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Chapter 14: Problem 90

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

Short Answer

Expert verified
a. \([\mathrm{OH}^−] = 0.00080 \mathrm{M}\), \(pOH = 3.10\), and \(pH = 10.90\) b. \([\mathrm{OH}^−] = 0.000446 \mathrm{M}\), \(pOH = 3.35\), and \(pH = 10.65\) c. \([\mathrm{OH}^−] = 3.750 \mathrm{M}\), \(pOH = -0.57\), and \(pH = 14.57\)

Step by step solution

01

Calculate the concentration of OH⁻ ions in Ca(OH)₂ solution

Since Ca(OH)₂ releases 2 OH⁻ ions, the concentration of OH⁻ ions would be twice of the concentration of Ca(OH)₂. \[ [\mathrm{OH}^-] = 2(0.00040 \mathrm{M}) \] \[ [\mathrm{OH}^-] = 0.00080 \mathrm{M} \]
02

Calculate pOH

Now we can calculate the pOH using the formula: \[ pOH = -\log_{10} [\mathrm{OH}^-] \] \[ pOH = -\log_{10}(0.00080) \]
03

Calculate pH

Finally, using the relationship between pH and pOH: \[ pH + pOH = 14 \] \[ pH = 14 - pOH \] b. A solution containing 25 g KOH per liter
04

Calculate the concentration of KOH

First, we need to find the molecular weight of KOH. \[ \mathrm{KOH} = 39.10 (\mathrm{K}) + 15.99 (\mathrm{O}) + 1.00 (\mathrm{H}) = 56.10 \frac{\mathrm{g}}{\mathrm{mol}} \] Now, we can calculate the concentration of KOH: \[ [\mathrm{KOH}] = \frac{25 \mathrm{g} \space \mathrm{KOH}}{56.10 \frac{\mathrm{g}}{\mathrm{mol}} \cdot 1 \mathrm{L}} \]
05

Calculate the concentration of OH⁻ ions

Since KOH releases 1 OH⁻ ion, the concentration of OH⁻ ions is equal to the concentration of KOH.
06

Calculate pOH and pH

Repeat steps 2 and 3 of solution a to find the pOH and pH values for this solution. c. A solution containing 150.0 g NaOH per liter
07

Calculate the concentration of NaOH

First, we need to find the molecular weight of NaOH. \[ \mathrm{NaOH} = 22.99 (\mathrm{Na}) + 15.99 (\mathrm{O}) + 1.00 (\mathrm{H}) = 40.00 \frac{\mathrm{g}}{\mathrm{mol}} \] Now, we can calculate the concentration of NaOH: \[ [\mathrm{NaOH}] = \frac{150 \mathrm{g} \space \mathrm{NaOH}}{40.00 \frac{\mathrm{g}}{\mathrm{mol}} \cdot 1 \mathrm{L}} \]
08

Calculate the concentration of OH⁻ ions

Since NaOH releases 1 OH⁻ ion, the concentration of OH⁻ ions is equal to the concentration of NaOH.
09

Calculate pOH and pH

Repeat steps 2 and 3 of solution a to find the pOH and pH values for this solution.

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