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When dealing with chemical equilibrium, the equilibrium constant, denoted as \( K_c \), is a crucial concept that quantifies the ratio of product concentrations to reactant concentrations at equilibrium. Each concentration is raised to a power equal to its coefficient in the balanced chemical equation. For the reaction \( \mathrm{SbCl}_5(g) \rightleftharpoons \mathrm{SbCl}_3(g) + \mathrm{Cl}_2(g) \), the expression for the equilibrium constant is formulated as: \[ K_c = \frac{[\mathrm{SbCl}_3][\mathrm{Cl}_2]}{[\mathrm{SbCl}_5]} \] This equation allows us to determine how far a reaction has proceeded to products at a given temperature, in this case at \(248^\circ C\). It's essential to note that \( K_c \) provides insight into the position of equilibrium:

• If \( K_c \) is much greater than 1, the reaction favors the formation of products.
• If \( K_c \) is much less than 1, the reactants are favored.
• A \( K_c \) value around 1 indicates a balance between products and reactants.

Understanding this constant will help predict how changes in conditions (like concentration or temperature) affect the equilibrium position.

An ICE table is a useful tool for organizing and keeping track of changes in concentrations for reaction species as a system moves from initial conditions to equilibrium. "ICE" stands for Initial, Change, and Equilibrium. Each of these headings corresponds to different phases: - **Initial**: This row starts with the concentration of each reactant and product before the reaction proceeds. For the exercise, we start with \([\mathrm{SbCl}_5] = 0.00357\,\mathrm{mol/L}\) and \([\mathrm{SbCl}_3] = [\mathrm{Cl}_2] = 0 \). - **Change**: Here, we define the change in concentrations. Typically, we use \(x\) to represent the amount that changes as the system shifts towards equilibrium. For our dissociation reaction, the change would be \(-x\) for \(\mathrm{SbCl}_5 \) and \(+x\) for both \(\mathrm{SbCl}_3 \) and \(\mathrm{Cl}_2 \). - **Equilibrium**: This row shows the concentrations of all species once equilibrium is established: \([\mathrm{SbCl}_5] = 0.00357 - x\), \([\mathrm{SbCl}_3] = x\), and \([\mathrm{Cl}_2] = x\). ICE tables simplify the process of setting up equations based on the equilibrium constants. They are particularly helpful in visualizing how concentrations evolve, making them indispensable for solving equilibrium problems systematically.

The Ideal Gas Law, an essential principle in chemistry, relates the pressure, volume, temperature, and number of moles of a gas. It's expressed as: \[ P = \frac{nRT}{V} \] Where:

• \(P\) is the pressure,
• \(n\) is the number of moles,
• \(R\) is the ideal gas constant (\(0.0821 \, \mathrm{L} \, \mathrm{atm/mol} \, \mathrm{K}\)),
• \(T\) is the temperature in Kelvin, and
• \(V\) is the volume.

In the given problem, after establishing the equilibrium concentrations, we calculate the total number of moles of gas at equilibrium. For \(\mathrm{SbCl}_3\) and \(\mathrm{Cl}_2\), this is simply the sum: \(0.01762\, \mathrm{mol} \). Using the ideal gas law allows one to calculate the pressure of the gas at equilibrium in a vessel of known volume. This relation highlights the interdependency of gas properties and is particularly useful in predicting how gases behave under different conditions. It merges the macroscopic (volumes and pressures) with the microscopic (moles and temperature) aspects of gases, making it a powerful tool in chemistry.