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Chapter 16: Problem 71

Describe an experiment that would allow you to prove that the system \(3 \mathrm{H}_{2}(\mathrm{g})+\mathrm{N}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{NH}_{3}(\mathrm{g})\) is a dynamic equilibrium. (Hint: Consider using a stable isotope such as \(15 \mathrm{N}\) or \(^{2} \mathrm{H}\).)

Short Answer

Expert verified
Label the nitrogen with \(^{15}\mathrm{N}\), allow equilibrium, and use mass spectrometry to show isotopic exchange in the products, confirming dynamic equilibrium.

Step by step solution

01

Understand Dynamic Equilibrium

A dynamic equilibrium occurs when the rate of the forward reaction equals the rate of the reverse reaction, allowing both reactions to occur simultaneously without changing the concentrations of reactants and products over time.
02

Choose a Stable Isotope for Tracing

Select a stable isotope, such as \(^{15}\mathrm{N}\) or \(^{2}\mathrm{H}\), which will be used to label one of the reactants. This labeling helps in tracking the movement of atoms in the reaction process.
03

Set Up the Experiment

Prepare a reaction vessel with the reactants \(3 \mathrm{H}_{2}\) and enriched \(^{15}\mathrm{N}_{2}\) at an appropriate temperature and pressure to facilitate the reaction to form \(2 \mathrm{NH}_{3}\). Allow the system to reach equilibrium.
04

Conduct Mass Spectrometry Analysis

Use mass spectrometry to periodically sample the hydrogen and ammonia within the reaction vessel. This will help to identify the presence of \(^{15}\mathrm{N}\) or \(^{2}\mathrm{H}\) in \(\mathrm{NH}_{3}\) and observe any isotopic exchange.
05

Demonstrate Isotopic Exchange

Observe if the \(^{15}\mathrm{N}\) isotope is found in both the nitrogen gas and ammonia after a period. The presence of isotopically labeled atoms in both the reactants and products indicates that forward and reverse reactions are occurring at the same rate, confirming dynamic equilibrium.

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Key Concepts

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

Stable Isotopes
Stable isotopes are variants of elements that do not decay over time. They have the same number of protons but different numbers of neutrons. This stability makes them excellent tools in scientific experiments because they won't alter or transform unexpectedly. When scientists use isotopes like \(^{15}\mathrm{N}\), they benefit from its non-radioactive nature, allowing them to track chemical reactions without introducing harmful radiation.
  • Non-radioactive: Safe and stable for experiments.
  • Allows for precise tracking of atoms within a chemical process.
  • Helps in studying dynamic equilibrium, as isotopes can be traced over time.
Isotopic Labeling
Isotopic labeling involves replacing an atom in a molecule with its isotopic counterpart. This labeling helps track how atoms move and transform during chemical reactions. In the context of dynamic equilibrium, using isotopic labeling can prove that both forward and reverse reactions are occurring.
  • Enables tracking of specific atoms in reactions.
  • Provides clear evidence of where isotopes end up during the process.
  • Shows exchange between reactants and products, confirming equilibrium.
For example, by using \(^{15}\mathrm{N}\) in nitrogen gas, we can determine if the nitrogen atoms are being incorporated into ammonia and then back into nitrogen gas, highlighting the dynamic nature of the equilibrium.
Mass Spectrometry
Mass spectrometry is a powerful analytical tool used to measure the masses of atoms and molecules. It helps identify the presence and quantity of isotopes in a sample by analyzing their mass-to-charge ratio. In dynamic equilibrium studies, mass spectrometry allows scientists to observe isotopic exchanges clearly and efficiently.
  • Accurately measures isotopic content in samples.
  • Helps visualize the progression of a reaction over time.
  • Confirms whether isotopes are found in both reactants and products.
By periodically sampling the reaction mixture, mass spectrometry reveals if isotopes like \(^{15}\mathrm{N}\) have shifted from reactants to products and vice versa, supporting the concept of simultaneous forward and reverse reactions.
Forward and Reverse Reactions
In a dynamic equilibrium, the forward and reverse reactions occur at the same rate. This balance results in stable concentrations of reactants and products. Despite a constant equilibrium state, these reactions are ongoing and dynamic, not static.
  • Forward reaction: Formation of products from reactants.
  • Reverse reaction: Reactants being reformed from products.
  • Balance: Equal rates maintain equilibrium state.
The presence of isotopic atoms like \(^{15}\mathrm{N}\) in both ammonia and nitrogen gas after reaching equilibrium is proof of these ongoing reactions, demonstrating the dynamic nature of chemical equilibria.

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Most popular questions from this chapter

The equilibrium constant for the dissociation of iodine molecules to iodine atoms $$ \mathrm{I}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{I}(\mathrm{g}) $$ is \(3.76 \times 10^{-3}\) at \(1000 \mathrm{K}\). Suppose 0.105 mol of \(\mathrm{I}_{2}\) is placed in a \(12.3-\mathrm{L}\). flask at \(1000 \mathrm{K}\). What are the concentrations of \(\mathrm{I}_{2}\) and \(\mathrm{I}\) when the system comes to equilibrium?

The equilibrium constant, \(K_{p},\) is 0.14 at \(25^{\circ} \mathrm{C}\) for the following reaction: $$ \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{g}) $$ If the total pressure of the gas mixture is 2.5 atm at equilibrium, what is the partial pressure of each gas?

Which of the following correctly relates the equilibrium constants for the two reactions shown? \(A+B \rightleftarrows 2 C \quad K_{1}\) \(2 \mathrm{A}+2 \mathrm{B} \rightleftharpoons 4 \mathrm{C} \quad K_{2}\) (a) \(K_{2}=2 K_{1} \quad\) (c) \(K_{2}=1 / K_{1}\) (b) \(K_{2}=K_{1}^{2}\) (d) \(K_{2}=1 / K_{1}^{2}\)

Boric acid and glycerin form a complex \(\mathrm{B}(\mathrm{OH})_{3}(\mathrm{aq})+\) glycerin \((\mathrm{aq}) \rightleftarrows \mathrm{B}(\mathrm{OH})_{3} \cdot\) glycerin \((\mathrm{aq})\) with an equilibrium constant of \(0.90 .\) If the concentration of boric acid is \(0.10 \mathrm{M}\), how much glycerin should be added, per liter, so that \(60 . \%\) of the boric acid is in the form of the complex?

\(K_{c}\) for the decomposition of ammonium hydrogen sulfide is \(1.8 \times 10^{-4}\) at \(25^{\circ} \mathrm{C}\) $$ \mathrm{NH}_{4} \mathrm{HS}(\mathrm{s}) \rightleftharpoons \mathrm{NH}_{3}(\mathrm{g})+\mathrm{H}_{2} \mathrm{S}(\mathrm{g}) $$ (a) When the pure salt decomposes in a flask, what are the equilibrium concentrations of \(\mathrm{NH}_{3}\) and \(\mathrm{H}_{2} \mathrm{S} ?\) (b) If \(\mathrm{NH}_{4} \mathrm{HS}\) is placed in a flask already containing \(0.020 \mathrm{mol} / \mathrm{L}\) of \(\mathrm{NH}_{3}\) and then the system is allowed to come to equilibrium, what are the equilibrium concentrations of \(\mathrm{NH}_{3}\) and \(\mathrm{H}_{2} \mathrm{S} ?\)
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