Question

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

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

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: \(H_{2}O(g) + CO(g) \rightleftharpoons H_{2}(g) + CO_{2}(g)\)

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.

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.

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.

Key concepts

Isotopic Labeling

Isotopic labeling is a fascinating technique used by chemists to track atoms through a chemical reaction. Imagine you've labeled a carbon atom in carbon monoxide (CO) with a radioactive isotope, such as carbon-14. This labeling helps scientists understand how atoms move and rearrange during reactions.

In our exercise, we start with CO that contains such a labeled carbon atom. As the reaction can reach equilibrium, involving a back and forth process, this carbon atom begins in the CO molecule. But, it doesn't stay there!

• The carbon-14 atom will participate directly in the reaction.
• It will combine with water (H₂O) to form hydrogen (H₂) and carbon dioxide (CO₂).
• Thus, the labeled carbon atom can end up in the CO₂.

This way, the isotopic labeling shows that the specific carbon atoms are involved in an ongoing process, illustrating their journey through different molecules as the reaction continues.

Dynamic Equilibrium

Dynamic equilibrium is a key principle in chemistry where, in a reversible reaction, the rate of the forward reaction equals the rate of the backward reaction. This state doesn't mean the molecules stop reacting; rather, there is a constant balance.

In the given exercise, both the forward reaction (forming H₂ and CO₂) and the backward reaction (forming H₂O and CO) occur at the same rate. This situation leads to:

• A constant concentration of reactants and products.
• A perpetual, yet balanced, exchange and interconversion of atoms.

For the labeled carbon-14, this means it will continuously switch between being part of CO and CO₂. So while the concentration remains the same, there is lively movement on a molecular level.

Chemical Reaction

A chemical reaction involves the transformation of some substances into others. It entails breaking and forming chemical bonds, which results in the production of new products from the reactants. In this scenario, the initial reactants, H₂O and CO, react to form H₂ and CO₂.

The reaction we consider is reversible, which means:

• It can proceed in both the forward and reverse directions.
• In equal conditions, like concentration and temperature, the reaction reaches an equilibrium state.

This balance is essential in understanding equilibrium dynamics. During the chemical reaction, especially in equilibrium, isotopic labeling helps reveal the pathways and the reallocation of molecules. Loose bonds make it possible for reactants like CO to transform into products like CO₂, but at equilibrium, the mixture forms dynamically and maintains a steady state. This understanding is fundamental to grasping the complex behavior of chemical reactions in dynamic systems.