How much Sodium Hydroxide solution of 0.05-mol/L is used to neutralize 100-mL of perchlorate acid with pH of 1

Question

a) 200-mL
b) 100-mL
c) 50-mL
d) 20-mL

Answer 1

Sodium Hydroxide reacts with perchlorate acid in a 1:1 ratio. That means that x moles of Sodium Hydroxide will always react with x moles of perchlorate acid.

If the pH (-log[H+]) is 1, then the concentration of H+ ions is
10^(-1) = 0.1mol/L. That also means that the concentration of the acid is 0.1mol/L. If you have 100mL (0.1L) of the acid, then the number of moles of the acid is

0.1mol/L * 0.1L = 0.01mol perchlorate acid. This means that 0.01mol of Sodium Hydroxide is needed to neutralize the acid.
If you have 0.01mol of 0.05M Sodium Hydroxide, the volume of the base is

0.01mol/(0.05mol/L) = 0.2L = 200mL.

Answer 2

a)
The reaction is: NaOH + HClO4 --> NaClO4 + H2O
The molar ratio is 1:1
So the number of moles of both substances must be the same.
pH = -log[H+], so [H+] = 10^-pH = 10^-1 = 0.1 mol/L
V(NaOH) = c(HClO4)*V(HClO4)/c(NaOH)
Insert numbers and you get an answer.