Find out the value of Kc for each of the following...

Find out the value of $K_{c}$ for each of the following equilibria from the value of $K_{p}:$ (i) $\quad 2 \mathrm{NOCl}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(g) ; K_{p}=1.8 \times 10^{-2}$ at $500 \mathrm{~K}$ (ii) $\quad \mathrm{CaCO}_{3}(\mathrm{~s}) \rightleftharpoons \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g}) ; K_{\mathrm{p}}=167$ at $1073 \mathrm{~K}$

Find out the value of $K_{c}$ for each of the following equilibria from the value of $K_{p}:$
(i) $\quad 2 \mathrm{NOCl}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(g) ; K_{p}=1.8 \times 10^{-2}$ at $500 \mathrm{~K}$
(ii) $\quad \mathrm{CaCO}_{3}(\mathrm{~s}) \rightleftharpoons \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g}) ; K_{\mathrm{p}}=167$ at $1073 \mathrm{~K}$

Key Concepts

Ideal Gas Law Constant and Temperature Dependency

The equation relating K_p and K_c involves the product RT, reflecting the influence of temperature on gas behavior as described by the ideal gas law. The value of R, the universal gas constant, must be consistent with the units used for pressure and concentration, and the temperature must always be in Kelvin to ensure accurate calculations.

Exclusion of Pure Phases from Equilibrium Expressions

In the context of equilibrium constant calculations, pure solids and liquids are omitted because their concentrations remain constant during the reaction. For example, in reactions where a solid decomposes releasing a gas, only the gaseous product is included in the equilibrium expression, simplifying the conversion between K_p and K_c.

Equilibrium Constant (K_c and K_p)

An equilibrium constant expresses the ratio of the concentrations or partial pressures of products to reactants at equilibrium. K_c is based on molar concentrations (typically in moles per liter), while K_p is based on partial pressures (usually in atmospheres). Both constants provide a measure of the extent to which a reaction proceeds under given conditions.

Relationship between K_p and K_c

The interconversion between K_p and K_c is governed by the equation K_p = K_c (RT)^(?n), where R is the universal gas constant, T is the temperature in Kelvin, and ?n is the difference in the number of moles of gaseous products and reactants. This relationship is essential when comparing or converting equilibrium constants expressed in terms of pressures to those expressed in concentrations.

Gaseous Reaction Stoichiometry and ?n

?n represents the change in the number of moles of gaseous species during a chemical reaction, calculated as the total moles of gases in the products minus the total moles of gases in the reactants. This value directly impacts how the equilibrium constant is converted from K_p to K_c and must be determined accurately from the balanced chemical equation.

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