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The equilibrium constant, represented as \(K_c\), is a key idea in chemical equilibrium. It provides a snapshot of the relative concentrations of products and reactants at equilibrium, specifically for reactions involving gases. Each chemical reaction has its own unique \(K_c\) value, showing how much the reaction favors products or reactants when it reaches equilibrium.
To express \(K_c\), we use the formula:\[K_c = \frac{[\text{products}]}{[\text{reactants}]}\] This expression is derived from the balanced chemical equation of the reaction. In our example, \(K_c\) is represented by\[K_c = \frac{[\mathrm{PCl}_5]}{[\mathrm{PCl}_3][\mathrm{Cl}_2]}\]Here, \([\mathrm{PCl}_5], [\mathrm{PCl}_3], [\mathrm{Cl}_2]\) are the molar concentrations of phosphorus pentachloride, phosphorus trichloride, and chlorine, respectively, at equilibrium. A larger \(K_c\) means products are favored; a smaller \(K_c\) implies reactants are favored. Calculating \(K_c\) effectively involves determining these concentrations at equilibrium and plugging them into the expression.

Chemical reactions involve the transformation of reactants into products. In the given reaction, phosphorus trichloride \(\mathrm{PCl}_3\) and chlorine \(\mathrm{Cl}_2\) react to form phosphorus pentachloride \(\mathrm{PCl}_5\). This process is reversible and reaches a state of equilibrium.
At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction. This balance means the concentrations of the reactants and products remain constant over time, though the reaction hasn't stopped. An equilibrium state is dynamic, with ongoing reactions happening in both directions. Still, their effects balance each other out, so there's no net change in the concentration of reactants or products.
Understanding these basics helps in grasping why the equilibrium constant \(K_c\) is meaningful, as it quantifies the balance between reactants and products. Each chemical reaction can have different equilibrium characteristics, altering its \(K_c\). Some reactions may heavily favor products, others reactants, based on their conditions and \(K_c\) values.

Molar concentration, or molarity, is a measure of the concentration of a chemical species in a solution, typically expressed in moles per liter (M). It serves as a crucial parameter in determining the equilibrium constant \(K_c\).
To calculate molar concentration, you divide the number of moles of a solute by the volume of the solution in liters. For example, in the problem, you can calculate the concentrations for each component as follows:

• Phosphorus trichloride \([\mathrm{PCl}_3]\) is \(0.0148\;\text{mol} / 4.00\;\text{L} = 0.0037\;\text{M}\)
• Chlorine \([\mathrm{Cl}_2]\) is \(0.0870\;\text{mol} / 4.00\;\text{L} = 0.02175\;\text{M}\)
• Phosphorus pentachloride \([\mathrm{PCl}_5]\) is \(0.0126\;\text{mol} / 4.00\;\text{L} = 0.00315\;\text{M}\)

Once you have these values, they can be substituted into the \(K_c\) equation. Molar concentration effectively links the amount of solute with the space it occupies, offering a clear picture of its role in the reaction and its equilibrium state. Understanding molarity is vital in comprehending how different factors affect chemical equilibrium.