Given the values of ΔH and ΔS, which of the following changes will be spontaneous at constant T

step 1 The question here gives us values of Delta, H, Delta S and, um, a temperature, and it wants its

Given the values of ΔH and ΔS, which of the following...

Given the values of $\Delta H$ and $\Delta S$, which of the following changes will be spontaneous at constant $T$ and $P ?$ a. $\Delta H=+25 \mathrm{~kJ}, \Delta S=+5.0 \mathrm{~J} / \mathrm{K}, T=300 . \mathrm{K}$ b. $\Delta H=+25 \mathrm{~kJ}, \Delta S=+100 . \mathrm{J} / \mathrm{K}, T=300 . \mathrm{K}$ c. $\Delta H=-10 . \mathrm{kJ}, \Delta S=+5.0 \mathrm{~J} / \mathrm{K}, T=298 \mathrm{~K}$ d. $\Delta H=-10 . \mathrm{kJ}, \Delta S=-40 . \mathrm{J} / \mathrm{K}, T=200 . \mathrm{K}$

Given the values of $\Delta H$ and $\Delta S$, which of the following changes will be spontaneous at constant $T$ and $P ?$
a. $\Delta H=+25 \mathrm{~kJ}, \Delta S=+5.0 \mathrm{~J} / \mathrm{K}, T=300 . \mathrm{K}$
b. $\Delta H=+25 \mathrm{~kJ}, \Delta S=+100 . \mathrm{J} / \mathrm{K}, T=300 . \mathrm{K}$
c. $\Delta H=-10 . \mathrm{kJ}, \Delta S=+5.0 \mathrm{~J} / \mathrm{K}, T=298 \mathrm{~K}$
d. $\Delta H=-10 . \mathrm{kJ}, \Delta S=-40 . \mathrm{J} / \mathrm{K}, T=200 . \mathrm{K}$

Key Concepts

Gibbs Free Energy

Gibbs free energy (?G) is the thermodynamic potential that measures the maximum amount of reversible work obtainable from a system at constant temperature and pressure. It is defined by the equation ?G = ?H - T?S. A negative value of ?G indicates a spontaneous process, while a positive value indicates a non-spontaneous process under the given conditions.

Enthalpy

Enthalpy (?H) represents the total heat content of a system. It measures the energy change during a reaction or process at constant pressure. A negative ?H implies that the process is exothermic (releases heat), which can favor spontaneity, while a positive ?H indicates an endothermic process (absorbs heat), which may not be spontaneous unless compensated by a sufficiently positive entropy change.

Entropy

Entropy (?S) quantifies the degree of disorder or randomness in a system. An increase in entropy (positive ?S) is generally favorable for spontaneity as it suggests a more probable arrangement of energy at the molecular level. However, the impact of entropy on spontaneity must be considered in relation to the enthalpy change and temperature.

Temperature Dependence

The temperature (T) plays a critical role in the Gibbs free energy equation by modulating the contribution of the entropy term (T?S). Even if a process has a positive ?H (endothermic), a sufficiently large positive ?S at a high temperature can result in a negative ?G, making the process spontaneous. Thus, both temperature and the balance between enthalpy and entropy changes determine the spontaneity of a process.

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