Chapter 12, Problem 12.13P

Interpretation Introduction

Interpretation:

The equilibrium constant for the ionization equilibrium of sodium atoms at 1000K has to be calculated.

Concept Introduction:

The expression for the equilibrium constant for the ionization of sodium is given below.

$N{a}_{\left(g\right)}\stackrel{}{\rightleftarrows }N{a}_{\left(g\right)}^{+}+1e_g^{-}$

$Equilibriumcons\tan t,K=\frac{q_m^{\Theta }\left(N{a}_{}^{+},g\right)\times q_m^{\Theta }\left(e^{-},g\right)}{q_m^{\Theta }\left(Na,g\right)\times N_A}{e}^{\frac{-\Delta E}{RT}}$

Where,

    $\begin{array}{c}{q}_m^{\Theta }\left(N{a}_{}^{+},g\right)=partitionfunctionofN{a}_{}^{+}\\ q_m^{\Theta }\left(e^{-},g\right)=partitionfunctionof{e}^{-}\\ q_m^{\Theta }\left(Na,g\right)=partitionfunctionofNa\\ N_A=avogadronumber=6.022\times {10}^{23}\\ \Delta E=differenceinmolarenergybetween\\ thegroundstateoftheproductandthatofreac\tan t\\ R=universalgascons\tan t=8.3145J/K/mol\\ T=temperatureinkelvinscale\end{array}$