g^'PCl5 ⇄ gPCl3+gCl2 For the dissociation of PCl5- Kc is 2 ×10^-7 at 27^∘ C. Find ΔS^∘ If ΔH^∘=2

step 1 In this problem we have given that PCL5 dissociates to give PCL3 and CL2. And the equilibrium co

G^'PCl5 ⇄ gPCl3+gCl2 For the dissociation of PCl5- Kc is 2...

$\underset{\mathrm{g}^{\prime}}{\mathrm{PCl}_5} \rightleftarrows \underset{\mathrm{~g}}{\mathrm{PCl}_3}+\underset{\mathrm{g}}{\mathrm{Cl}_2}$ For the dissociation of $\mathrm{PCl}_{5-} \mathrm{K}_{\mathrm{c}}$ is $2 \times 10^{-7}$ at $27^{\circ} \mathrm{C}$. Find $\Delta \mathrm{S}^{\circ}$ If $\Delta \mathrm{H}^{\circ}=28.4 \mathrm{KJ} / \mathrm{m}$ (a) $-0.0336 \mathrm{KJ} / \mathrm{K}$ (b) $0.0336 \mathrm{KJ} / \mathrm{K}$ (c) $-0.0818 \mathrm{KJ} / \mathrm{K}$ (d) $0.338 \mathrm{KJ} / \mathrm{K}$

$\underset{\mathrm{g}^{\prime}}{\mathrm{PCl}_5} \rightleftarrows \underset{\mathrm{~g}}{\mathrm{PCl}_3}+\underset{\mathrm{g}}{\mathrm{Cl}_2}$

For the dissociation of $\mathrm{PCl}_{5-} \mathrm{K}_{\mathrm{c}}$ is $2 \times 10^{-7}$ at $27^{\circ} \mathrm{C}$. Find $\Delta \mathrm{S}^{\circ}$ If $\Delta \mathrm{H}^{\circ}=28.4 \mathrm{KJ} / \mathrm{m}$
(a) $-0.0336 \mathrm{KJ} / \mathrm{K}$
(b) $0.0336 \mathrm{KJ} / \mathrm{K}$
(c) $-0.0818 \mathrm{KJ} / \mathrm{K}$
(d) $0.338 \mathrm{KJ} / \mathrm{K}$

Key Concepts

Chemical Equilibrium Constant

This concept refers to the ratio of the concentrations (or pressures) of products to reactants at equilibrium. In thermodynamics, the equilibrium constant (Kc for concentrations) is a measure of the extent to which a chemical reaction proceeds, and its value is related to the standard Gibbs free energy change of the reaction.

Standard Gibbs Free Energy Change

The standard Gibbs free energy change (?G°) of a reaction determines its spontaneity under standard conditions. It is linked to the equilibrium constant by the relationship ?G° = -RT ln K, where R is the gas constant and T is the absolute temperature. This relation allows one to connect thermodynamic properties with observed equilibrium compositions.

Thermodynamic Relationship between ?H°, ?S°, and ?G°

This key relationship is given by the equation ?G° = ?H° - T?S°. It connects the enthalpy change (?H°), the entropy change (?S°), and the temperature (T) to predict whether a reaction will be spontaneous. With known values of ?G° and ?H°, one can solve for the reaction entropy (?S°), providing insight into the disorder change associated with the reaction.

Role of Temperature in Chemical Equilibria

Temperature has a significant influence on chemical equilibria. It not only appears in the Gibbs free energy equation but also affects the value of the equilibrium constant through the van’t Hoff equation. Understanding this temperature dependence is crucial for predicting how changes in temperature can shift the position of equilibrium and affect reaction spontaneity.

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