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Chapter 4: Problem 101

Hard water contains \(\mathrm{Ca}^{2+}, \mathrm{Mg}^{2+}\), and \(\mathrm{Fe}^{2+}\), which interfere with the action of soap and leave an insoluble coating on the insides of containers and pipes when heated. Water softeners replace these ions with \(\mathrm{Na}^{+} .\) Keep in mind that charge balance must be maintained. (a) If \(1500 \mathrm{~L}\) of hard water contains \(0.020 \mathrm{M} \mathrm{Ca}^{2+}\) and \(0.0040 \mathrm{M} \mathrm{Mg}^{2+}\), how many moles of Nat are needed to replace these ions? (b) If the sodium is added to the water softener in the form of \(\mathrm{NaCl}\), how many grams of sodium chloride are needed?

Short Answer

Expert verified
(a) The number of moles of Na⁺ ions needed to replace Ca²⁺ and Mg²⁺ ions in the hard water is 72 moles. (b) The mass of sodium chloride (NaCl) needed is 4203.68 g.

Step by step solution

01

Identify the given values

We are given the volume of hard water: - Volume = 1500 L - Concentration of Ca²⁺ ions = 0.020 M - Concentration of Mg²⁺ ions = 0.0040 M
02

Calculate the number of moles of Ca²⁺ and Mg²⁺ ions in the water

We'll use the formula for moles: Moles = Volume × Concentration Moles of Ca²⁺ = 1500 L × 0.020 M = 30 moles Moles of Mg²⁺ = 1500 L × 0.0040 M = 6 moles
03

Calculate the total positive charge from the original ions

Total charge of Ca²⁺ = Moles of Ca²⁺ × Charge of Ca²⁺ ion Total charge of Mg²⁺ = Moles of Mg²⁺ × Charge of Mg²⁺ ion Total charge of Ca²⁺ = 30 moles × 2 = 60 Total charge of Mg²⁺ = 6 moles × 2 = 12 Total positive charge = 60 + 12 = 72
04

Calculate the number of moles of Na⁺ ions

To maintain charge balance, the number of moles of Na⁺ = Total positive charge of original ions (Ca²⁺ and Mg²⁺) / Charge of Na⁺ ion. Number of moles of Na⁺ = 72 / 1 = 72 moles
05

Calculate the mass of NaCl to add

The molar mass of NaCl = 58.44 g/mol Mass of NaCl = number of moles of Na⁺ × molar mass of NaCl Mass of NaCl = 72 moles × 58.44 g/mol = 4203.68 g (a) The number of moles of Na⁺ ions needed to replace Ca²⁺ and Mg²⁺ ions in the hard water is 72 moles. (b) The mass of sodium chloride (NaCl) needed is 4203.68 g.

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Most popular questions from this chapter

Federal regulations set an upper limit of 50 parts per million (ppm) of \(\mathrm{NH}_{3}\) in the air in a work environment [that is, 50 molecules of \(\mathrm{NH}_{3}(g)\) for every million molecules in the air]. Air from a manufacturing operation was drawn through a solution containing $1.00 \times 10^{2} \mathrm{~mL}\( of \)0.0105 \mathrm{MHCl} .\( The \)\mathrm{NH}_{3}$ reacts with HCl according to: $$ \mathrm{NH}_{3}(a q)+\mathrm{HCl}(a q) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(a q) $$ After drawing air through the acid solution for \(10.0 \mathrm{~min}\) at a rate of \(10.0 \mathrm{~L} / \mathrm{min},\) the acid was titrated. The remaining acid needed \(13.1 \mathrm{~mL}\) of \(0.0588 \mathrm{M} \mathrm{NaOH}\) to reach the equivalence point. (a) How many grams of \(\mathrm{NH}_{3}\) were drawn into the acid solution? (b) How many ppm of \(\mathrm{NH}_{3}\) were in the air? (Air has a density of \(1.20 \mathrm{~g} / \mathrm{L}\) and an average molar mass of \(29.0 \mathrm{~g} / \mathrm{mol}\) under the conditions of the experiment.) (c) Is this manufacturer in compliance with regulations?

Which of the following ions will always be a spectator ion in a precipitation reaction? (a) $\mathrm{Cl}^{-},(\mathbf{b}) \mathrm{NO}_{3}^{-}$, (d) \(\mathrm{S}^{2-}\), (c) \(\mathrm{NH}_{4}^{+}\) (e) \(\mathrm{SO}_{4}^{2-} .[\) Section 4.2\(]\)

(a) Which will have the highest concentration of sodium ions: \(0.25 \mathrm{MNaCl}, 0.15 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3},\) or \(0.075 \mathrm{MNa}_{3} \mathrm{PO}_{4} ?(\mathbf{b})\) Which will contain the greater number of moles of sodium ion: \(20.0 \mathrm{~mL}\) of \(0.15 \mathrm{M} \mathrm{NaHCO}_{3}\) or $15.0 \mathrm{~mL}\( of \)0.04 \mathrm{M} \mathrm{Na}_{2} \mathrm{~S} ?$

A \(4.36-g\) sample of an unknown alkali metal hydroxide is dissolved in $100.0 \mathrm{~mL}$ of water. An acid-base indicator is added, and the resulting solution is titrated with \(2.50 \mathrm{MHCl}(a q)\) solution. The indicator changes color, signaling that the equivalence point has been reached, after \(17.0 \mathrm{~mL}\) of the hydrochloric acid solution has been added. (a) What is the molar mass of the metal hydroxide? (b) What is the identity of the alkali metal cation: $\mathrm{Li}^{+}, \mathrm{Na}^{+}, \mathrm{K}^{+}, \mathrm{Rb}^{+},\( or \)\mathrm{Cs}^{+} ?$

You choose to investigate some of the solubility guidelines for two ions not listed in Table \(4.1,\) the chromate ion \(\left(\mathrm{CrO}_{4}^{2-}\right)\) and the oxalate ion \(\left(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\right) .\) You are given \(0.01 \mathrm{M}\) solutions \((\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D})\) of four water- soluble salts: \begin{tabular}{lll} \hline Solution & Solute & Color of Solution \\ \hline \(\mathrm{A}\) & \(\mathrm{Na}_{2} \mathrm{CrO}_{4}\) & Yellow \\ \(\mathrm{B}\) & $\left(\mathrm{NH}_{4}\right)_{2} \mathrm{C}_{2} \mathrm{O}_{4}$ & Colorless \\ \(\mathrm{C}\) & \(\mathrm{AgNO}_{3}\) & Colorless \\ \(\mathrm{D}\) & \(\mathrm{CaCl}_{2}\) & Colorless \\ \hline \end{tabular} When these solutions are mixed, the following observations are made: \begin{tabular}{lll} \hline Experiment Number & Solutions Mixed & Result \\ \hline 1 & \(\mathrm{~A}+\mathrm{B}\) & Noprecipitate, yellow solution \\ 2 & \(\mathrm{~A}+\mathrm{C}\) & Red precipitate forms \\ 3 & \(\mathrm{~A}+\mathrm{D}\) & Yellow precipitate forms \\ 4 & \(\mathrm{~B}+\mathrm{C}\) & White precipitate forms \\ 5 & \(\mathrm{~B}+\mathrm{D}\) & White precipitate forms \\ 6 & \(\mathrm{C}+\mathrm{D}\) & White precipitate forms \\ \hline \end{tabular} (a) Write a net ionic equation for the reaction that occurs in each of the experiments. (b) Identify the precipitate formed, if any, in each of the experiments.
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