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Thermodynamics — Chemistry STD 11 Science — Question

Gujarat 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 $V _{ A }$ and the number of moles in the reactants is $n _{ A }$. Similarly, the volume of the products is $V _{ B }$ and the number of moles in the product is $n _{ B }$. We know that according to the ideal gas equation,
$\text{pv}_\text{A}=\text{n}_\text{A}\text{RT}$
$\text{pv}_\text{B}=\text{n}_\text{B}\text{RT}$
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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