Posted by **jessica** on Tuesday, November 23, 2010 at 2:38pm.

The Ka of hypochlorous acid (HClO) is 3.0 × 10-8 at 25°C. Calculate the pH of a 0.0385-M hypochlorous acid solution?

i got help with this problem, but i dont 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 dont get that number.

start

0.0385

change

-x. . . . .. . +x. . . .+x

at equilibrium

0.0385-x. .. x..... . .x

Ka = 3.0 x 10^-8 = [H+][ClO-]/ [HClO]= (x)(x)/ 0.0385-x

x = [H+]= 3.4 x 10^-5 M

pH = - log 3.4 x 10^-5=4.5

- chemistry -
**J**, Tuesday, November 23, 2010 at 3:17pm
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/(0.0385-x)

Bring (0.0385-x) over to the left hand side,

Hence 3X10^-8(0.0385-x) = 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^2-4ac)]/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**, Tuesday, November 23, 2010 at 3:26pm
where is 1.155X10^-9 from?

- chemistry -
**J**, Wednesday, November 24, 2010 at 7:43am
That comes from multiplying 3X10^-8 and 0.0385 when we expand 3X10^-8(0.0385-x).

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