Posted by jessica on .
The Ka of hypochlorous acid (HClO) is 3.0 × 108 at 25°C. Calculate the pH of a 0.0385M hypochlorous acid solution?
i got help with this problem, but i don't get where one of the numbers came from (3.4 x 10^5)??? i tried makeing 3.0 x 10^8 the x but i still don't get that number.
start
0.0385
change
x. . . . .. . +x. . . .+x
at equilibrium
0.0385x. .. x..... . .x
Ka = 3.0 x 10^8 = [H+][ClO]/ [HClO]= (x)(x)/ 0.0385x
x = [H+]= 3.4 x 10^5 M
pH =  log 3.4 x 10^5=4.5

chemistry 
J,
Hiya,
From what you said it seems that you understand everything up till "x = [H+]= 3.4 x 10^5 M"
So we know that 3X10^8 = x^2/(0.0385x)
Bring (0.0385x) over to the left hand side,
Hence 3X10^8(0.0385x) = x^2
Then we expand the left hand side,
1.155X10^9  3X10^8x = x^2
From there we bring all terms to the right hand side to give
x^2 + 3X10^8x  1.155X10^9 = 0
Then we use our quadratic formula to solve for x > x = [b +/ sqrt(b^24ac)]/2a and reject the negative answer since x = concentration of H+ which cannot be negative. Then we get 3.4X10^5 M.
Alternatively, if the math is a little too tedious, we can approximate x to be near zero since HClO is a weak acid which only dissociates very little in aqueous solution. Then we get 3X10^8 = x^2/0.0385 which should be slightly simpler to solve.
Hope I helped! 
chemistry 
jessica,
where is 1.155X10^9 from?

chemistry 
J,
That comes from multiplying 3X10^8 and 0.0385 when we expand 3X10^8(0.0385x).