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When dealing with chemical reactions involving gases, we often encounter two types of equilibrium constants: \(K_c\) and \(K_p\). The key difference between these constants lies in their expression: \(K_c\) is used for concentrations in molarity, while \(K_p\) pertains to partial pressures. To convert \(K_c\) to \(K_p\), we utilize the equation: \[K_p = K_c (RT)^{\Delta n}\] where:

• \(R\) is the ideal gas constant \(0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1}\)
• \(T\) is the temperature in Kelvin
• \(\Delta n\) is the change in moles of gaseous products minus reactants

This equation helps compute \(K_p\) when \(K_c\) is known, as long as the reaction occurs under conditions where ideal gas laws apply. The exponential term \((RT)^{\Delta n}\) accounts for the pressure effects due to the change in gaseous moles, ensuring accurate conversion.

The ideal gas constant, represented by \(R\), is a fundamental value in the ideal gas law, establishing the link between pressure, volume, temperature, and amount of gas. In the context of equilibria where pressure is significant, \(R\) aids in translating concentration-based equilibrium constants \(K_c\) into pressure-based \(K_p\).Key points about the ideal gas constant:

• It is commonly valued at \(0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1}\).
• \(R\) is derived from the ideal gas law equation \(PV = nRT\).
• It ensures the compatibility of units when calculating \(K_p\) from \(K_c\) given that pressures or volumes of gases are involved.

The role of \(R\) in reactions involving gases is crucial for prediction and calculation of behavior under various conditions, especially where interconversion of different forms of the equilibrium constant is needed.

In chemical reactions involving gases, the change in the number of moles of gas, \(\Delta n\), plays a pivotal role in determining pressure-based equilibrium constants like \(K_p\). This value is calculated by subtracting the total moles of gaseous reactants from those of gaseous products.Steps for calculating \(\Delta n\):

• Count the moles of all gaseous products.
• Count the moles of all gaseous reactants.
• Subtract the reactant moles from the product moles: \(\Delta n = \text{(moles of products)} - \text{(moles of reactants)}\).

In our given reaction, \(\text{F}(g) + \text{O}_2(g) \rightleftharpoons \text{O}_2\text{F}(g)\), \(\Delta n\) is calculated as follows:- 1 mole of \(\text{O}_2\text{F}(g)\) (product) vs. 2 moles of reactants (1 mole of \(\text{F}(g)\) + 1 mole of \(\text{O}_2(g)\)).- Therefore, \(\Delta n = 1 - 2 = -1\).Taking into account \(\Delta n\) allows us to accurately determine \(K_p\) from \(K_c\), adjusting for the volume and pressure changes happening in the gas phase.