HW Key _12 s problems part a

# HW Key _12 s problems part a - S45 One mole of an ideal gas...

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S45. One mole of an ideal gas is allowed to expand reversibly and isothermally (25 °C) at a pressure of 1 atm to a pressure of 0.1 atm. a. What is the change in free energy Starting with the Gibbs equation for dG dG = SdT + VdP For constant temperature we obtain dG = VdP Using the ideal gas law and integrating from P 1 to P 2 we obtain dG = nRT dP P Δ G = nRT ln P 2 P 1 This is the expression for finding the change in Gibbs Free Energy for an isothermal reversible expansion of an ideal gas. Δ G = (1 mole)(8.31451 J/mol-K)(298 K)ln 0.1 atm 1.0 atm = 5.7 kJ b. What would be the change in free energy if the process occurred irreversible? Δ G = 5.7 kJ It doesn’t matter if the expansion is reversible or not because G is a state function; therefore, it is independent of path. S46. Consider the spontaneous process for one mole of water going from H 2 O ( ) at 110 °C and 1.00 atm to H 2 O (g) at 110 °C and 1.00 atm. Calculate H , and S and show that S > Q /T. The enthalpy of vaporization of water at 100 °C is found on p. 746 while the heat capacities of liquid water and steam can be assumed constant at 4.18 J/g K and

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