To calculate the pH of a solution when given the hydroxide ion concentration \([OH^-]\), we can follow these steps:
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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: \[ \text{pOH} \approx -(\log(4.5) + \log(10^{-3})) \] \[ \text{pOH} \approx -0.653 + 3 \approx 2.347 \]
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Calculate the pH: We can use the relationship between pH and pOH: \[ \text{pH} + \text{pOH} = 14 \] Solving for pH gives: \[ \text{pH} = 14 - \text{pOH} = 14 - 2.347 \approx 11.653 \]
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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: \[ \text{pH} \approx 12 \]