Octane (C8 H18) is a liquid hydrocarbon at room temperature...

Octane $\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)$ is a liquid hydrocarbon at room temperature that is the primary constituent of gasoline. (a) Write a balanced equation for the combustion of $\mathrm{C}_{8} \mathrm{H}_{18}(l)$ to form $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(l) .$ (b) Without using thermochemical data, predict whether $\Delta G^{\circ}$ for this reaction is more negative or less negative than $\Delta H^{\circ}$.

Octane $\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)$ is a liquid hydrocarbon at room temperature that is the primary constituent of gasoline.
(a) Write a balanced equation for the combustion of $\mathrm{C}_{8} \mathrm{H}_{18}(l)$ to form $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(l) .$ (b) Without using thermochemical data, predict whether $\Delta G^{\circ}$ for this reaction is more negative or less negative than $\Delta H^{\circ}$.

Key Concepts

Relationship between Enthalpy and Gibbs Free Energy

Enthalpy (?H) represents the heat change during a reaction at constant pressure, while Gibbs free energy (?G) indicates the spontaneity of a reaction. They are related by the equation ?G = ?H - T?S. This relationship shows that even if a reaction is highly exothermic (negative ?H), the free energy (?G) also depends on the entropy change of the system, which may adjust the overall spontaneity depending on the temperature and disorder changes.

Entropy in Chemical Reactions

Entropy (?S) measures the degree of disorder or randomness in a system. In many combustion reactions, the phase of the products versus reactants can lead to changes in entropy. For instance, if a reaction involves a decrease in the number of gas molecules or changes phases from gas to liquid, the entropy may decrease. This decrease in entropy (negative ?S) contributes a positive term in the free energy equation, making ?G less negative compared to ?H.

Combustion Reaction

A combustion reaction involves a substance (usually a hydrocarbon) reacting with oxygen to produce products such as carbon dioxide and water. These reactions are typically exothermic, meaning they release energy in the form of heat, which is a key characteristic of fuels like gasoline and their use in energy conversion processes.

Stoichiometry and Balancing Chemical Equations

Balancing a chemical equation ensures that the law of conservation of mass is maintained, meaning the number of atoms for each element is equal on both sides of the reaction. This requires careful accounting of reactants and products, particularly in complex reactions like combustion where multiple species (gases, liquids) are involved.

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