population is given by

$\frac{N_{upper}}{N_{lower}}=e^{-(\frac{E_1-E_2}{kT})}$

Putting all values as above theory of question

$\frac{15.6}{100\times1000}=e^{-(\frac{3090\times10^3}{8.314\times T})}$

$\frac{10^6}{156}=e^{(\frac{3090\times10^3}{8.314\times T})}$

Taking natural logrithm

And temperature

$T=\frac{3090\times1000}{8.314\times8.8}=42234K$