RDGEquilCalc - Using Quadratic Formula to find Eq Conc If...

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Using Quadratic Formula to find Eq Conc If 0.200 mol CO & 0.100 mol H 2 O are reacted in 100 mL flask at 900 K according to the rxn: CO(g) + H 2 O(g) ' CO 2 (g) + H 2 (g), K c = 1.56. What are [equilibrium]? [CO] i = 0.200 mol / 0.100 L = 2.00 M [H 2 O] i = 0.100 mol / 0.100 L = 1.00 M Conc. (M) CO(g) + H 2 O(g) ' CO 2 (g) + H 2 (g) Initial 2.00 1.00 0 0 Change x x +x +x Equilibrium 2.00 – x 1.00 – x x x K c = [CO 2 ][H 2 ] = (x)(x) = x 2 =1.56 [CO][H 2 O] (2.00 – x)(1.00 – x) (x 2 – 3x +2) 1.56 (x 2 – 3x +2) = x 2 Æ 1.56x 2 – 4.68x +3.12 = x 2 Quadratic Eqn: ax 2 + bx +c = 0 0.56x 2 – 4.68x +3.12 = 0 Quadratic Formula: x = –b ± (b 2 – 4ac) ½ 2a x = 4.68 ± ((–4.68) 2 – 4(1.56)(3.12)) ½ = 7.6 M & 0.73 M 2 (0.56) x = 0.73 M gives correct equilibrium positions: Conc. (M) CO(g) + H 2 O(g) ' CO 2 (g) + H 2 (g) Equilibrium 2.00 – x 1.00 – x x x x = 7.6 5.6 5.6 7.6 7.6 x = 0.73 1.27 0.27 0.73 0.73 Check answer by solving for K c : K c = [CO 2 ][H 2 ] = (0.73)(0.73) = 1.6 [CO][H 2 O] (1.27)(0.27)
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Simplifying Assumption w/ small K & large initial conc For rxn: C(O)Cl 2 (g) ' CO(g) + Cl 2 (g) K c = 8.3 x 10 -4 (at 360 ° C) Calculate [CO] eq , [Cl 2 ] eq , and [C(O)Cl
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This note was uploaded on 11/20/2010 for the course CHEMISTRY Chem 1LE taught by Professor Dr.kimberlyedwards during the Spring '10 term at UC Irvine.

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RDGEquilCalc - Using Quadratic Formula to find Eq Conc If...

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