Calculate the pH of a solution that has [OH^-] = 4.5 × 10^-3 M. Be sure your answer has the correct number of significant figures.

1 answer

To calculate the pH of a solution when given the hydroxide ion concentration \([OH^-]\), we can follow these steps:

  1. Calculate the pOH: The pOH can be calculated using the formula: \[ \text{pOH} = -\log[OH^-] \] Given that \([OH^-] = 4.5 \times 10^{-3} , M\): \[ \text{pOH} = -\log(4.5 \times 10^{-3}) \]

    Using a calculator, we find: \[ \text{pOH} \approx -(\log(4.5) + \log(10^{-3})) \] \[ \text{pOH} \approx -0.653 + 3 \approx 2.347 \]

  2. Calculate the pH: We can use the relationship between pH and pOH: \[ \text{pH} + \text{pOH} = 14 \] Solving for pH gives: \[ \text{pH} = 14 - \text{pOH} = 14 - 2.347 \approx 11.653 \]

  3. Significant Figures: The concentration \([OH^-] = 4.5 \times 10^{-3}\) has 2 significant figures, which indicates that we should round our final answer to 2 significant figures.

Therefore, rounding 11.653 to 2 significant figures gives us: \[ \text{pH} \approx 12 \]

Final answer: \[ \text{pH} \approx 12 \]