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Chemical reactions reach a state of balance known as chemical equilibrium, where the rate of the forward reaction equals the rate of the reverse reaction. In this state, the concentrations of the reactants and products remain constant over time. The equilibrium constant, denoted as \(K_c\) for reactions involving concentrations, quantifies this balance. It gives a ratio of the products' concentrations to the reactants' concentrations, each raised to the power of their coefficients in the balanced equation.

In the reaction \( \text{C}(s) + \text{CO}_2(g) \rightleftharpoons 2 \text{CO}(g) \), \(K_c\) is expressed in terms of the concentrations of carbon monoxide \([\mathrm{CO}]\) and carbon dioxide \([\mathrm{CO}_2]\):

• Solids like carbon (\(\mathrm{C}(s)\)) are omitted from the \(K_c\) expression because their activity is constant.
• Thus, the expression becomes:\[ K_c = \frac{[\mathrm{CO}]^2}{[\mathrm{CO}_2]} \]

This formula helps in calculating \(K_c\) using the concentrations at equilibrium. Interpret \(K_c\) values to determine if a reaction has a higher tendency to produce more products or reactants under specific conditions.

Calculating the concentrations of reactants and products at equilibrium is crucial for finding the equilibrium constant \(K_c\). Concentration, typically measured in moles per liter (M), indicates how much of each substance is present in a given volume of the reaction mixture.

Consider the scenario where the gaseous mixture is 90.55% CO by mass. To calculate the moles of each gas, you should:

- Assume a specific mass of the mixture for simplicity (e.g., 100 g), leading to precise mole calculations.
- Utilize molar masses for the transformation: - Molar mass of CO is 28.01 g/mol. - Molar mass of CO2 is 44.01 g/mol.

• Moles of CO from 90.55 g will be \(\frac{90.55}{28.01} = 3.234\) mol.
• Moles of CO2 from 9.45 g will be \(\frac{9.45}{44.01} = 0.215\) mol.

These calculated moles are essential inputs when applying the ideal gas law, as they allow us to determine the volume in which the gases reside and, consequently, their concentrations.

The Ideal Gas Law is a fundamental equation that relates the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed as \(PV = nRT\), where:

• \(P\) represents pressure.
• \(V\) is volume.
• \(n\) is the number of moles.
• \(R\) is the ideal gas constant, \(0.0821 \text{ L}\cdot\text{atm}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}\).
• \(T\) is temperature in Kelvin.

This law allows the prediction and calculation of how gases behave under different conditions, assuming they behave ideally.

By applying this law, you can determine the volume of the gas at given temperature and pressure conditions. For the reaction involving CO and CO2 at 850°C (or 1123 K) and 1 atm:

• Calculate the total number of moles from step 3: 3.234 mol CO + 0.215 mol CO2 = 3.449 mol.
• Then, using \( V = \frac{nRT}{P} \), the total volume is found to be \(317.46 \text{ L}\).

With this volume, you can calculate the molarity of each gas, which is necessary for determining the equilibrium constant.