Question

Consider a chemical reaction in which X and Y combine to form XY at equilibrium: X + Y ⇌ XY The equilibrium constant for the reaction is Kc = 1.2x10^-4. Initially, [X] = 0.2 M and [Y] is unknown. If 0.1 M of Y is added to the reaction mixture, what will be the new equilibrium concentration of XY?

Answer 1

To solve this problem, we will use the equilibrium constant expression and an ICE  Initial, Change, Equilibrium  table. The equilibrium constant expression for the given reaction is:Kc = [XY] /  [X] * [Y] Given Kc = 1.2 x 10^-4 , [X] = 0.2 M initially, and 0.1 M of Y is added. Let's assume the initial concentration of Y is y M. Then, the initial concentration of XY is 0 M.Now, we can set up the ICE table:          X      +      Y          XYInitial: 0.2 M          y M             0 MChange:  -x M         -x M           +x MEquilibrium:  0.2-x  M  y-x  M       x MSince 0.1 M of Y is added, the new equilibrium concentration of Y will be  y + 0.1 - x  M.Now, we can plug these equilibrium concentrations into the equilibrium constant expression:1.2 x 10^-4  = x /   0.2 - x  *  y + 0.1 - x  We need to find the value of x, which represents the equilibrium concentration of XY. However, we have two unknowns  x and y  in the equation. To solve for x, we need to make an assumption.Since Kc is very small  1.2 x 10^-4  , we can assume that the reaction does not proceed significantly to the right. Therefore, x will be very small compared to 0.2 and y. With this assumption, we can simplify the equation:1.2 x 10^-4   x /   0.2  *  y + 0.1  Now, we can solve for x:x  1.2 x 10^-4  *  0.2  *  y + 0.1 Unfortunately, we cannot find the exact value of x without knowing the initial concentration of Y  y M . However, we now have an equation that relates x to y. If the initial concentration of Y is known, we can use this equation to find the new equilibrium concentration of XY.