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When dealing with gaseous reactions, the equilibrium constant can be expressed in terms of partial pressures of the gases involved. This is known as the pressure equilibrium constant, denoted by \( K_p \). - **Understanding \( K_p \):** It's particularly useful for reactions involving gases because pressure can be directly measured as opposed to concentration which requires knowing the volume of the gas. - **The Equation:** The relationship between the concentration equilibrium constant \( K_c \) and \( K_p \) is commonly captured by the equation: \[ K_p = K_c (RT)^{\Delta n} \] - **Variables Explained:** - \( R \) is the ideal gas constant, discussed in greater detail later. - \( T \) is the absolute temperature measured in Kelvin. - \( \Delta n \) is the change in moles of gas during the reaction, which is calculated as the moles of gaseous products minus the moles of gaseous reactants. - **Significance:** A higher \( K_p \) indicates that, at equilibrium, the reaction favors the formation of products in the gaseous phase. Conversely, a lower \( K_p \) would suggest equilibrium is skewed toward the reactants.

In a chemical equilibrium system, the concentration equilibrium constant, \( K_c \), describes the ratio of the concentration of products to reactants at equilibrium. It's specific to the concentrations of the substances involved.- **Understanding \( K_c \):** This form of equilibrium constant is useful when the concentrations of products and reactants in a solution or mixture are more practical to measure or calculate than pressure. - For our given reaction, \( K_c = 1.8 \) at \( 250^\circ \text{C} \). This numerical value is crucial for calculating \( K_p \) using the formula linking \( K_c \) and \( K_p \).- **Relation to \( K_p \):** - While both \( K_c \) and \( K_p \) serve similar purposes, \( K_p \) is especially beneficial for gaseous reactions due to the direct measurement of pressure.- **Importance in Calculations:** Knowing \( K_c \) allows us to determine \( K_p \) in a pragmatic manner, especially when we can accurately convert known parameters as outlined in the original solution.- **Formula Recollection:** - Depending on whether a reaction involves gases or solutions, knowing if the system favors products or reactants helps in comprehending the reaction's dynamics at equilibrium.

The ideal gas constant, denoted by \( R \), is a fundamental constant used in various equations related to gases.- **Role in Calculations:** - It prominently appears in the formula bridging \( K_c \) and \( K_p \), as well as in the ideal gas law \( PV = nRT \).- **Value Variety:** - The value of \( R \) depends on the units involved. For calculations involving pressure in atm, it commonly takes the value \( 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \).- **Temperature and Units:** - To ensure consistency and accuracy in calculations, \( R \) should align with the units used for pressure, volume, and temperature. - Temperature must always be calculated in Kelvin when utilizing \( R \). Converting Celsius to Kelvin uses the simple formula: \( T_K = T_C + 273.15 \).- **Application:** - In the given exercise, \( R \) plays a critical role by facilitating the computation of \( K_p \) through its incorporation in the equation \( K_p = K_c (RT)^{\Delta n} \). - The consistent application of the ideal gas constant in these scenarios emphasizes its utility across diverse chemical and physical calculations.