When CO2(g) is put in a sealed container at 701 K and a pressure of 10.0 atm and is heated to 14

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When CO2(g) is put in a sealed container at 701 K and a...

When $\mathrm{CO}_{2}(g)$ is put in a sealed container at 701 $\mathrm{K}$ and a pressure of 10.0 atm and is heated to $1401 \mathrm{K},$ the pressure rises to 22.5 $\mathrm{atm}$ . Some of the $\mathrm{CO}_{2}$ decomposes to CO and $\mathrm{O}_{2}$ . Calculate the mole percent of $\mathrm{CO}_{2}$ that decomposes.

Key Concepts

Ideal Gas Law

This fundamental principle relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. In problems involving changes in temperature and pressure in a sealed container (where volume is constant), the ideal gas law is used to calculate how changes in temperature affect the pressure if there were no chemical reaction. It sets the baseline for comparing observed pressure changes to those expected without reaction, thereby indicating the occurrence of a reaction that alters the number of moles of gas.

Reaction Stoichiometry

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction as described by the balanced chemical equation. For the decomposition of CO2 into CO and O2, stoichiometric ratios determine precisely how many moles of products are formed from each mole of CO2 that decomposes. Understanding these ratios is crucial for linking the extent of the reaction with the overall change in the gas moles and, by extension, the pressure observed in the container.

Extent of Reaction

The extent of reaction quantifies how much of a reactant has been converted into products relative to the initial amount. In scenarios where a gas reaction leads to a change in the total number of moles, such as the decomposition of CO2, determining the fraction of CO2 that has reacted is key to explaining the observed pressure deviations from those predicted solely by the ideal gas law. This concept facilitates the calculation of percentage conversion necessary to account for the additional gas moles generated during the reaction.

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