For each reaction, calculate ΔH°_rxn, ΔS°_rxn, and ΔG°_rxnat 25 °C and state whether or not the reaction is spontaneous. If the reaction is not spontaneous, would a change in temperature make it spontaneous? If so, should the temperature be raised or lowered from 25 °C? a. 2 CH₄(g) → C₂H₆(g) + H₂(g)

검증된 단계별 안내

Identify the standard enthalpy change (ΔH°) for the reaction by using standard enthalpies of formation (ΔH°f) for each compound involved. Use the formula: ΔH°rxn = ΣΔH°f(products) - ΣΔH°f(reactants).

Determine the standard entropy change (ΔS°) for the reaction using standard molar entropies (S°) for each compound. Use the formula: ΔS°rxn = ΣS°(products) - ΣS°(reactants).

Calculate the standard Gibbs free energy change (ΔG°) for the reaction at 25 °C using the equation: ΔG°rxn = ΔH°rxn - TΔS°rxn, where T is the temperature in Kelvin (298 K).

Assess the spontaneity of the reaction by evaluating the sign of ΔG°rxn. If ΔG°rxn is negative, the reaction is spontaneous at 25 °C. If positive, it is non-spontaneous.

If the reaction is non-spontaneous, consider the signs of ΔH°rxn and ΔS°rxn to determine if a change in temperature could make it spontaneous. If ΔH°rxn is positive and ΔS°rxn is positive, increasing the temperature may make the reaction spontaneous. If ΔH°rxn is negative and ΔS°rxn is negative, decreasing the temperature may help.

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주요 개념

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Thermodynamic Functions (ΔH, ΔS, ΔG)

ΔH°rxn represents the change in enthalpy, indicating the heat absorbed or released during a reaction. ΔS°rxn denotes the change in entropy, reflecting the disorder or randomness of the system. ΔG°rxn, the Gibbs free energy change, determines the spontaneity of a reaction; a negative ΔG indicates spontaneity at constant temperature and pressure.

Spontaneity of Reactions

A reaction is spontaneous if it occurs without external intervention, which is determined by the sign of ΔG. If ΔG is negative, the reaction is spontaneous; if positive, it is non-spontaneous. The relationship between ΔH, ΔS, and temperature (T) is given by the equation ΔG = ΔH - TΔS, which helps predict spontaneity under varying conditions.

Temperature's Effect on Spontaneity

The temperature can influence the spontaneity of a reaction, particularly when ΔH and ΔS have opposite signs. If ΔH is positive and ΔS is positive, increasing temperature may make ΔG negative, thus making the reaction spontaneous. Conversely, if ΔH is negative and ΔS is negative, lowering the temperature may be necessary for spontaneity.