Question

D S c) Uvs. S Part II. Solve the following problems. (68 pts) 5" (10 pts) Calculate as and ΔG。f mixing for a mixture of 1 mole of He, 3.0 moles of Ne, 2.0 mole of Ar, and 2.5 mole of Xe at T 298. 15K and P 1bar. The heat of mixing is zero. Based on your result, is the mixing spontaneous? 6. (10 pts) Consider a heat pump that removes heat from a cold reservoir (external ambient air) and deposits the heat into a cold reservoir (living room). Let's assume that the outside air is 25 C and the living room is 20°C Calculate the maxium efficiency of the heat pump operating between these two temperatures. How much work (in joules) must be done by the heat pump to supply 100 | of heat to the living room. a) b)

Answer 1

moles of H_c = 1 moles moles of N_e = 3 moles moles of A_r = 2 moles moles of x_e = 2.5 moles Total moles = 1 + 3 + 2 + 25 = 8.5 moles moles fraction of the = moles of the /Total moles - 1/0.5 = 0.1176 moles fraction of N_e = 3/8.5 = 0.3529 mole fraction of Ar = 2/8.5 = 0.2353 mole fraction of x_e = 2.5/8.5 = 0.2941 temperature (T) = 298.15k Heat of mixing is zero Implies Delta H = 0 Delta G mix = -n R (I_A ln T_A + x_B ln x_B + x_c ln x_c + x_B ln x_0) -8.5 times 8.34 {(0.1176 times s (0.1176)) + (0.3529 ln (0.3529)) + (0.2353 ln (0.2353)) + (0.2941))} Delta G mix = 93.2599 j/mole Delta G mix = -7 = -298.15 times 93.599 Delta G mix = -27814.38 j/mole Delta G mix = 93.2599 j/mole.k Delta G mix = -27814.38 j/mol yes, the reaction is spontaneous because the Delta c_1 is negative Delta c_1 < a Implies the reaction is spontaneous (a) Implies Temperature of outside air