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Chapter 14: Problem 89

Calculate the pH of the following solutions. a. 0.10\(M\) NaOH b. \(1.0 \times 10^{-10} M \mathrm{NaOH}\) c. 2.0 \(\mathrm{M} \mathrm{NaOH}\)

Short Answer

Expert verified
The pH of the NaOH solutions are approximately: a. 13.00 for the 0.10 M NaOH solution b. 4.00 for the \(1.0 \times 10^{-10} M \) NaOH solution c. 13.70 for the 2.0 M NaOH solution

Step by step solution

01

Write the dissociation equation for NaOH

NaOH is a strong base, and when it dissolves in water it dissociates completely into its constituent ions: \[ \ce{NaOH -> Na+ + OH-} \]
02

Calculate the hydroxide ion concentration

The concentration of hydroxide ions (\( [\mathrm{OH^-}] \)) is equal to the initial concentration of NaOH. a. For the 0.10 M NaOH solution, \[ [\mathrm{OH^-}] = 0.10 \; M \] b. For the \(1.0 \times 10^{-10} M \) NaOH solution, \[ [\mathrm{OH^-}] = 1.0 \times 10^{-10} \; M \] c. For the 2.0 M NaOH solution, \[ [\mathrm{OH^-}] = 2.0 \; M \]
03

Calculate pOH for each solution

The pOH of each solution can be calculated using the formula: \[ \mathrm{pOH} = -\log_{10}[\mathrm{OH^-}] \] a. For the 0.10 M NaOH solution, \[ \mathrm{pOH} = -\log_{10}(0.10) \approx 1.00 \] b. For the \(1.0 \times 10^{-10} M \) NaOH solution, \[ \mathrm{pOH} = -\log_{10}(1.0 \times 10^{-10}) = 10.00 \] c. For the 2.0 M NaOH solution, \[ \mathrm{pOH} = -\log_{10}(2.0) \approx 0.30 \]
04

Calculate pH using the relationship between pH and pOH

The relationship between pH and pOH is given by: \[ \mathrm{pH} + \mathrm{pOH} = 14 \] a. For the 0.10 M NaOH solution, \[ \mathrm{pH} = 14 - \mathrm{pOH} = 14 - 1.00 \approx 13.00 \] b. For the \(1.0 \times 10^{-10} M \) NaOH solution, \[ \mathrm{pH} = 14 - \mathrm{pOH} = 14 - 10.00 = 4.00 \] c. For the 2.0 M NaOH solution, \[ \mathrm{pH} = 14 - \mathrm{pOH} = 14 - 0.30 \approx 13.70 \] So, the pH of the NaOH solutions are approximately 13.00, 4.00, and 13.70 for a), b), and c), respectively.

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