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Chemical equilibrium refers to a state in a chemical reaction where the rate at which the reactants convert into products equals the rate at which the products convert back into reactants. In the case of the phosgene gas decomposition, the reaction achieves equilibrium once the concentrations of CO, Cleightsub>2, and COCleightsub>2 no longer change over time.
A key feature of chemical equilibrium is that it is dynamic. This means although the concentrations remain constant, the molecules continue to react with each other. The forward and reverse reactions occur simultaneously and at the same rate.
At equilibrium, the system is governed by the equilibrium constant, \( K_c \), which provides critical insight into the relative concentrations of reactants and products. Understanding this balance helps us predict how a system responds to changes in conditions.

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It's essential to understand reaction stoichiometry to calculate changes in concentrations as a reaction approaches equilibrium.
In our example, the decomposition of phosgene ( COCl eightsub>2) into carbon monoxide (CO) and chlorine ( Cl eightsub>2) follows a 1:1:1 stoichiometric ratio. This implies that every molecule of phosgene decomposes to form one molecule of CO and one molecule of Cl eightsub>2.
This 1:1:1 ratio means that any change in the concentration of one component in the reaction mixture results in an equivalent change in the concentrations of the others. For example, a decrease of 0.046 M in phosgene results in an increase of 0.046 M each for carbon monoxide and chlorine.

In the context of a chemical reaction approaching equilibrium, changes in concentration are pivotal. We begin with initial concentrations and need to calculate how these change over time until equilibrium is established.
For the decomposition of phosgene, the initial concentration of COCl eightsub>2 is given as 0.500 M, while both CO and Cl eightsub>2 start at 0 M. As the reaction proceeds, phosgene decreases by 0.046 M, and simultaneously, the concentrations of CO and Cl eightsub>2 increase by 0.046 M each.
It is crucial to monitor these changes, as they allow us to calculate the equilibrium concentrations of each component. This information is then used to determine the equilibrium constant. Understanding these shifts helps in predicting how the system will react if conditions change.

The equilibrium expression is a mathematical equation that uses the concentrations of reactants and products to calculate the equilibrium constant, \( K_c \). This expression depends on the balanced chemical equation and the stoichiometry.
For the reaction \( \mathrm{COCl}_2(g) \leftrightharpoons \mathrm{CO}(g) + \mathrm{Cl}_2(g) \), the equilibrium expression is \[ K_c = \frac{[\mathrm{CO}][\mathrm{Cl}_2]}{[\mathrm{COCl}_2]} \].
Plugging in the equilibrium concentrations yields: \([\mathrm{CO}] = 0.046 \mathrm{M}\), \([\mathrm{Cl}_2] = 0.046 \mathrm{M}\), and \([\mathrm{COCl}_2] = 0.454 \mathrm{M}\).
This gives us the equation: \[ K_c = \frac{(0.046)(0.046)}{0.454} \approx 0.00466 \].
Understanding and setting up the equilibrium expression is critical for calculating \( K_c \), and it provides insights into the extent to which reactants are converted into products in a reaction.