A sealed container was filled with 1 mol of A_2(g), 1 mol B_2(g) at 800 K and total pressure 1.00 bar. Calculate the amounts of the components in the mixture at equilibrium given that K = 1 for the reaction : A_2(g)+ B_2(g)hArr 2AB(g)

A sealed container was filled with 1 mol of A_2(g), 1 mol B_2(g) at 80

1.	A sealed container was filled with 1 mol of A_2(g), 1 mol B_2(g) at 800 K and total pressure 1.00 bar. Calculate the amounts of the components in the mixture at equilibrium given that K = 1 for the reaction : A_2(g)+ B_2(g)hArr 2AB(g)
Answer» Solution :`A_2(g) + B_2(g) hArr 2AB(g)` Total no. of moles `= 1-x+ 1 - x + 2x=2` `K_P = ((P_(AB))^2)/((P_(A_2))(P_(B_2))) =(((2x)/2xxP)^2)/((((1-x))/2xxP)(((1-x))/2xxP))` `K_P = (4x^2)/((1-x)^2)` Given that `K_P = (4x^2)/((1-x)^2) = 1` `RARR 4x^2 = (1-x)^2 rArr 4x^2 =1 +x^2 -2x` `3x^2 + 2x -1 = 0` `x = (-2 pmsqrt(4 - 4 xx 3 xx (-1)))/(2(3))` `x = (-2 pmsqrt(4 + 12))/6 = (-2pm sqrt16)/6 = (-2+4)/6,(-2-4)/6 = 2/6, (-6)/6` ` x = 0.33 , -1` (not posoible) `:.[A_2]_(eq) = 1 - x =1 - 0.33 = 0.67` `[B_2]_(eq) = 1- x = 1-0.33 = 0.67` `[AB]_(eq) = 2x = 2 xx 0.33 = 0.66`