question_answer 93)

  Derive the relationship between \[\Delta H\]and \[\Delta U\]for an ideal gas. Explain each term involved in the equation.

Answer:

  We know \[H=U+PV\] \[({{H}_{2}}-{{H}_{1}})=({{U}_{2}}-{{U}_{1}})+P({{V}_{2}}-{{V}_{1}})\]                 \[\Delta H=\Delta U+P\Delta V\] For ideal gas \[PV=nRT\,\,\,\,\,\,\,\,\,\,\,......(i)\] \[\therefore \]\[P\Delta V=\Delta {{n}_{g}}RT\] From (i) and (ii) \[\Delta H=\Delta U+\Delta {{n}_{g}}RT\] Where \[\Delta {{n}_{g}}=({{n}_{2}}-{{n}_{1}})\] = Number of gaseous moles of products - Number of gaseous moles of reactants