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Chapter 4: Problem 44

Identify the ions that exist in each aqueous solution, and specify the concentration of each ion. (a) \(0.12 \mathrm{M} \mathrm{BaCl}_{2}\) (b) \(0.0125 \mathrm{M} \mathrm{CuSO}_{4}\) (c) \(0.500 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\)

Short Answer

Expert verified
(a) BaCl鈧�: [Ba虏鈦篯 = 0.12 M, [Cl鈦籡 = 0.24 M; (b) CuSO鈧�: [Cu虏鈦篯 = 0.0125 M, [SO鈧劼测伝] = 0.0125 M; (c) K鈧侰r鈧侽鈧�: [K鈦篯 = 1.000 M, [Cr鈧侽鈧嚶测伝] = 0.500 M.

Step by step solution

01

Determine Dissociation of Compounds for (a)

The solute given is barium chloride (\(\text{BaCl}_2\)). When it dissolves in water, it dissociates into its constituent ions:\[\text{BaCl}_2 \rightarrow \text{Ba}^{2+} + 2\, \text{Cl}^-\]This means one mole of \(\text{BaCl}_2\) produces one mole of \(\text{Ba}^{2+}\) ions and two moles of \(\text{Cl}^-\) ions.
02

Calculate Ion Concentrations for (a)

The initial concentration of \(\text{BaCl}_2\) is 0.12 M. Therefore:- The concentration of \(\text{Ba}^{2+}\) is 0.12 M.- The concentration of \(\text{Cl}^-\) is 2 \(\times\) 0.12 M = 0.24 M.
03

Determine Dissociation of Compounds for (b)

The solute given is copper (II) sulfate (\(\text{CuSO}_4\)). When it dissolves, it dissociates into:\[\text{CuSO}_4 \rightarrow \text{Cu}^{2+} + \text{SO}_4^{2-}\]This indicates that one mole of \(\text{CuSO}_4\) yields one mole of \(\text{Cu}^{2+}\) ions and one mole of \(\text{SO}_4^{2-}\) ions.
04

Calculate Ion Concentrations for (b)

The initial concentration of \(\text{CuSO}_4\) is 0.0125 M. Thus:- The concentration of \(\text{Cu}^{2+}\) is 0.0125 M.- The concentration of \(\text{SO}_4^{2-}\) is 0.0125 M.
05

Determine Dissociation of Compounds for (c)

The solute given is potassium dichromate (\(\text{K}_2\text{Cr}_2\text{O}_7\)). It dissociates into:\[\text{K}_2\text{Cr}_2\text{O}_7 \rightarrow 2\, \text{K}^+ + \text{Cr}_2\text{O}_7^{2-}\]This suggests that one mole of \(\text{K}_2\text{Cr}_2\text{O}_7\) gives two moles of \(\text{K}^+\) ions and one mole of \(\text{Cr}_2\text{O}_7^{2-}\) ions.
06

Calculate Ion Concentrations for (c)

The initial concentration of \(\text{K}_2\text{Cr}_2\text{O}_7\) is 0.500 M. Therefore:- The concentration of \(\text{K}^+\) is 2 \(\times\) 0.500 M = 1.000 M.- The concentration of \(\text{Cr}_2\text{O}_7^{2-}\) is 0.500 M.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Aqueous Solutions
An aqueous solution is formed when a substance is dissolved in water. It is a vital concept in chemistry because many reactions occur in aqueous environments. When substances like salts are dissolved, they dissociate into ions. This dissociation is essential as it allows the compound to conduct electricity and participate in chemical reactions. Understanding how these compounds behave when dissolved aids in predicting the outcomes of these reactions.
Molarity Calculation
Molarity is an important measure of concentration in chemistry. It is defined as the number of moles of solute per liter of solution, denoted by the symbol M. Calculating molarity is critical when preparing solutions for experiments or determining how much solute is present in a given volume of solution. To calculate the molarity, you need to know the amount of solute in moles and the volume of the solution in liters. Understanding molarity is essential for accurately gauging how solutions will interact and react in experiments.
Chemical Equations
Chemical equations provide a concise way to represent chemical reactions. They display the reactants and products involved in the reaction. Dissociation reactions, such as those occurring when ionic compounds dissolve in water, are typically represented using chemical equations, showing how compounds split into their respective ions. For example, when barium chloride (\(\text{BaCl}_2\)) dissolves in water, it separates into \(\text{Ba}^{2+}\) and \(2 \text{Cl}^-\). Balancing these equations is crucial as it ensures that the same number of atoms is present on both sides of the equation, adhering to the law of conservation of mass.
Ion Concentration
Understanding ion concentration is key to studying solutions, as it impacts factors like reactivity and conductivity. When ionic compounds dissociate in water, the concentration of each ion can be determined based on the initial concentration of the compound and the stoichiometry of the dissociation reaction. For example, in a solution of \(\text{BaCl}_2\) with a molarity of 0.12 M, \(\text{Ba}^{2+}\) would have the same concentration of 0.12 M, while \(\text{Cl}^-\) would have a concentration of 0.24 M because there are two chloride ions per formula unit. Calculating these concentrations helps in predicting how the solution will behave chemically, especially regarding its reactivity and participation in further reactions.

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Most popular questions from this chapter

\(A A .000-g\) sample containing \(K C l\) and \(K C 1 O_{4}\) was dis. solved in sufficient water to give \(250.00 \mathrm{mL}\) of solution. A \(50.00-\mathrm{mL}\) portion of the solution required \(41.00 \mathrm{mL}\) of \(0.0750 \mathrm{M} \mathrm{AgNO}_{3}\) in a Mohr titration (page 187 ). Next, a \(25.00-\mathrm{mL}\), portion of the original solution was treated with \(\mathrm{V}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) to reduce the perchlorate ion to chloride, \(8 \mathrm{V}^{3+}(\mathrm{aq})+\mathrm{ClO}_{4}^{-}(\mathrm{aq})+12 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow\) $$ \mathrm{Cl}^{-}(\mathrm{aq})+8 \mathrm{VO}^{2+}(\mathrm{aq})+8 \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq}) $$ and the resulting solution was tirrated with AgNO, This titration required \(38.12 \mathrm{mL}\) of \(0.0750 \mathrm{M} \mathrm{AgNO}_{3} .\) What is the mass percent of \(\mathrm{KCl}\) and \(\mathrm{KClO}_{4}\) in the mixture?

A Sulfuric acid is listed in a catalog with a concentration of \(95-98 \% .\) A bottle of the acid in the stockroom states that 1.00 I. has a mass of \(1.84 \mathrm{kg} .\) To determine the concentration of sulfuric acid in the stockroom bottle, a student dilutes \(5.00 \mathrm{mL}\) to \(500 .\) mL. She then takes four \(10.00-\mathrm{mL}\). samples and titrates each with standardized sodium hydroxide \((c=0.1760 \mathrm{M}).\) \(\begin{array}{lcccc}\text { Sample } & 1 & 2 & 3 & 4 \\ \text { Volume NaOH (mL) } & 20.15 & 21.30 & 20.40 & 20.35\end{array}\) (a) What is the average concentration of the diluted sulfuric acid sample? (b) What is the mass percent of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in the original bottle of the acid?

Which has the larger concentration of hydronium ions, \(0.015 \mathrm{M} \mathrm{HCl}\) or aqueous \(\mathrm{HCl}\) with a \(\mathrm{pH}\) of \(1.20 ?\)

A noncarbonated soft drink contains an unknown amount of citric acid, \(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7} .\) If \(100 .\) mL of the soft drink requires \(33.51 \mathrm{mL}\) of \(0.0102 \mathrm{M} \mathrm{NaOH}\) to neutralize the citric acid completely, what mass of citric acid does the soft drink contain per \(100 .\) mL? The reaction of citric acid and NaOH is \(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq})+3 \mathrm{NaOH}(\mathrm{aq}) \rightarrow\) $$ \mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq})+3 \mathrm{H}_{2} \mathrm{O}(\ell) $$

In the photographic developing process, silver bromide is dissolved by adding sodium thiosulfate. \(\mathrm{AgBr}(\mathrm{s})+2 \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}(\mathrm{aq}) \rightarrow\) $$ \mathrm{Na}_{3} \mathrm{Ag}\left(\mathrm{S}_{2} \mathrm{O}_{3}\right)_{2}(\mathrm{aq})+\mathrm{NaBr}(\mathrm{aq}) $$ If you want to dissolve \(0.225 \mathrm{g}\) of \(\mathrm{AgBr}\), what volume of \(0.0138 \mathrm{M} \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3},\) in milliliters, should be used? (IMAGE CANNOT COPY)
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