Question

Derive the relationship between ΔH and ΔU for an ideal gas. Explain each term involved in the equation.
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Answer 1

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☞༆Solids and liquids do not show significant change in the volume when heated. Thus if change in volume, ∆V is insignificant ∆H=∆U+P∆V ∆H=∆U+P(0) ∆H=∆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,Read more on Sarthaks.com - https://www.sarthaks.com/123098/derive-the-relationship-between-and-for-ideal-gas-explain-each-term-involved-the-equation.

Answer 2

Answer:

The relationship between ΔH and ΔU for an ideal gas can be written as,

ΔH = ΔU + ΔnRT

where R is the universal gas constant, T is the temperature and Δn is the change in the number of moles.

Explanation:

Consider a chemical reaction is processing at a constant temperature, T and constant pressure, P. The volume of the reactants is V and the number of moles in the reactants is n. Similarly, the volume of the products is V' and the number of moles in the product is n'.

According to the Ideal gas law equation,

For reactants, PV = nRT

For products, PV' = n'RT

Subtracting both the equation,

PV - PV' = nRT - n'RT

PΔV = ΔnRT

The ΔH and ΔU can be related as,

ΔH = ΔU + PΔV

Hence,

ΔH = ΔU + ΔnRT

Hence, the relationship between ΔH and ΔU for an ideal gas is ΔH = ΔU + ΔnRT.

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