Answer
The volume is equal to 0.104 L
Work Step by Step
1. Find the hydroxide concentration.
$$[H_3O^+] = 10^{-pH} = 10^{-12.4} = 4.0 \times 10^{-13} \space M$$
$$[OH^-] = \frac{1.0 \times 10^{-14}}{[H_3O^+]} = \frac{1.0 \times 10^{-14}}{ 4.0 \times 10^{-13} } = 2.5 \times 10^{-2} \space M$$
2. Since KOH is a strong base: $[KOH] = [OH^-] = 2.5 \times 10^{-2} \space M$
3. Use the dilution expression to find the volume of original solution:
$$c_1v_1 = c_2v_2$$
$$(0.855)v_1=(2.5 \times 10^{-2})(3.55)$$
$v_1 = 0.104 \space L$
