Question

Calculate \(\left[\mathrm{OH}^{-}\right], \mathrm{pOH}\), and \(\mathrm{pH}\) for each of the following. a. \(0.00040 \mathrm{M} \mathrm{Ca}(\mathrm{OH})_{2}\) b. a solution containing \(25 \mathrm{~g}\) KOH per liter c. a solution containing \(150.0 \mathrm{~g} \mathrm{NaOH}\) per liter

Short answer

a. \(\left[\mathrm{OH}^{-}\right] = 0.00080 \mathrm{M}\), \(\mathrm{pOH} = 3.10\), \(\mathrm{pH} = 10.90\) b. \(\left[\mathrm{OH}^{-}\right] = 0.64 \mathrm{M}\), \(\mathrm{pOH} = 0.19\), \(\mathrm{pH} = 13.81\) c. \(\left[\mathrm{OH}^{-}\right] = 3.75 \mathrm{M}\), \(\mathrm{pOH} = -0.57\), \(\mathrm{pH} = 14.57\)

Step-by-step solution

Determining the concentration of \(\mathrm{OH}^{-}\) ions in solution

Since \(1 \mathrm{Ca}(\mathrm{OH})_{2}\) molecule dissociates into \(2 \mathrm{OH}^-\) ions in aqueous solutions, we have: \(\left[\mathrm{OH}^{-}\right] = 2 \times 0.00040 \mathrm{M} = 0.00080 \mathrm{M}\).

Calculate pOH

To find the pOH, we use the formula \(\mathrm{pOH}=-\log_{10}\left[\mathrm{OH}^{-}\right]\). So, \(\mathrm{pOH} = -\log_{10}(0.00080) = 3.10\).

Calculate pH

We can now find the pH using the formula \(\mathrm{pH} = 14 - \mathrm{pOH}\). Therefore, \(\mathrm{pH} = 14 - 3.10 = 10.90\). b. a solution containing \(25 \mathrm{~g}\) KOH per liter

Determine the concentration of \(\mathrm{OH}^{-}\) ions in solution

First, we need to find the molar concentration of KOH in the solution. The molar mass of KOH is approximately \(39.10 \mathrm{~g/mol}\). So, the molar concentration is \(\frac{25 \mathrm{~g}}{39.10 \mathrm{~g/mol}} = 0.64 \mathrm{M}\). Since every KOH molecule forms one \(\mathrm{OH}^-\) ion, the concentration of \(\left[\mathrm{OH}^{-}\right] = 0.64 \mathrm{M}\).

Calculate pOH

Using the formula \(\mathrm{pOH}=-\log_{10}\left[\mathrm{OH}^{-}\right]\), the pOH is \(\mathrm{pOH} = -\log_{10}(0.64) = 0.19\).

Calculate pH

To find the pH, use the formula \(\mathrm{pH} = 14 - \mathrm{pOH}\). Thus, \(\mathrm{pH} = 14 - 0.19 = 13.81\). c. a solution containing \(150.0 \mathrm{~g} \mathrm{NaOH}\) per liter

Determine the concentration of \(\mathrm{OH}^{-}\) ions in solution

First, find the molar concentration of NaOH in the solution. The molar mass of NaOH is about \(40.00 \mathrm{~g/mol}\). So, the molar concentration is \(\frac{150.0 \mathrm{~g}}{40.00 \mathrm{~g/mol}} = 3.75 \mathrm{M}\). Since every NaOH molecule forms one \(\mathrm{OH}^-\) ion, the concentration of \(\left[\mathrm{OH}^{-}\right] = 3.75 \mathrm{M}\).

Calculate pOH

Using the formula \(\mathrm{pOH}=-\log_{10}\left[\mathrm{OH}^{-}\right]\), the pOH is \(\mathrm{pOH} = -\log_{10}(3.75) = -0.57\).

Calculate pH

To find the pH, use the formula \(\mathrm{pH} = 14 - \mathrm{pOH}\). Thus, \(\mathrm{pH} = 14 - (-0.57) = 14.57\).