1. The problem is to calculate the pH given the hydrogen ion concentration $0.50$ moles per liter (m). 2. The formula for pH is given by $$\text{pH} = -\log_{10} [\text{H}^+]$$ where $[\text{H}^+]$ is the hydrogen ion concentration. 3. Substitute the given concentration into the formula: $$\text{pH} = -\log_{10} (0.50)$$ 4. Calculate the logarithm: $$\log_{10} (0.50) = \log_{10} \left(5 \times 10^{-1}\right) = \log_{10} 5 + \log_{10} 10^{-1} = 0.6990 - 1 = -0.3010$$ 5. Apply the negative sign: $$\text{pH} = -(-0.3010) = 0.3010 \approx 0.30$$ 6. Therefore, the pH of the solution is approximately $0.30$.