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Chapter 13: Problem 13

Consider the following reaction: $$\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)$$ Amounts of \(\mathrm{H}_{2} \mathrm{O}, \mathrm{CO}, \mathrm{H}_{2},\) and \(\mathrm{CO}_{2}\) are put into a flask so that the composition corresponds to an equilibrium position. If the CO placed in the flask is labeled with radioactive \(^{14} \mathrm{C}\) will \(^{14} \mathrm{C}\) be found only in \(\mathrm{CO}\) molecules for an indefinite period of time? Explain.

Short Answer

Expert verified
In equilibrium, radioactive carbon (C-14) will not be found only in CO molecules for an indefinite period of time. Instead, it will continuously exchange between the CO and CO2 molecules because the reaction is still taking place, and the isotope will be distributed evenly among the CO and CO2 molecules at equilibrium. The dynamic nature of equilibrium allows for the constant interconversion of reactants and products without changing the proportions of the substances involved.

Step by step solution

01

Understand Equilibrium

When a reaction is in equilibrium, the rate of the forward reaction equals the rate of the reverse reaction. In other words, the reactants and products are still interconverting but the total amounts of each substance remain constant. For this particular reaction: \(H_{2}O(g) + CO(g) \rightleftharpoons H_{2}(g) + CO_{2}(g)\)
02

Determine Isotope Distribution at Equilibrium

After reaching equilibrium, the reaction is still continuously occurring but the rates of the forward and reverse reactions are constant. The C-14 is initially placed just in CO molecules, but as the reaction proceeds, these will react with H2O to form H2 and CO2, transferring C-14 isotopes to CO2 molecules.
03

Describe the Dynamic Nature of Equilibrium in terms of Isotope Distribution

At equilibrium, the reaction is still taking place, which means that C-14 isotopes will also be found in CO2 molecules as the gas is involved in the reaction. As CO molecules with radioactive \(\mathrm{^{14}C}\) participate in the equilibrium reaction, some of the \(\mathrm{^{14}C}\) will end up in \(\mathrm{CO}_{2}\) molecules. Once the equilibrium reaction has distributed the \(\mathrm{^{14}C}\) evenly among \(\mathrm{CO}\) and \(\mathrm{CO}_{2}\) molecules, it will continue to change its position in response to any external factors like temperature or pressure changes without changing the proportion of the radioactive isotope in the molecular pool.
04

Conclude the Isotope Distribution at Equilibrium

Due to the dynamic nature of the equilibrium, radioactive carbon (C-14) will not be found solely in CO molecules for an indefinite period of time. Instead, it will continuously exchange between the CO and CO2 molecules as the reaction takes place at equilibrium.

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Most popular questions from this chapter

Predict the shift in the equilibrium position that will occur for each of the following reactions when the volume of the reaction container is increased. a. $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$ b. $\mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)$ c. \(\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{HF}(g)\) d. \(\mathrm{COCl}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{Cl}_{2}(g)\) e. $\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$

In which direction will the position of the equilibrium $$2 \mathrm{HI}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g)$$ be shifted for each of the following changes? a. \(\mathrm{H}_{2}(g)\) is added. b. \(\mathrm{I}_{2}(g)\) is removed. c. \(\operatorname{HI}(g)\) is removed. d. In a rigid reaction container, some Ar(g) is added. e. The volume of the container is doubled. f. The temperature is decreased (the reaction is exothermic).

The gas arsine, \(\mathrm{AsH}_{3},\) decomposes as follows: $$2 \mathrm{AsH}_{3}(g) \rightleftharpoons 2 \mathrm{As}(s)+3 \mathrm{H}_{2}(g)$$ In an experiment at a certain temperature, pure \(\mathrm{AsH}_{3}(g)\) was placed in an empty, rigid, sealed flask at a pressure of 392.0 torr. After 48 hours the pressure in the flask was observed to be constant at 488.0 torr. a. Calculate the equilibrium pressure of \(\mathrm{H}_{2}(g)\) b. Calculate \(K_{\mathrm{p}}\) for this reaction.

At a particular temperature a \(2.00-\mathrm{L}\) flask at equilibrium contains \(2.80 \times 10^{-4}\) mole of \(\mathrm{N}_{2}, 2.50 \times 10^{-5}\) mole of \(\mathrm{O}_{2},\) and \(2.00 \times 10^{-2}\) mole of $\mathrm{N}_{2} \mathrm{O}\( . Calculate \)K$ at this temperature for the reaction $$2 \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{N}_{2} \mathrm{O}(g)$$ If $\left[\mathrm{N}_{2}\right]=2.00 \times 10^{-4} M,\left[\mathrm{N}_{2} \mathrm{O}\right]=0.200 M,\( and \)\left[\mathrm{O}_{2}\right]=\( \)0.00245 M,$ does this represent a system at equilibrium?

For the following reactions, predict whether the mole fraction of the reactants or products increases or remains the same when the volume of the reaction vessel is increased. a. $\operatorname{Br}_{2}(g)+\mathrm{H}_{2}(g) \leftrightharpoons 2 \mathrm{HBr}(g)$ b. $2 \mathrm{CH}_{4}(g) \leftrightharpoons \mathrm{C}_{2} \mathrm{H}_{2}(g)+3 \mathrm{H}_{2}(g)$ c. \(2 \mathrm{HI}(g) \leftrightharpoons \mathrm{I}_{2}(s)+\mathrm{H}_{2}(g)\)
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