Question

A sample containing 2.50 moles of He (1 bar, 345 K ) is mixed with 1.75 mol of Ne (1 bar, 345 K ) and 1.50 mol of Ar (1 bar, 345 K ).

Calculate ΔGmixing. Calculate ΔSmixing. Express your answer with the appropriate units. Calculate ΔA for the isothermal compression of 3.11 mol of an ideal gas at 321 K from an initial volume of 60.0 L to a final volume of 20.5 L.​ Does it matter whether the path is reversible or irreversible?​

Part A

Under anaerobic conditions, glucose is broken down in muscle tissue to form lactic acid according to the reaction:
C6H12O6→2CH3CHOHCOOH
Thermodynamic data at T= 298 K for glucose and lactic acid are given below.

	ΔH∘f(kJ⋅mol−1)	C∘p(J⋅K−1⋅mol−1)	S∘(J⋅K−1⋅mol−1)
Glucose	-1273.1	219.2	209.2
Lactic Acid	-673.6	127.6	192.1

Calculate ΔG∘R at T= 298 K. Assume all heat capacities are constant in this temperature interval.

Express your answer with the appropriate units.

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Part B

Calculate ΔG∘R at 318 K . Assume all heat capacities are constant in this temperature interval.

Express your answer with the appropriate units.

Answer 1

Mole fraction of He = 2.5/ (2.5 +1.75 +1.50) = 0.435

Mole fraction of Ne = 1.75/  (2.5 +1.75 +1.50) = 0.30

Mole fraction of Ar = 1.50/ (2.5 +1.75 +1.50) =0.26

Total moles = 5.75 moles

Gmix = nRT xiln xi

= 5.75 moles * 8.314 J/K/mol * 345 K [(0.435 *ln0.435) + (0.30 ln 0.30) + (0.26ln 0.26)]

= 17705.6 J/mol

Smix = -nR xiln xi = -51.32 J/mol/K

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PV = nRT

P = nRT/ V = 3.11 mol * 0.082 L atm/K/mol * 321 K/ 60 L = 1.36 atm

dA = -PdV -SdT

as this is a isothermal process, so, dT=0

dA = -PdV = -1.36 atm (20.5-60)L = 53.72 L.atm