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Suppose a 500. mL flask is filled with 0.50 mol of N, and 0.60 mol of NO, The following reaction becomes possible: N,(g)+0,(g) 2NO(g) The equilibrium constant K for this reaction is 1,78 at the temperature of the flask, Calculate the equilibrium molarity of N,. Round your answer to two decimal places. Execanation The key to solving an equilibrium composition problem is the connection between the equilibrium molarities of each reactant and the equilibrium constant K: wh] 2 NO Peto =K_ The equilibrium constant expression is on the left side of this equation. 2)L2] You can use this equation to calculate A from the equilibrium molarities. But if you know instead, you can use the equation "backwards" to calculate the equilibrium molarities. First, set up a reaction table: [N.] [92] Exo]. initial j 1 0 0 12 Since we're after the equilibrium molarity of N, we might as well let x stand for the change in molarity of change x x -2x | Ny equilibrium ||.0+x| x (1.22x Example = Next, substitute the expressions in the last row of the reaction table for the molarities in the equilibrium constant expression: [N, ][.] (1.04+x)(x) Finally, substitute the equilibrium constant for K and solve the equation for x: (1.2-2x)" =1,78 Here's the equation. (1.0+x)(x) (1.2-2x) =1.78 (1.044) (x) Clear the fraction. 1.444.8x+437 =1.78x+ 1.7837 Multiply out both sides. 2.2247 6.58x+1.44=0 Collect terms. - a\\2 d- . x= 6.584y (~ 6.58)" 4-2.22-1.44 Use the quadratic formula to solve for x, 22.22 x=2.726, 0.2379 There are two possible values for x. Althouoh the quadratic formula cives vou two wales for rv only one is nhwsically reasonable. Which one? lonk hack at the enuilibrium molarities in the = Example (1.2-2x)? =1.78(1.0+2)(x) Clear the fraction. 1.44-4.8x+4x" =1.78x+ 1.78x" Multiply out both sides. 2.22y? 6.58x+1.44=0 Collect terms. a\" 2-2.22 Use the quadratic formula to solwe for x. x=2.726, 0.2379 There are two possible values for x. Although the quadratic formula gives you two values for x, only one is physically reasonable. Which one? Look back at the equilibrium molarities in the equilibrium table. None of them can be negative -- a negative molarity makes no physical sense. In this case, using the first value (x =2.726) would make at least one equilibrium molarity negative, so using this value for x makes no physical sense. Now that you know +, go back to the last row of the reaction table and use it to calculate N