Answer
The pH of the solution is approximately 1.60206.
Work Step by Step
1. Find the nº of moles in the solution.
nº of moles = concentration $\times$ volume
nº of moles = 0.25 $\times$ 0.005
nº of moles = 0.00125.
2. Now, find the concentration of $HClO_4$ after the dilution.
concentration = nº of moles $\div$ volume
concentration = 0.00125 $\div$ 0.05
concentration = 0.025
$[HClO_4] = [H^+]$ = 0.025
3. With the concentration of $H^+$, calculate the pH of the solution:
$pH = -log[H^+]$
$pH = -log(0.025)$
$pH \approx 1.60206$
