For the reversible system PCl3+Cl2 ⇌PCl5, the relationship between degree of dissociation (α) of

step 1 In this problem we have given that for the reversible system PCL3 reacts with CL2 to give PCL5.

For the reversible system PCl3+Cl2 ⇌PCl5, the relationship...

For the reversible system $\mathrm{PCl}_3+\mathrm{Cl}_2 \rightleftharpoons \mathrm{PCl}_5$, the relationship between degree of dissociation $(\alpha)$ of $\mathrm{PCl}_5$ and the equilibrium constant $\mathrm{K}_{\mathrm{p}}$ of the above equilibrium is (a) $\frac{\mathrm{K}_{\mathrm{p}}}{\sqrt{\mathrm{P}+\mathrm{K}_{\mathrm{p}}}}$ (b) $\sqrt{\frac{K_p}{1+P \cdot K_p}}$ (c) $\frac{1}{\sqrt{\mathrm{P}+\mathrm{K}_{\mathrm{p}}}}$ (d) $\sqrt{\frac{1}{1+\mathrm{P} \cdot \mathrm{K}_{\mathrm{P}}}}$

For the reversible system $\mathrm{PCl}_3+\mathrm{Cl}_2 \rightleftharpoons \mathrm{PCl}_5$, the relationship between degree of dissociation $(\alpha)$ of $\mathrm{PCl}_5$ and the equilibrium constant $\mathrm{K}_{\mathrm{p}}$ of the above equilibrium is
(a) $\frac{\mathrm{K}_{\mathrm{p}}}{\sqrt{\mathrm{P}+\mathrm{K}_{\mathrm{p}}}}$
(b) $\sqrt{\frac{K_p}{1+P \cdot K_p}}$
(c) $\frac{1}{\sqrt{\mathrm{P}+\mathrm{K}_{\mathrm{p}}}}$
(d) $\sqrt{\frac{1}{1+\mathrm{P} \cdot \mathrm{K}_{\mathrm{P}}}}$

Key Concepts

Chemical Equilibrium

This concept involves the state at which the forward and reverse reactions occur at the same rate, so the concentrations or partial pressures of all species remain constant. In chemical systems at equilibrium, an equilibrium constant (such as Kp for gases) is defined in terms of the partial pressures or concentrations of the reactants and products.

Equilibrium Constant Expression

For gas?phase reactions, the equilibrium constant (Kp) is expressed in terms of the partial pressures of the products and reactants. This expression serves as a critical relationship that quantifies the position of equilibrium and allows one to connect the measurable quantities (pressure) with the underlying reaction dynamics.

Degree of Dissociation

The degree of dissociation is a measure of the fraction of the initial amount of a substance that has dissociated into products at equilibrium. It is a key parameter in the study of equilibria because it directly affects the mole numbers of all species in the reaction mixture and, consequently, their partial pressures.

Partial Pressure and Mole Fractions

Partial pressure in a gas mixture is determined by the mole fraction of a component times the total pressure. This concept is essential in calculating the partial pressures of the reacting species at equilibrium when the overall pressure and the composition (as determined by the degree of dissociation) are known.

Algebraic Manipulation in Equilibrium Calculations

When relating the equilibrium constant to the degree of dissociation, algebraic manipulation of the equilibrium expressions is required. This involves combining the mole balance (from the degree of dissociation) with the expression for total pressure to derive a formula that links the equilibrium constant directly to the degree of dissociation.

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