x2- solution

Question

3) Elements of group 16 form hydrides with the generic formula H2X. When gaseous H2X is bubbled through a solution containing 0.3M HCl, the solution becomes saturated and [H2X] = 0.1M. The following equilibria exist in this solution:

H2X (aq) + H2O (l) ⇔HX-(aq) + H3O+ (aq) K1 = 8.3 x 10-8

HX-(aq) + H2O (l) ⇔ X2- + H3O+ (aq) K2 = 1 x 10-14

Calculate the concentration of X2- in solution.

Answer 1

K1 = 8.3x10^-8 = [HX^-][H3O+]/H2X] = (x)(x)/0.1 - x (neglect x in denominator assuming it is small relative to 0.1M)

x^2 = 8.3x10^-9

x = 9.1x10^-5 M (which is certainly small relative to 0.1 M, so assumption was valid)

x = 9.1x10^-5 M is the [HX^-] from the first dissociation.  Using this in the second dissociation....

 

K2 = 1x10^-14 = [X^2-][[H3O+]/[HX^-]

1x10^-14 = (x)(x)/9.1x10^-5 - x (making same assumption as above)....

x^2 = 9.1x10^-19

x = [X^2-] = 9.5x10^-10 M