1. **State the problem:** Find the pH of a solution when the concentration of hydrogen ions $[H^+]$ is 0.0053 moles per liter. 2. **Recall the formula:** pH is defined as $$\text{pH} = -\log [H^+]$$ where $[H^+]$ is the hydrogen ion concentration. 3. **Substitute the given value:** $$\text{pH} = -\log(0.0053)$$ 4. **Calculate the logarithm:** First, express 0.0053 in scientific notation: $$0.0053 = 5.3 \times 10^{-3}$$ 5. **Use log properties:** $$\log(5.3 \times 10^{-3}) = \log(5.3) + \log(10^{-3}) = \log(5.3) - 3$$ 6. **Evaluate $\log(5.3)$:** approximately 0.7243 7. **Calculate pH:** $$\text{pH} = - (0.7243 - 3) = -0.7243 + 3 = 2.2757$$ 8. **Final answer:** $$\boxed{\text{pH} \approx 2.28}$$ This means the solution is acidic since pH is less than 7.