# For the reaction 2 Na ( g ) ⇌ Na 2 ( g ) the following values of K have been determined (C. T. Ewing et al., J. Chem. Phys . 1967 , 71 , 473 ): T (K) K 900 1.32 1000 0.47 1100 0.21 1200 0.10 From these data, estimate Δ rxn H ° for the reaction.

### Physical Chemistry

2nd Edition
Ball + 3 others
ISBN: 9781133958437

Chapter
Section

### Physical Chemistry

2nd Edition
Ball + 3 others
ISBN: 9781133958437
Chapter 5, Problem 5.42E
Textbook Problem
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## For the reaction 2 Na ( g ) ⇌ Na 2 ( g ) the following values of K have been determined (C. T. Ewing et al., J. Chem. Phys. 1967 , 71 , 473 ): T (K) K 900 1.32 1000 0.47 1100 0.21 1200 0.10 From these data, estimate Δ rxn H ° for the reaction.

Interpretation Introduction

Interpretation:

The value of ΔrxnH° from the given data is to be predicted.

Concept introduction:

The relationship between equilibrium constants at two different temperatures is expressed as,

lnK2K1=ΔH°R(1T11T2)

### Explanation of Solution

The relationship between ΔrxnH° and K is expressed as,

dlnK=ΔrxnH°Rd1T

The slope obtained from the graph plotted between 1T and lnK is equal to ΔrxnH°R.

The y-axis of the graph is lnK and the x-axis of the graph is 1T.

The value of 1T and lnK from the given data is,

 T(K) K 1T lnK 900 1.32 0.0011 0.278 1000 0.47 0.001 −0.755 1100 0.21 0.00091 −1.56 1200 0.10 0.00083 −2.30

The graph plotted between 1T and lnK is shown in Figure 1.

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