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Chapter 4: Problem 10

An aqueous solution contains 1.2 \(\mathrm{mM}\) of total ions. (a) If the solution is NaCl(aq), what is the concentration of chloride ion? (b) If the solution is \(\mathrm{FeCl}_{3}(a q),\) what is the concentration of chloride ion? [Section 4.5\(]\)

Short Answer

Expert verified
The concentration of chloride ions in the NaCl(aq) solution is 1.2 mM, while in the FeCl3(aq) solution it is 0.9 mM.

Step by step solution

01

Making sense of the given data

The exercise tells us that the aqueous solution contains 1.2 mM of total ions. That means the sum of the concentrations of each type of ion in the solution is equal to 1.2 mM.
02

Determine chloride ion concentration for NaCl(aq)

In this case, the dissociation of NaCl(aq) in water is given by the following equation: \[NaCl \rightarrow Na^+ + Cl^-\] Each formula unit of NaCl dissociates into one Na+ ion and one Cl- ion. Since the total ion concentration of the solution is 1.2 mM, and NaCl gives one chloride ion per formula unit, the concentration of chloride ions will be equal to the total ion concentration. Therefore, the concentration of chloride ion in the NaCl(aq) solution is 1.2 mM.
03

Determine chloride ion concentration for FeCl3(aq)

In this case, the dissociation of FeCl3(aq) in water is given by the following equation: \[FeCl_{3} \rightarrow Fe^{3+}+3 Cl^-\] Each formula unit of FeCl3 dissociates into one Fe3+ ion and three Cl- ions. Let the concentration of Fe3+ ion be x mM. Since 3 chloride ions are produced per formula unit of FeCl3, the concentration of chloride ions will be 3x mM. The sum of the concentrations of the two ions should be equal to the total ion concentration, which is 1.2 mM. So we have the following equation: \[x+3x=1.2\]
04

Solve for x

Solve the equation from Step 3 for x: \[4x=1.2\] \[x=\frac{1.2}{4}\] \[x=0.3\, mM\] Finally, we can calculate the concentration of Cl- ions: Concentration of Cl- ions = 3x = 3 × 0.3 mM = 0.9 mM The concentration of chloride ions in the FeCl3(aq) solution is 0.9 mM.

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Most popular questions from this chapter

Classify each of the following substances as a nonelectrolyte, weak electrolyte, or strong electrolyte in water: (a) \(\mathrm{H}_{2} \mathrm{SO}_{3}\) , (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) (ethanol), \((\mathbf{c}) \mathrm{NH}_{3},(\mathbf{d}) \mathrm{KClO}_{3}\), \((\mathbf{e}) \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\).

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