For the reaction between carbon monoxide and chlorine to form phosgene, the equilibrium constant calculated from partial pressures is \(K=0.20 .\) How does this value relate to the equilibrium constant, \(K_{\mathrm{C}}\), under the same conditions, calculated from molar concentrations? $$ \mathrm{CO}(g)+\mathrm{Cl} 2(g) \rightleftarrows \mathrm{COCl} 2(g) $$

Chemical equilibrium is a state in a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction. In this balanced situation, the concentrations of the reactants and products remain constant over time, although both reactions are still occurring. It's essential to understand that reaching equilibrium does not imply that the reactants and products are present in equal amounts, but rather that their rates of formation are equivalent, leading to a steady state.

When the reaction
\[\mathrm{CO}(g) + \mathrm{Cl}_2(g) \rightleftarrows \mathrm{COCl}_2(g)\]
reaches equilibrium, the ratio of the products to the reactants remains unchanged. This ratio is described by the equilibrium constant (\(K\)), which is a numerical value unique to every chemical reaction at a given temperature. Understanding how to calculate and interpret this constant is fundamental for predicting how changes in conditions (like concentration, pressure, and temperature) can shift the equilibrium, impacting the yield of a reaction.

Partial pressures are a way of expressing the pressure contributed by each gas in a mixture of gases. According to Dalton's Law of Partial Pressures, the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases. At chemical equilibrium involving gases, the partial pressures play a crucial role in expressing the equilibrium constant, denoted as \(K_p\).

The equilibrium constant from partial pressures, \(K_p\), applies to gaseous reactions and is calculated as the pressure of the products raised to their stoichiometric coefficients divided by the pressure of the reactants raised to their coefficients. Understanding partial pressures is vital because it pertains directly to gas laws and can affect chemical reactions, such as the synthesis of phosgene from carbon monoxide and chlorine.

Molar concentrations, often expressed in moles per liter (M), are measures of the amount of a substance per unit volume of a solution. This concept is essential when discussing reactions taking place in solution phase, but it can also apply to gases if one refers to their concentration in a volume of space. In a gaseous system, the molar concentration is related to the pressure through the ideal gas law.

In the context of equilibrium, the molar concentrations of reactants and products are used to calculate the equilibrium constant, denoted as \(K_c\). This value is determined by the ratio of the concentrations of the products to the reactants, each raised to the power of their stoichiometric coefficients. For educators and students alike, grasping the relationship between \(K_p\) and \(K_c\) is critical when predicting the outcome of a reaction and understanding how different states of matter are accounted for in equilibrium expressions.