Calculate ΔG^∘ for the following reactions and state whether...

Calculate $\Delta G^{\circ}$ for the following reactions and state whether each reaction is spontaneous under standard conditions at $298 \mathrm{~K}$. (a) $2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{NO}_{2}(\mathrm{~g})$ (b) $\mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow \mathrm{COCl}_{2}(\mathrm{~g})$

Calculate $\Delta G^{\circ}$ for the following reactions and state whether each reaction is spontaneous under standard conditions at $298 \mathrm{~K}$.
(a) $2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{NO}_{2}(\mathrm{~g})$
(b) $\mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow \mathrm{COCl}_{2}(\mathrm{~g})$

Key Concepts

Reaction Spontaneity

The spontaneity of a reaction under standard conditions is determined by the sign of the Gibbs free energy change (?G°). If ?G° is negative, the reaction is exergonic and can occur spontaneously; conversely, if ?G° is positive, the reaction is endergonic and non-spontaneous under those conditions.

Gibbs Free Energy

Gibbs free energy is a thermodynamic potential that measures the maximum reversible work obtainable from a reaction at constant temperature and pressure. It is defined by the equation ?G = ?H - T?S, where ?H is the change in enthalpy, T is the temperature in Kelvin, and ?S is the change in entropy. This concept allows chemists to predict the direction of chemical reactions and determine equilibrium positions.

Standard Gibbs Free Energy of Formation

The standard Gibbs free energy of formation (?G°f) is the change in free energy when one mole of a compound is formed from its elements in their most stable form under standard conditions (1 atm pressure and 298 K). It provides the basis for calculating the overall free energy change of a reaction by summing the formation energies of products and subtracting those of the reactants.

Standard State Conditions

Standard state conditions refer to a set of agreed-upon criteria, typically 1 bar or 1 atm pressure and 298 K temperature, under which thermodynamic properties like Gibbs free energy are reported. These conditions facilitate the comparison and calculation of thermodynamic data for different substances and reactions.

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