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# ENV4001 Assignment 2 Answer - G Chen Summer 2011 ENV4001...

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1 G. Chen Summer 2011 ENV4001 Environmental Engineering Problem Set # 2 (Due May 23, 2011) 1. Calcium carbonate (CaCO 3 ) is added to pure water. If solid CaCO 3 remains at equilibrium, what is the equilibrium molarity of calcium ions at 25 o C? What is the equilibrium molarity of calcium ions at 50 o C?  Solution: At 25 o C, ] CO ][ Ca [ K 2 3 2 sp + = Since there is no initial [Ca 2+ ] or [CO 3 2- ] in the solution, [Ca 2+ ] = [CO 3 2- ] M 10 07 . 7 M 10 5 K ] Ca [ ] Ca [ ] CO ][ Ca [ K 5 2 9 sp 2 2 2 2 3 2 sp + + + × = × = = = = For 50 o C, ) 25 15 . 273 1 50 15 . 273 1 ( 10 1.987 2.95 - ) T 1 T 1 ( R H K K Ln Kcal 95 . 2 45 . 288 63 . 161 77 . 129 H H H H 3 - 25 50 25 50 3 CaCO 32 CO 2 Ca + + × = = = + = + = + K 50 = 7.35× 10 -9 M 2 M 10 57 . 8 M 10 35 . 7 K ] Ca [ ] Ca [ ] CO ][ Ca [ K 5 2 9 sp 2 2 2 2 3 2 50 + + + × = × = = = = 2. Calculate the pH of the following solution using numerical methods.  Solution: a. Unknows: [H + ], [OH - ],[HA],[A - ]

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2 Equation 1: [H + ][OH - ]=K w =10 -14 Equation 2: ] HA [ ] A ][ H [ K 1 A + = Equation 3: [H + ]=[OH - ]+[A - ] Equation 4: C A =[ HA]+[A - ] Solve these four equations, we get 0 K K ) K K C ( ] H [ K ] H [ ] H [ A w w A A A 2 3 = + + + + + K A = 10 -4.7
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