Use the \" x is small \" approximation to find the concentration of the products

Question

Use the "x is small" approximation to find the concentration of the products in the following reaction which initially contains only 0.85 M HCN. Decide whether using the approximation was valid or invalid.

HCN(aq) H+(aq) + CN-(aq), Kc= 6.17 x 10-10

[H+] = [CN-] = 1.15 x 10-5 and the assumption was invalid

[H+] = [CN-] = 1.15 x 10-5 and the assumption was valid

[H+] = [CN-] = 2.29 x 10-5 and the assumption was invalid

[H+] = [CN-] = 2.29 x 10-5 and the assumption was valid

[H+] = [CN-] = 1.15 x 10-5 and the assumption was invalid

Explanation / Answer

          HCN(aq) <----> H+(aq) + CN-(aq),    Kc= 6.17 x 10-10

initial   0.85 M           0        0

change     -x              +x       +x

equil   0.85-x              x        x

Kc = [H+][CN-]/[HCN]

(6.17*10^-10) = (X*X)/(0.85-X)

X = 2.29*10^-5

[H+]= [CN-] = 2.29*10^-5 and the assumption was valid

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