Answer 12

Step 1

The first equilibrium. Since the two dissociations differ by 5 orders of magnetude we make the approximation that they can be treated in sequence. First, calculate the concentrations from the first equilibrium and second, using these concentrations find the final equilibrium concentrations.

species          []     H^+     []  
initial          1.00       0              0
change           -x          x              x
equilibrium      1.00 -x    x              x

[H^+] = [H_2PO_3^-]

[H^+]^2/(1 - [H^+]) = 0.01M; [H^+] = 0.0951M (solving the quadratic equation, but [H^+] = 0.1 M may be good enough!)

Step 2

species          []     H^+      
initial          0.0951M       0.0951M              0
change           -x          x              x
equilibrium      0.0951M -x    0.0951M + x              x

(0.0951M + x)(x)/(0.0951M - x) = 2.6 x 10^-7

Neglecting x with respect to 0.0951M gives x = = 2.6 x 10^-7M

[H^{^+}] = 0.0951M + x = 0.0951M + 2.6 x 10^-7M = 0.0953M

return