2N_2O_5(s) rightleftharpoons 4NO_2(g) + O_2(g)2N2O5(s)⇌4NO2(g)+O2(g)
Use DeltaG^o = -RTlnK_c" => K_c = e^(-(DeltaG^o"/"RT"))
DeltaG^o = DeltaH^o - TDeltaS^o
T = 298.15K
DeltaH^o = Sigman*DeltaH_f^o(Products) - Sigman*DeltaH_f^o(Reactants)
= [4DeltaH_f^o(NO_2(g)) + 1DeltaH_f^o(O_2(g))] - [2DeltaH_f^o(N_2O_5(s))]
= [4(33.18) + 1(0)]Kj - [2(11.3)] Kj
= +110.12Kj
DeltaS^o = Sigman*S^o(Products) - Sigman*S^o(Reactants)
= [4S^o(NO_2(g)) + 1S^o(O_2(g))] - [2S^o(N_2O_5(s))]
= [4(239.95) + 1(205.03)]J/K - [2(347.19)]J/K
= +470.45J/K = +0.47045"Kj"/K
DeltaG^o at (298.15K):
DeltaG^o = DeltaH^o - TDeltaS^o
= [110.12Kj] - (298.15K)[0.47045"Kj"/K]
= -30.14Kj
DeltaG^o = -RTlnK_c"
=> lnK_c = -(DeltaG^o"/"R*T")= - [(-30.14)/(0.008314*298.15)]"mole"
= 12.18322mol"; drop units in final value of K_c
K_c = e^12.18322 =1.96x10^5
