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You add \(50.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{HCl}\) to \(50.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{AgNO}_{3}\). What are the final concentrations of \(\mathrm{H}_{3} \mathrm{O}^{+}\) and \(\mathrm{Cl}^{-}\) in the solution?

Short Answer

Expert verified
Final concentrations: \([H_3O^+] = 0.100 \text{ M}\); \([Cl^-] = 0 \text{ M}.\)

Step by step solution

01

Determine Initial Moles of Reactants

Calculate the initial moles of each reactant. For both HCl and AgNO鈧:\[\text{Moles} = \text{Concentration} \times \text{Volume (in L)}\]For HCl:\[\text{Moles of HCl} = 0.100 \text{ M} \times 0.050 \text{ L} = 0.005 \text{ moles}\]For AgNO鈧:\[\text{Moles of AgNO鈧儅 = 0.100 \text{ M} \times 0.050 \text{ L} = 0.005 \text{ moles}\]
02

Identify Reaction Type

Recognize the reaction between HCl (hydrochloric acid) and AgNO鈧 (silver nitrate) forms AgCl (silver chloride) and HNO鈧 (nitric acid). The balanced chemical equation is:\[\text{HCl} + \text{AgNO}_{3} \rightarrow \text{AgCl} \downarrow + \text{HNO}_{3}\]
03

Determine Limiting Reactant and Reaction Completion

Since the moles of HCl and AgNO鈧 are equal, all of the reactants will completely react, and AgCl will precipitate out. After the reaction, there will be no HCl or AgNO鈧 left in the solution.
04

Calculate Concentration of \\([H_3O^+]\\)

The strength of HNO鈧, being a strong acid, dissociates completely in water. Therefore, the concentration of hydronium ions \\([H_3O^+] = \text{initial concentration of } HNO_3 = 0.100 \text{ M}\)\([\text{note that volume doubling does not affect concentration of } \text{H}_3\text{O}^+ \text{ as } HNO_3 \text{ is fully ionizable}\)]
05

Calculate Concentration of \\([Cl^-]\\)

As all of the Cl鈦 ions initially from HCl react to form AgCl, no free Cl鈦 ions remain in the solution. Therefore:\[[Cl^-] = 0 \text{ M}\]

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Key Concepts

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

Limiting Reactant
In every chemical reaction, there's always a reactant that gets used up first, known as the limiting reactant. This reactant determines how much of the product can be formed. Once the limiting reactant is consumed, the reaction stops, and no more product is created. In the reaction between hydrochloric acid (HCl) and silver nitrate (AgNO鈧), the problem states they are of equal moles鈥0.005 moles each.
Since both reactants are present in equal amounts, neither reactant is in excess. This means they run out at the same time, making both the limiting reactants. In cases where the moles of reactants are equal, the reactants limit each other. They fully convert into products, leaving no leftovers of the reactants in the solution.
  • Determining the limiting reactant is crucial for predicting the amount of product formed.
  • Equal moles of reactants often result in complete reactions.
  • In this scenario, both HCl and AgNO鈧 are completely used up.
Hydrochloric Acid
Hydrochloric acid, also known as HCl, is a strong acid commonly used in various chemical reactions. In the context of this exercise, HCl reacts with silver nitrate (AgNO鈧) in a 1:1 ratio. When you think about a strong acid like HCl, it's essential to remember its ability to dissociate completely in water, releasing hydrogen ions ( H鈦 ) and forming hydronium ions ( H鈧僌鈦 ).
The balanced reaction in this problem is: HCl + AgNO鈧 鈫 AgCl鈫 + HNO鈧 . Here, the HCl is used to precipitate silver out as silver chloride (AgCl). After the reaction, because all HCl reacts, there are no remaining chlorine ions.
  • HCl is a strong, fully dissociable acid.
  • It reacts completely with equivalent molar amounts of AgNO鈧.
  • Contributes to the formation of hydronium ions in the final solution.
Silver Nitrate
Silver nitrate (AgNO鈧) is a versatile chemical compound widely used in laboratory and chemical reactions. It participates in the reaction with hydrochloric acid (HCl) in this exercise. Silver nitrate is known for reacting with chloride ions to produce a precipitate, silver chloride (AgCl). The reaction follows the balanced equation: HCl + AgNO鈧 鈫 AgCl鈫 + HNO鈧.
What makes silver nitrate interesting in this context is its role in the precipitation reaction. As it combines with chloride ions from HCl, a solid white precipitate of AgCl forms and falls out of the solution.
No AgNO鈧 remains in the solution after reacting, similar to HCl.
  • Silver nitrate participates in precipitation reactions.
  • Combines with chloride ions to form a solid precipitate.
  • Is completely used up in this balanced reaction.
Concentration Calculation
Concentration calculations determine the amount of a substance present in a specific volume of solution. In this exercise, after the reaction involving HCl and AgNO鈧, we calculate the concentrations of resulting ions in the solution. Starting experts calculate initial moles using:\(\text{Moles} = \text{Concentration} \times \text{Volume (L)}\). The initial solutions were mixed in equal volumes (50.0 mL each), leading to a doubling of the total solution volume to 100 mL.
Post-reaction, only HNO鈧 remains as a notable contributor to hydronium ion concentration. Since HNO鈧 is fully ionizable, its initial concentration equals the final concentration of hydronium ions, remaining at 0.100 M. Meanwhile, all chloride ions reacted away, leaving a zero concentration of chloride ions.
  • Concentration is measured in moles per liter (M).
  • After the chemical reaction, hydronium ions remain at 0.100 M due to full ionization of HNO鈧.
  • No chloride ions remain post-reaction.

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Most popular questions from this chapter

Solid KSCN was added to a \(2.00 \mathrm{M} \mathrm{Fe}^{3+}\) solution so that it was also initially \(2.00 \mathrm{M} \mathrm{SCN}^{-}\). These ions then reacted to give the complex ion \(\mathrm{Fe}(\mathrm{SCN})^{2+},\) whose formation constant is \(9.0 \times 10^{2} .\) What is the concentration of \(\mathrm{Fe}^{3+}(a q)\) at equilibrium? Be sure to check any simplifying assumption you make.

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