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Prove that Delta H = Delta U + Delta ngR...

Prove that `Delta H = Delta U + Delta` ngRT.

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Cosider a chemical between gases occuring at constant temperature (T) and and pressure (p)
Let, voluem of reacting gases = `V_(r)`
Volume of product gases = `V_(p)`
Number of moles of reactant gases = `n_(r)`
Number of moles of product gases = `n_(P)`
`therefore` According to ideal gas equation `p_(V) = nRT`
Ideal gas equation, For reactants, `pV_(r) = n_(r)RT` (at constant T and P)
For products, `pV_(P) = n_(p)RT`
Subtracting equation (ii) from (iii), we get
`p(V_(p) - V_(r)) = (n_(P) - n_(r)) RT`
Or `pDelta V = Delta n_(g) RT`
`[therefore Delta n_(g) = n_(p) - n_(l) , Delta V= V_(p) - V-r)]`
By putting value of `PDeltaV` in equation = `Delta H = Delta U + pDelta V`, we get
`Delta H = Delta U + Delta n_(g)RT`
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