Question

The ka of hypochlorous acid (hclo) is 3.0 ⋅ 10−8 at 25.0 °c. calculate the ph of a 0.0375m hypochlorous acid solution.

Answer 1

We can set up an ICE table for the reaction:                      
                      HClO          H+     ClO-
Initial              0.0375       0        0
Change         -x               +x      +x
Equilibrium    0.0375-x     x        x

We calculate [H+] from Ka:     
     Ka = 3.0x10^-8 = [H+][ClO-]/[HClO] = (x)(x)/(0.0375-x)

Approximating that x is negligible compared to 0.0375 simplifies the equation to         
     3.0x10^-8 = (x)(x)/0.0375     
     3.0x10^-8 = x2/0.0375     
     x2 = (3.0x10^-8)(0.0375) = 1.125x10^-9     
     x = sqrt(1.125x10^-9) = 0.0000335 = 3.35x10^-5 = [H+]
in which 0.0000335 is indeed negligible compared to 0.0375.

We can now calculate pH:     
     pH = -log [H+] = - log (3.35 x 10^-5) = 4.47