For the reaction 2 HI(g) ⇌H2( g)+I2( g) if the degree of dissociation is αand Kp is the equilibr

step 1 In this problem we have given that 2 moles of H .I. gas reacts reversibly to give H2 gas and I2

For the reaction 2 HI(g) ⇌H2( g)+I2( g) if the degree of...

For the reaction $2 \mathrm{HI}(\mathrm{g}) \rightleftharpoons \mathrm{H}_2(\mathrm{~g})+\mathrm{I}_2(\mathrm{~g})$ if the degree of dissociation is $\alpha$ and $K_p$ is the equilibrium constant, then (a) $\alpha=\frac{\sqrt{2 \mathrm{~K}_{\mathrm{p}}}}{1+\sqrt{2 \mathrm{k}_{\mathrm{p}}}}$ (b) $\alpha=\frac{2 \sqrt{K_p}}{1+2 \sqrt{K_p}}$ (c) $\sqrt{2 \mathrm{~K}_{\mathrm{p}}}=\left(\frac{\alpha}{1-\alpha}\right)$ (d) $2 \sqrt{\mathrm{~K}_{\mathrm{P}}}=\left(\frac{\alpha}{1-\alpha}\right)$

For the reaction $2 \mathrm{HI}(\mathrm{g}) \rightleftharpoons \mathrm{H}_2(\mathrm{~g})+\mathrm{I}_2(\mathrm{~g})$ if the degree of dissociation is $\alpha$ and $K_p$ is the equilibrium constant, then
(a) $\alpha=\frac{\sqrt{2 \mathrm{~K}_{\mathrm{p}}}}{1+\sqrt{2 \mathrm{k}_{\mathrm{p}}}}$
(b) $\alpha=\frac{2 \sqrt{K_p}}{1+2 \sqrt{K_p}}$
(c) $\sqrt{2 \mathrm{~K}_{\mathrm{p}}}=\left(\frac{\alpha}{1-\alpha}\right)$
(d) $2 \sqrt{\mathrm{~K}_{\mathrm{P}}}=\left(\frac{\alpha}{1-\alpha}\right)$

Key Concepts

Equilibrium Constant (Kp)

The equilibrium constant in gas-phase reactions, denoted as Kp, is defined using the partial pressures of the reactants and products at equilibrium. It reflects the ratio of the product of the pressures of the products, each raised to their stoichiometric coefficients, to that of the reactants similarly raised. This constant helps predict the position of equilibrium and how the system responds to changes in conditions (such as pressure or temperature).

Degree of Dissociation (?)

The degree of dissociation is a measure of the fraction of the initial amount of a reactant that dissociates into products at equilibrium. It is a key parameter in quantifying the extent of a reaction and, when known, can be used to relate the concentrations or partial pressures of the components in the equilibrium system.

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationships between reactants and products as dictated by the balanced chemical equation. It is crucial for determining the changes in mole numbers from the initial state to equilibrium, which in turn is necessary for expressing the equilibrium constant in terms of the degree of dissociation.

Relating Partial Pressures and the Degree of Dissociation

In gaseous equilibria, the calculation of partial pressures is directly linked to mole fractions and the total pressure of the system. By applying stoichiometric relationships and the degree of dissociation, one can derive expressions that relate Kp to ?. These expressions are instrumental in solving problems where the extent of dissociation and the equilibrium constant are interdependent.

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