The reaction 2 C4 H10(g)+13 O2(g) ⟶8 CO2(g)+10 H2 O(g) has ΔG^∘=-5407 kJ . Determine the value

step 1 Knowing the delta G standard for this reaction, then we can look up the delta Gs of formation of

The reaction 2 C4 H10(g)+13 O2(g) ⟶8 CO2(g)+10 H2 O(g) has...

The reaction $$ 2 \mathrm{C}_{4} \mathrm{H}_{10}(g)+13 \mathrm{O}_{2}(g) \longrightarrow 8 \mathrm{CO}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g) $$ has $\Delta G^{\circ}=-5407 \mathrm{~kJ} .$ Determine the value of $\Delta G_{\mathrm{f}}^{\circ}$ for $\mathrm{C}_{4} \mathrm{H}_{10}(g) .$ Calculate the value of $K_{\mathrm{c}}$ for the reaction at $25^{\circ} \mathrm{C}$

The reaction
$$
2 \mathrm{C}_{4} \mathrm{H}_{10}(g)+13 \mathrm{O}_{2}(g) \longrightarrow 8 \mathrm{CO}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)
$$
has $\Delta G^{\circ}=-5407 \mathrm{~kJ} .$ Determine the value of $\Delta G_{\mathrm{f}}^{\circ}$ for $\mathrm{C}_{4} \mathrm{H}_{10}(g) .$ Calculate the value of $K_{\mathrm{c}}$ for the reaction at $25^{\circ} \mathrm{C}$

Key Concepts

Standard Gibbs Free Energy of Formation

This concept refers to the change in Gibbs free energy when one mole of a compound is formed from its elements in their standard states. In thermodynamic calculations, these values are used as building blocks to determine the reaction’s overall free energy change. It is a crucial parameter in assessing the stability of compounds and predicting the spontaneity of formation reactions.

Gibbs Free Energy Change for a Reaction (?G° Reaction)

The standard Gibbs free energy change of a reaction is calculated by taking the sum of the Gibbs free energies of formation of the products (multiplied by their stoichiometric coefficients) minus the sum for the reactants. This value predicts whether a reaction will proceed spontaneously under standard conditions and provides a direct link to the reaction’s equilibrium constant.

Relationship Between ?G° and the Equilibrium Constant

A fundamental thermodynamic relation is given by the equation ?G° = –RT ln K, which connects the standard Gibbs free energy change with the equilibrium constant (K) of the reaction at a given temperature. This relation allows one to compute K, providing insights into the position of equilibrium, thus linking thermodynamics with chemical kinetics and equilibrium concepts.

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. It is essential for correctly summing the contributions of each reactant and product when applying thermodynamic formulas, such as when computing the overall ?G° from individual Gibbs free energies of formation.

Standard State Conditions

Standard state conditions, typically 1 bar pressure for gases and 1 M concentration for solutions, define the reference state for all thermodynamic quantities. These conditions ensure consistency and comparability of thermodynamic data such as ?G° and ?Gf°, and they are necessary when using formulas like ?G° = –RT ln K to relate thermodynamic quantities to equilibrium constants.

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