An important step in the commercial production of sulphuric...

An important step in the commercial production of sulphuric acid involves synthesis of sulphur trioxide, in the reaction $$ 2 \mathrm{SO}_2+\mathrm{O}_2 \leftrightharpoons 2 \mathrm{SO}_3 $$ At $298 \mathrm{kelvin}$, one finds $\Delta H=-1.9824 \times 10^5 \mathrm{~J}$ and $\Delta S=-189.79 \mathrm{~J} / \mathrm{K}$ per mole of oxygen molecules in this reaction. Assuming these values are independent of temperature, find the reaction quotient at $T=300 \mathrm{~K}$ and at $T=1200 \mathrm{~K}$. Hence establish whether the reaction favours production or dissociation of $\mathrm{SO}_3$ at these two temperatures.

An important step in the commercial production of sulphuric acid involves synthesis of sulphur trioxide, in the reaction
$$
2 \mathrm{SO}_2+\mathrm{O}_2 \leftrightharpoons 2 \mathrm{SO}_3
$$
At $298 \mathrm{kelvin}$, one finds $\Delta H=-1.9824 \times 10^5 \mathrm{~J}$ and $\Delta S=-189.79 \mathrm{~J} / \mathrm{K}$ per mole of oxygen molecules in this reaction. Assuming these values are independent of temperature, find the reaction quotient at $T=300 \mathrm{~K}$ and at $T=1200 \mathrm{~K}$. Hence establish whether the reaction favours production or dissociation of $\mathrm{SO}_3$ at these two temperatures.

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Key Concepts

Gibbs Free Energy

Gibbs free energy (?G) is a thermodynamic potential that combines enthalpic and entropic contributions to determine the spontaneity of a reaction at constant temperature and pressure. It is given by the equation ?G = ?H - T?S, where ?H is the change in enthalpy, T is the absolute temperature, and ?S is the change in entropy. A negative ?G indicates a spontaneous process, whereas a positive value suggests non-spontaneity.

Reaction Quotient

The reaction quotient (Q) measures the relative amounts of products and reactants present during a reaction at any point in time. It is defined using the same expression as the equilibrium constant but applies to non-equilibrium states. The relationship ?G = ?G° + RT ln Q connects the reaction quotient to the Gibbs free energy, allowing one to assess how far a reaction is from equilibrium.

Temperature Effects on Equilibrium

Temperature has a crucial impact on chemical equilibrium by affecting the balance between enthalpy and entropy contributions to the Gibbs free energy. As temperature increases, the T?S term becomes more significant, potentially reversing the sign of ?G. This temperature dependence determines whether a reaction will be favored in the forward or reverse direction, influencing the position of equilibrium and the production or dissociation of products.

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