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# Lec 15 - Temperature Dependence of Water Autoionization Use...

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1 1 Use the following information to determine the pH of pure water at 50 o C. 2H 2 O(l) H 3 O + (aq) + OH (aq) K w = [H 3 O + ][OH ] = 5.48 x 10 -14 at 50 o C. pH = - log [H 3 O + ] A) pH = 7.4 B) pH = 7.0 C) pH = 6.6 Temperature Dependence of Water Autoionization 2 For pure water at 50 o C 2H 2 O H 3 O + + OH K w = [H 3 O + ] [OH - ] =5.48 x 10 -14 and the pH = 6.6 At this temperature, water is __________. A) acidic: [H 3 O + ] > [OH - ] B) neutral: [H 3 O + ] = [OH - ] C) basic: [H 3 O + ] < [OH - ]

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2 3 The auto-ionization equilibrium constant for water increases with increasing temperature. K w (298 K) = 1.0 x 10 -14 K w (323 K) = 5.5 x 10 -14 What properties of water cause this increase in K w ? 4 What properties of water cause this increase in K w with increasing temperature? Thermodynamics provides the answer! G = H – T S G = G o +RT ln(Q) G o = –RT ln(K) 1 ln( ) o o H S K R T R  
3 5 The auto-ionization equilibrium constant for water increases with increasing temperature. This fact reveals _________ when water autoionizes. A) that energy is released (exothermic) B) that energy is absorbed (endothermic) C) nothing about the change in energy 1 ln( ) o o H S K R T R   6 H o /R = 6964.2 H o = 57.90 kJ/mol S o /R = 8.841 S o = 73.50 J/mol Temperature Dependence of Water Autoionization y = -6964.2x - 8.841 -34 -33 -32 -31 -30 0.0030 0.0031 0.0032 0.0033 0.0034 0.0035 0.0036 1/T with T in K ln(K) 1 ln( ) o o H S K R T R  

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