Chapter 4, Problem 4.30NP

Interpretation Introduction

Interpretation:

The values of ΔU, ${\text{ΔU}}_{\text{R}}^{\text{0}}$ and the relative errorneed to be calculated for the reaction:

  ${\text{C}}_{\text{2}}{\text{H}}_{\text{4}}{\text{(g) + H}}_{\text{2}}\text{(g) }\to {\text{ C}}_{\text{2}}{\text{H}}_{\text{6}}\text{(g)}$

Concept Introduction:

Internal energy (U) is a thermodynamic function which depends on the initial and final state of the system and independent of the path

The change in internal energy for a given reaction can be deduced from the difference in the bond energies of the product and reactants i.e.

  $\text{ΔU = }{\displaystyle \sum \text{Bond energy }}\text{(products) - }{\displaystyle \sum \text{Bond energy}}\text{(reactants) ------(1)}$

The standard internal energy change for a reaction ${\text{ΔU}}_{\text{R}}^{\text{0}}$ is given in terms of the standard enthalpy change ${\text{ΔH}}_{\text{R}}^{\text{0}}$ as:

  ${\text{ΔU}}_{\text{R}}^{\text{0}}\text{ = }\Delta {\text{H}}_R^0-\Delta \text{nRT ------(2)}$

Here, Δn = change in the number of moles of products and reactants

R = gas constant

T = temperature