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Thermodynamics — Chemistry STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceChemistryThermodynamics5 Marks
Question
Derive the relationship between $\Delta\text{H}$ and $\Delta\text{U}$ for an ideal gas. Explain each term involved in the equation.
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Answer

Solids and liquids do not show significant change in the volume when heated. Thus ifchange in volume, $\Delta\text{V}$ is insignificant,

$\Delta\text{H}=\Delta\text{U}+\text{P}\Delta\text{V}$

$\Delta\text{H}=\Delta\text{U}+\text{P}(0)$

$\Delta\text{H}=\Delta\text{U}$

The difference between the change in internal energy and enthalpy becomes significant when gases are involved in the reaction.

Consider a chemical reaction occurring at constant temperature, T and constant pressure, P. Now, let’s say that the volume of the reactants is VA and the number of moles in the reactants is nA. Similarly, the volume of the products is VB and the number of moles in the product is nB.

We know that according to the ideal gas equation,

$\text{Pv}=\text{nRT}$

$\text{pv}_\text{A}=\text{n}_\text{A}\text{RT}$

$\text{pv}_\text{B}=\text{n}_\text{B}\text{RT}$

Thus $\text{pv}_\text{B}-\text{pv}_\text{B}=\text{n}_\text{B}\text{RT}-\text{n}_\text{A}\text{RT}$

$\text{p}(\text{v}_\text{B}-\text{v}_\text{A})=\text{RT}(\text{n}_\text{B}-\text{n}_\text{A})$

$\text{p}\Delta\text{v}=\Delta\text{n}_\text{g}\text{RT}$

$\Delta\text{H}=\Delta\text{U}+\text{p}\Delta\text{v}$

$\Delta\text{H}=\Delta\text{U}+\Delta\text{n}_\text{g}\text{RT}$

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