Whenconcentrationof reactantisdecreasedequilibrium

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Unformatted text preview: tion of H2? 19 Chemistry 102 Chapter 14 CALCULATIONS INVOLVING QUADRATIC EQUATIONS · Some of the problems invo lving equilibrium invo lve use of the quadratic equation in order to determine the unknown variable. The example below shown one such problem. Example 6: ¾¾ ® PCl5 (g) ¬¾ PCl3 (g) + Cl2 (g) ¾ If the init ial concentration of PCl5 is 1.00 M, what is the equilibrium co mposit ion of the gaseous mixt ure at 160 °C? Kc at 160 °C is 0.0211 PCl5 decomposes when heated: ¾¾ ® PCl5 (g) ¬¾ ¾ PCl3 (g) + Cl2 (g) Init ial 1.00 M 0 0 D –x +x +x Equilibrium 1.00–x x x K c = [PCl3 ][Cl2 ] (x)(x) = = 0.0211 [PCl5 ] (1.00 x) 2 (0.0211)(1.00 – x) = x 2 0.0211 – 0.0211 x = x 2 x + 0.0211 x – 0.0211 = 0 2 ax + bx + c = 0 x1 ,x 2 = 2 x + 0.0211 x – 0.0211 = 0 x = 2 0.0211 ± (0.0211) 2 4( 0.0211) = 2 b ± b 2a 4ac 0.0211 ±0.2913 2 · In theory: There are two mathemat ical so lut ions · In practice: Only one so lution makes physical sense 20 Quadratic Equation Chemistry 102 x 1 = Chapter 14 0.0211 + 0.29 3 1 = 0. 351 1 2 x 2 = 0.0211 0.29...
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