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Chapter 17: Problem 115

Excess \(\mathrm{Ca}(\mathrm{OH})_{2}\) is shaken with water to produce a saturated solution. The solution is filtered, and a 50.00 -mL sample titrated with \(\mathrm{HCl}\) requires \(11.23 \mathrm{~mL}\) of \(0.0983 \mathrm{MHCl}\) to reach the end point. Calculate \(K_{s p}\) for \(\mathrm{Ca}(\mathrm{OH})_{2} .\) Compare your result with that in Appendix D. Suggest a reason for any differences you find between your value and the one in Appendix D.

Short Answer

Expert verified
The calculated solubility product, \(K_{sp}\), for \(\mathrm{Ca}(\mathrm{OH})_{2}\) is \(5.35 \times 10^{-6}\). Differences between this value and the one provided in Appendix D might be due to experimental errors or variations in temperature, as solubility products are temperature-dependent.

Step by step solution

01

Determine the concentration of hydroxide ions from titration

The titration tells us that 50.00 mL of the saturated calcium hydroxide solution was neutralized by 11.23 mL of 0.0983 M HCl. We can use the volume and concentration of HCl to find the number of moles of HCl and then the number of moles of hydroxide ions. Moles of HCl = Volume x Concentration = (11.23 mL) x (0.0983 mol/L) Convert the mL to L: Moles of HCl = (0.01123 L) x (0.0983 mol/L) = 0.00110 mol Since the reaction between HCl and OH- is 1:1, the moles of HCl are equal to the moles of OH- ions. So, moles of OH- = 0.00110 mol
02

Calculate the concentration of hydroxide ions in the saturated solution

To find the concentration of hydroxide ions, we will divide the number of moles by the volume of the solution. Concentration of OH- = moles of OH- / volume of saturated solution = 0.00110 mol / 0.05000 L = 0.0220 mol/L
03

Calculate the concentration of calcium ions

In \(\mathrm{Ca}(\mathrm{OH})_{2}\), for every one calcium ion, there are two hydroxide ions. Therefore, the concentration of calcium ions will be half that of hydroxide ions. Concentration of Ca²⁺ = 1/2 x Concentration of OH- = 1/2 x 0.0220 mol/L = 0.0110 mol/L
04

Calculate the solubility product, \(K_{sp}\)

The \(K_{sp}\) for \(\mathrm{Ca}(\mathrm{OH})_{2}\) is given by the equation: \(K_{sp} = [\mathrm{Ca}^{2+}] [\mathrm{OH}^-]^2\) We can plug in the concentrations we calculated in steps 3 and 2, respectively: \(K_{sp} = (0.0110~\text{mol/L}) (0.0220~\text{mol/L})^2 = 5.35 \times 10^{-6}\)
05

Compare the calculated value with Appendix D and analyze differences

Now, compare the calculated \(K_{sp}\) value with the one given in Appendix D. If the values are different, it could be due to experimental errors, such as inaccuracies in measuring the volume of the saturated solution or the concentration of HCl, or due to variations in temperature. Keep in mind that solubility products are temperature-dependent, and the value in Appendix D is likely to be reported for a standard temperature (such as 25°C), which may not be the same as the temperature at which the experiment was conducted.

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Most popular questions from this chapter

(a) True or false: "solubility" and "solubility-product constant" are the same number for a given compound. (b) Write the expression for the solubility- product constant for each of the following ionic compounds: \(\mathrm{MnCO}_{3}, \mathrm{Hg}(\mathrm{OH})_{2},\) and \(\mathrm{Cu}_{3}\left(\mathrm{PO}_{4}\right)_{2}\).

You are asked to prepare a pH \(=2.50\) buffer solution starting from $1.50 \mathrm{~L}\( of a \)0.75 \mathrm{M}$ solution of hydrofluoric acid (HF) and any amount you need of sodium fluoride (NaF). (a) What is the \(\mathrm{pH}\) of the hydrofluoric acid solution prior to adding sodium fluoride? (b) How many grams of sodium fluoride should be added to prepare the buffer solution? Neglect the small volume change that occurs when the sodium fluoride is added.

A buffer is prepared by adding \(15.0 \mathrm{~g}\) of sodium acetate \(\left(\mathrm{CH}_{3} \mathrm{COONa}\right)\) to \(500 \mathrm{~mL}\) of a \(0.100 \mathrm{M}\) acetic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) solution. (a) Determine the pH of the buffer. (b) Write the complete ionic equation for the reaction that occurs when a few drops of nitric acid are added to the buffer. (c) Write the complete ionic equation for the reaction that occurs when a few drops of potassium hydroxide solution are added to the buffer.

Consider a beaker containing a saturated solution of \(\mathrm{PbI}_{2}\) in equilibrium with undissolved \(\mathrm{PbI}_{2}(s) .\) Now solid KI is added to this solution. (a) Will the amount of solid \(\mathrm{PbI}_{2}\) at the bottom of the beaker increase, decrease, or remain the same? (b) Will the concentration of \(\mathrm{Pb}^{2+}\) ions in solution increase or decrease? (c) Will the concentration of I \(^{-}\) ions in solution increase or decrease?

A sample of \(7.5 \mathrm{~L}\) of \(\mathrm{NH}_{3}\) gas at $22^{\circ} \mathrm{C}\( and 735 torr is bubbled into a 0.50-L solution of \)0.40 \mathrm{M}\( HCl. Assuming that all the \)\mathrm{NH}_{3}$ dissolves and that the volume of the solution remains \(0.50 \mathrm{~L},\) calculate the \(\mathrm{pH}\) of the resulting solution.
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