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Chapter 16: Problem 48

Calculate the concentration of an aqueous solution of \(\mathrm{Ca}(\mathrm{OH})_{2}\) that has a \(\mathrm{pH}\) of \(10.05 .\)

Short Answer

Expert verified
The concentration of the aqueous solution of Ca(OH)₂ with a pH of 10.05 is approximately \( 5.6 \times 10^{-5} \) M.

Step by step solution

01

Determine pOH from pH

To find the concentration of OH⁻ ions in the solution, it is necessary to convert the given pH value into the pOH value. This can be done using the following relationship: pH + pOH = 14 Substitute the given pH value: 10.05 + pOH = 14 Now, solve for pOH: pOH = 14 - 10.05 pOH = 3.95
02

Calculate the concentration of OH⁻ ions

The pOH value represents the negative base-10 logarithm of the concentration of OH⁻ ions. To find the concentration of OH⁻ ions, use the following equation: pOH = -logₓ[OH⁻] We can convert the pOH value to the concentration of OH⁻ ions using the following formula: [OH⁻] = 10^{-pOH} Now, substitute the pOH value: [OH⁻] = 10^{-3.95} [OH⁻] ≈ 1.12 × 10^-4 M
03

Calculate the concentration of Ca(OH)₂

Since each calcium hydroxide (Ca(OH)₂) dissociates into two hydroxide ions (OH⁻), the stoichiometry of the reaction is as follows: Ca(OH)₂ → Ca²⁺ + 2OH⁻ So, for every one Ca(OH)₂ dissolved, two OH⁻ ions are produced. To find the concentration of Ca(OH)₂, divide the concentration of OH⁻ by the stoichiometric coefficient (2): [Ca(OH)₂] = [OH⁻]/2 Now, substitute the concentration of OH⁻ ions: [Ca(OH)₂] = (1.12 × 10^-4 M)/2 [Ca(OH)₂] ≈ 5.6 × 10^-5 M The concentration of the aqueous solution of Ca(OH)₂ with a pH of 10.05 is approximately 5.6 × 10⁻⁵ M.

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Most popular questions from this chapter

Label each of the following as being a strong acid, a weak acid, or a species with negligible acidity. In each case write the formula of its conjugate base, and indicate whether the conjugate base is a strong base, a weak base, or a species with negligible basicity: (a) \(\mathrm{HCOOH},\) (b) \(\mathrm{H}_{2},\) (c) \(\mathrm{CH}_{4}\), (d) \(\mathrm{HF}\) (e) \(\mathrm{NH}_{4}^{+}\).

If a substance is an Arrhenius base, is it necessarily a BronstedLowry base? Is it necessarily a Lewis base? Explain.

Butyric acid is responsible for the foul smell of rancid butter. The \(\mathrm{p} K_{a}\) of butyric acid is \(4.84 .\) (a) Calculate the \(\mathrm{p} K_{b}\) for the butyrate ion. (b) Calculate the \(\mathrm{pH}\) of a \(0.050 \mathrm{M}\) solution of butyric acid. (c) Calculate the pH of a \(0.050 \mathrm{M}\) solution of sodium butyrate.

Carbon dioxide in the atmosphere dissolves in raindrops to produce carbonic acid \(\left(\mathrm{H}_{2} \mathrm{CO}_{3}\right),\) causing the \(\mathrm{pH}\) of clean, \(\mathrm{un}^{-}\) polluted rain to range from about 5.2 to \(5.6 .\) What are the ranges of \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) in the raindrops?

Deuterium oxide \(\left(\mathrm{D}_{2} \mathrm{O},\right.\) where \(\mathrm{D}\) is deuterium, the hydrogen- 2 isotope) has an ion-product constant, \(K_{w^{+}}\) of \(8.9 \times 10^{-16}\) at \(20^{\circ} \mathrm{C}\). Calculate \(\left[\mathrm{D}^{+}\right]\) and \(\left[\mathrm{OD}^{-}\right]\) for pure (neutral) \(\mathrm{D}_{2} \mathrm{O}\) at this temperature.
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