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# ln13s08 - Lecture 13 Complex Equilibria What to do when...

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Lecture 13: Complex Equilibria -- What to do when assumptions aren't okay To this point in creating acid base equilibria we have made our lives simple by working with compounds and amounts that reduce calculations to 4 forms: [H + ] = C a [H + ] = (K a C a ) 1/2 [H + ] = K a (C a /C b ) [H + ] = (K a1 K a2 ) 1/2 To do this we either used monoprotic acids and bases with K values between 10 -4 and 10 -10 , or we used polyprotic acids with well separated K values in that K range. And we always used high concentrations, like C = 0.1M. Armed with these two simple approximation ideas: high C and K far apart, we could do a lot of water chemistry problems very simply. But these approximations don’t always work. For example, we couldn't work problems like What is the pH of 0.1M sulfuric acid? Reason: (K s too close) What is the pH of 0.1M HClO 2 (K a =10 -2 )? Reason: (K a too close to strong acid case) What is the pH of 0.1M CH 3 OH (K a =10 -14 )? Reason: (K a too close to K w ) What is the pH of 10 -8 M HCl or 10 -8 M NaOH? Reason: (C too small so K w matters) To illustrate, consider the problem if - 0.1 M H 2 SO 4 : this should be a strong acid case but there are multiple sources of H + from three dissociations K a1 = = infinity K a2 = = 1.1 x 10 -2 K w = (H + )(OH - ) = 1 x 10 -14 and while we can ignore the H + from K w , we can’t ignore the H + from the K a2 and simply use H + = C a if this was a simple strong acid case like 0.1M HBr. (H + )(HSO 4 - ) ----------------- (H 2 SO 4 ) ----------------- (H + )(SO 4 - ) (HSO 4 - ) 10^3 greater for K's for C has to be 10^-3 or greater

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- 0.1M HClO 2 : this should be a weak acid case but while we can ignore K w because it is far from K a =10 -2 we can’t make the assumption that yields H + =(KC) 1/2 and instead must use the quadratic solution from the RICE expression HA HA + + A - C 0 0 -x +x +x C-x x x - 0.1M CH 3 OH: this should be a weak acid case but the K a and K w are too close so we have to consider both the methanol as a weak acid and the water as a weak acid at the same time
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ln13s08 - Lecture 13 Complex Equilibria What to do when...

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