PCl5 at 1.00 M decomposes to PCl3 and Cl2 with Kc = 0.0211. What is [PCl5] at equilibrium?

1. With no product present at the start, Q is zero, so the reaction proceeds to the right. 2. Let x be the rise in each product, so the equilibrium rows read 1.00 minus x, x and x. 3. Substituting gives 0.0211 = x squared divided by (1.00 minus x). 4. Rearranged this is x squared plus 0.0211x minus 0.0211 = 0. 5. The discriminant is 0.0211 squared plus 4 x 0.0211, which is 0.0848, whose root is 0.291. 6. So x = (minus 0.0211 plus 0.291) divided by 2 = 0.135 M. 7. The other root, minus 0.156, is rejected because a negative change gives negative concentrations. 8. Subtract: 1.00 minus 0.135 = 0.87 M, while 0.135 M is the value for each product. _Source: OpenStax Chemistry (CC BY 4.0), Ch 13 "Fundamental Equilibrium Concepts", section 13.4 Equilibrium Calculations_