Hydrochloric acid is diluted with pure water until its concentration is $5.0 \times 10^{-8}\ \text{mol L}^{-1}$. What is the pH of this solution at $298\ \text{K}$? Take $K_w = 1.0 \times 10^{-14}$ at $298\ \text{K}$, and remember that water itself ionises.