At 700 K , the equilibrium constant Kp for the reaction 2 SO3( g) ⇌2 SO2( g)+O2( g) is 1.80 ×10^

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At 700 K , the equilibrium constant Kp for the reaction 2...

At 700 K , the equilibrium constant $\mathrm{K}_{\mathrm{p}}$ for the reaction $2 \mathrm{SO}_3(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g})$ is $1.80 \times 10^{-3}$. What is the numerical value in mole per litre of equilibrium constant $\mathrm{K}_{\mathrm{c}}$ for this reaction at the same temperature? [2002] (a) $8.1 \times 10^{-8}$ (b) $9.1 \times 10^{-9} \mathrm{~mol} \mathrm{~L}^{-1}$ (c) $3.1 \times 10^{-7}$ (d) $6.1 \times 10^{-7} \mathrm{~mol} \mathrm{~L}^{-1}$

At 700 K , the equilibrium constant $\mathrm{K}_{\mathrm{p}}$ for the reaction $2 \mathrm{SO}_3(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g})$ is $1.80 \times 10^{-3}$. What is the numerical value in mole per litre of equilibrium constant $\mathrm{K}_{\mathrm{c}}$ for this reaction at the same temperature?
[2002]
(a) $8.1 \times 10^{-8}$
(b) $9.1 \times 10^{-9} \mathrm{~mol} \mathrm{~L}^{-1}$
(c) $3.1 \times 10^{-7}$
(d) $6.1 \times 10^{-7} \mathrm{~mol} \mathrm{~L}^{-1}$

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Key Concepts

Ideal Gas Law and its Role in Equilibrium

The ideal gas law links pressure, volume, temperature, and number of moles, and its constant R appears in the relationship between Kp and Kc. This illustrates how temperature and pressure conditions influence chemical equilibria, particularly in gaseous systems.

Equilibrium Constant Definitions

Equilibrium constants quantify the ratio of the concentrations or partial pressures of products to reactants when a chemical reaction reaches balance. Kc uses molar concentrations while Kp uses partial pressures. These constants provide insights into the position of equilibrium and the relative amounts of species present under specific conditions.

Conversion between Kp and Kc

The relationship between Kp and Kc is given by the equation Kp = Kc(RT)^?n, where R is the ideal gas constant, T is the absolute temperature in Kelvin, and ?n is the difference in moles of gaseous products and reactants. This conversion is essential when comparing equilibria expressed in different units.

Reaction Stoichiometry and ?n

The term ?n represents the net change in the number of moles of gas during the reaction, calculated as the total moles of gaseous products minus the total moles of gaseous reactants. Correctly determining ?n from the balanced equation is crucial for applying the conversion between Kp and Kc.

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