A mixture of CO(g) and O2(g) in a 1.0 L container at 1.0 ×10^3 K has a total pressure of 2.2

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A mixture of CO(g) and O2(g) in a 1.0 L container at 1.0...

A mixture of $\mathrm{CO}(g)$ and $\mathrm{O}_{2}(g)$ in a $1.0 \mathrm{~L}$ container at $1.0 \times 10^{3} \mathrm{~K}$ has a total pressure of $2.2 \mathrm{~atm}$. After some time the total pressure falls to $1.9 \mathrm{~atm}$ as the result of the formation of $\mathrm{CO}_{2}$. Determine the mass (in grams) of $\mathrm{CO}_{2}$ that forms.

Key Concepts

Pressure Change and Reaction Progress

In a closed system where volume and temperature are constant, the change in total pressure reflects the change in the number of moles of gas due to the reaction. By comparing the initial and final pressures, one can deduce the net change in gas moles, which can then be used to calculate the extent of the reaction and the amount of product formed.

Molar Mass and Conversion to Mass

Once the number of moles of a substance is determined from the reaction stoichiometry and ideal gas law, it is necessary to convert this value to mass using the molar mass. This conversion is fundamental for expressing the final amount of product in grams rather than moles.

Ideal Gas Law

The ideal gas law (PV = nRT) is essential for relating pressure, volume, temperature, and the amount of gas (in moles). In this problem, it enables the calculation of the number of moles present before and after the reaction, which is directly correlated to the measured pressures in a constant volume system.

Stoichiometry of Gas Reactions

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. For gaseous reactions, the change in total pressure can be directly related to the change in the number of moles, which is linked to the reaction’s balanced equation. This concept is crucial for determining the extent of the reaction and the moles of product formed.

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