The ratio of Kp / Kc for the reaction CO(g)+1 / 2 O2( g) ⇌CO2( g) is (a) 1 (b) RT (c) (RT)^1 / 2

step 1 In this problem we have given a reaction. Carbon monoxide reacts with half moles of O2 reversibl

The ratio of Kp / Kc for the reaction CO(g)+1 / 2 O2( g)...

The ratio of $K_{p} / K_{c}$ for the reaction $\mathrm{CO}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})$ is
(a) 1
(b) RT
(c) $(\mathrm{RT})^{1 / 2}$
(d) $(\mathrm{RT})^{-1 / 2}$

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Key Concepts

Equilibrium Constant Relationship

This concept relates the two forms of equilibrium constants for gaseous reactions: Kp, which is expressed in terms of partial pressures, and Kc, which is expressed in terms of concentration. The relationship is given by the formula Kp = Kc (RT)^?n, where ?n is the change in the number of moles of gas, R is the gas constant, and T is the temperature. This formula shows how changes in temperature and the stoichiometry of the reaction affect the conversion between Kp and Kc.

Change in Moles of Gas (?n)

?n represents the difference between the total moles of gaseous products and the total moles of gaseous reactants. It is a key parameter in linking Kp and Kc, as it directly influences the exponent in the (RT)^?n term. Understanding ?n allows one to predict how the equilibrium constant will change when expressed in terms of pressure versus concentration.

Ideal Gas Law

The ideal gas law, represented by PV = nRT, is fundamental in connecting the macroscopic properties of gases (pressure, volume, temperature) with the number of moles. This law underpins the derivation of the relationship between Kp and Kc because it provides the basis for incorporating the temperature and gas constant into the equilibrium expressions, thereby relating pressure and concentration in a consistent manner.

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