Answer
$$pH_{initial} = 7.00$$ $$pH_{final} = 1.70$$
Work Step by Step
1. Calculate the $HCl$ concentration:
$$\frac{0.010 \space moles \space HCl}{500.0 \space mL} \times \frac{1000 \space mL}{1 \space L}= 0.020 \space M \space HCl$$
2. In a pure water solution, the initial pH is neutral
$$pH_{initial} = 7.00$$
3. Since $HCl$ is a strong acid, we can assume that:
$$[H_3O^{+}] = [HCl] = 0.020 \space M \space HCl$$
Thus: $$pH_{final} = -log(0.020) = 1.70$$
