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Four solutions are prepared and mixed in the following order: (1) Start with \(100.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{BaCl}_{2}\) (2) Add \(50.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{AgNO}_{3}\) (3) Add \(50.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) (4) Add \(250.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{NH}_{3}\) Write an equation for any reaction that occurs after each step, and calculate the concentrations of \(\mathrm{Ba}^{2+}, \mathrm{Cl}^{-}, \mathrm{NO}_{3}^{-}, \mathrm{NH}_{3}\), and \(\mathrm{NH}_{4}^{+}\) in the final solution, assuming that all reactions go to completion.

Short Answer

Expert verified
Final concentrations are: [Cl鈦籡 = 0.0333 M, [NO鈧冣伝] = 0.0111 M, [NH鈧僝 = 0.0556 M. Ba虏鈦 precipitated as BaSO鈧.

Step by step solution

01

Analyze the Initial Mixture

We begin with 100.0 mL of 0.100 M BaClequiv 2, thus you have BaCl鈧. The initial number of moles of each ion is determined by multiplying the volume (in L) by the molarity: \[ \text{moles of } \text{Ba}^{2+} = 0.100 \, \text{L} \times 0.100 \, \text{mol/L} = 0.0100 \, \text{mol} \]\[ \text{moles of } \text{Cl}^- = 2 \times 0.0100 \, \text{mol} = 0.0200 \, \text{mol} \]
02

Reaction with AgNO3

Add 50.0 mL of 0.100 M AgNO鈧. AgNO鈧 reacts with BaCl鈧 to form AgCl, which precipitates:\[ \text{Ag}^{+} + \text{Cl}^{-} \rightarrow \text{AgCl(s)} \]Determine moles of Ag鈦 added:\[ \text{moles of } \text{Ag}^{+} = 0.0500 \, \text{L} \times 0.100 \, \text{mol/L} = 0.00500 \, \text{mol} \]Ag鈦 reacts completely with Cl鈦, producing 0.00500 mol of AgCl and leaving 0.0150 mol Cl鈦 unreacted.
03

Reaction with H2SO4

Add 50.0 mL of 0.100 M H鈧係O鈧. BaCl鈧 reacts with H鈧係O鈧 to form BaSO鈧, a precipitate:\[ \text{Ba}^{2+} + \text{SO}_4^{2-} \rightarrow \text{BaSO}_4(\text{s}) \]Calculate moles of \(\text{SO}_4^{2-}\):\[ \text{moles of } \text{SO}_4^{2-} = 0.0500 \, \text{L} \times 0.100 \, \text{mol/L} = 0.00500 \, \text{mol} \]All \(\text{Ba}^{2+}\) (0.0100 mol) reacts with \(\text{SO}_4^{2-}\) to form BaSO鈧, leaving 0 mol \(\text{Ba}^{2+}\).
04

Final Addition of NH3

Add 250.0 mL of 0.100 M NH鈧. \(\text{NH}_3\) mainly acts as a base forming \(\text{NH}_4^+\):\[ \text{NH}_3 + \text{H}_2\text{O} \rightleftharpoons \text{NH}_4^+ + \text{OH}^- \]Calculate the moles of \(\text{NH}_3\):\[ \text{moles of } \text{NH}_3 = 0.2500 \, \text{L} \times 0.100 \, \text{mol/L} = 0.0250 \, \text{mol} \]
05

Final Concentration Calculations

Calculate the total volume after mixing all solutions:\[ \text{Total Volume} = 100.0 \, \text{mL} + 50.0 \, \text{mL} + 50.0 \, \text{mL} + 250.0 \, \text{mL} = 450.0 \, \text{mL} = 0.450 \, \text{L} \]Determine concentrations for ions:- Remaining \(\text{Cl}^-\): \[ [\text{Cl}^-] = \frac{0.0150 \, \text{mol}}{0.450 \, \text{L}} = 0.0333 \, \text{M} \]- \(\text{NO}_3^-\) from AgNO鈧 (no reaction occurred with it affecting): \[ [\text{NO}_3^-] = \frac{0.00500 \, \text{mol}}{0.450 \, \text{L}} = 0.0111 \, \text{M} \]- \(\text{NH}_3\) (not all turns to \(\text{NH}_4^+\)): \[ [\text{NH}_3] = \frac{0.0250 \, \text{mol}}{0.450 \, \text{L}} = 0.0556 \, \text{M} \]- No \(\text{Ba}^{2+}\) remains; formed \(\text{BaSO}_4\) precipitate.
06

Additional Consideration for NH4+

Given \(\text{NH}_3\) reacts to form \(\text{NH}_4^+\), assuming minor dissociation, \([\text{NH}_4^+]\) is minimal. Therefore, based on the primary reactions and concentrations, \(\text{NH}_4^+\) concentration from \(\text{NH}_3\) equilibrium is negligible.

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Key Concepts

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

Precipitation Reactions
Precipitation reactions occur when two soluble salts in aqueous solutions combine to form an insoluble salt, or a precipitate. When the ions of the soluble salts exchange partners, they create a new pair of ions that is not soluble in water. In our exercise, this concept is beautifully illustrated with the reactions of BaCl鈧 and AgNO鈧, as well as BaCl鈧 and H鈧係O鈧.

This process can be summarized with general chemical reactions showing the formation of a precipitate. For example, when AgNO鈧 is added to BaCl鈧, Ag鈦 ions react with Cl鈦 ions to form AgCl, an insoluble compound that appears as a precipitate. This can be represented by the equation: \[ \text{Ag}^{+} + \text{Cl}^{-} \rightarrow \text{AgCl(s)} \]Similarly, when H鈧係O鈧 is added to a solution containing BaCl鈧, a precipitation reaction occurs: \[ \text{Ba}^{2+} + \text{SO}_4^{2-} \rightarrow \text{BaSO}_4(\text{s}) \]These reactions are crucial in studying the behavior of ions in solution and predicting which insoluble salts will form under specific conditions. Understanding precipitation reactions helps in various fields, including chemical manufacturing and wastewater treatment.
Stoichiometry
Stoichiometry is the calculation of reactants and products in chemical reactions. It is foundational in determining the quantitative relationships between substances as they participate in a chemical reaction. Might sound daunting, but it's simpler once you break it down into manageable parts.

In the case of our problem, stoichiometry helps us figure out how much of each reactant is needed to produce a certain amount of product. For example, when we start with 0.100 M BaCl鈧 and react it with 0.100 M AgNO鈧, we use stoichiometry to calculate the moles of AgCl formed and how much Cl鈦 is left unreacted. Similarly, for BaSO鈧 formation, the moles of Ba虏鈦 available dictate how much BaSO鈧 can precipitate from the reaction with H鈧係O鈧.

Generally, stoichiometry involves:
  • Balancing the chemical equation.
  • Converting volumes of reactants to moles using molarity.
  • Using mole ratios from the balanced equation to calculate other substances in the reaction.
Understanding stoichiometry allows chemists to predict the quantitative outcomes of reactions, ensuring optimal amounts of reactants are used to avoid waste and ensure complete reactions.
Molarity Calculations
Molarity is a measure of the concentration of a solute in a solution, expressed as the number of moles of solute per liter of solution (mol/L). Calculating molarity is essential in experiments where precise outcomes depend on reactant concentrations.

In our given exercise, molarity calculations help us find the concentration of ions after each reaction. For instance, when 0.100 M of a solute is added, you calculate the moles by multiplying the volume (in L) by the molarity. Subsequently, you can determine new concentrations after they participate in chemical reactions.

To calculate molarity:
  • Determine the number of moles of solute, as illustrated with the initial moles of Ba虏鈦 and Cl鈦.
  • Add together the volumes of all solutions to find the total volume.
  • Divide the moles of remaining solute by this total volume to obtain the final molarity.
This importance of molarity calculations lies in their use to maintain control over chemical reactions, ensuring desired reactions occur effectively by maintaining ideal conditions in terms of reactant ratios.

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