Asample containing 2.50 mol of an ideal gas at 298 k is expanded from an initial volume of 10.0 l to a final volume of 50.0 l. calculate δg and δa for this process for:
(a) an isothermal reversible path and (b) an isothermal expansion against a constant external pressure of 0.750 bar. explain why δg and δa do or do not differ from one another.

a) ΔG=ΔA= -33.452 J

b) ΔG=ΔA=0

Explanation:

a) according to the first law of thermodynamics the change in Gibbs free energy and Helmholtz free energy is

dG=VdP - SdT

dA=  -PdV - SdT

for an isothermal path dT=0 , therefore

ΔG=∫VdP = ∫(nRT/P)dP= nRT ln P2/P1

ΔA= ∫ (-P)dV = ∫ (-nRT/V)dV = nRT ln V1/V2

also from the ideal gas equation from an isothermal process

P1*V1= nRT = P2*V2 → P2/P1 = V1/V2

ΔG= nRT ln V1/V2 = 2.5 mol * 8.314 J/mol K P ln (10L/50L) = -33.452 J

for Helmholtz free energy is also

ΔA= nRT ln V1/V2 = -33.452 J

since the final energy is lower than the initial one , the process is spontaneous

for an isothermal process and isobaric process, dT=0 and dP=0, therefore

ΔG= VdP - SdT = 0

since → P2/P1 = V1/V2= constant → dV=0

ΔA=0

ΔG=ΔA for an ideal gas in an isothermal process since G and A differ only in the H and U terms , but since these ones depends only on temperature for an ideal gas (H(T)=U(T) + PV = U(T) + nRT) , they stay constant under an isothermal process and therefore ΔG=ΔA.

the reaction mixture contains some ammonia, plus a lot of unreacted nitrogen and hydrogen. the mixture is cooled and compressed, causing the ammonia gas to condense into a liquid. the liquefied ammonia is separated and removed. the unreacted nitrogen and hydrogen are then recycled back into the reactor .

hydrocarbons are organic compounds that contain only hydrogens and carbons. they can be saturated (those which contain only carbon-carbon single bonds) or unsaturated (those which contain carbon-carbon double or triple bonds) in nature. hydrocarbons can undergo several reactions like substitution, elimination etc.  

on substituting one or more hydrogen atoms in hydrocarbon it results in the formation of haloalkane. as the halogen atoms are large compared to the carbon and hydrogen atoms, due to which the molecular weight increases and the bond become polar because of presence electronegative halogen atom and results in the increase in boiling point of the haloalkane.

thus, the correct option is (b) that is the boiling point of the new compound increases on substituting a hydrogen atom with a halogen in a hydrocarbon.