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The combustion of a fuel will be spontaneous at T=0 because it is an exothermic reaction, but will it stay that way when the temperature increases? Choose a hypothesis: a) Delta G will stay negative b) Delta G will change sign when T gets high enough

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The combustion of a fuel will be spontaneous at T=0 because it is an exothermic reaction, but will it stay that way when the temperature increases? Choose a hypothesis: a) Delta G will stay negative b) Delta G will change sign when T gets high enough

The combustion of a fuel will be spontaneous at T=0 because it is an exothermic reaction, but will it stay that way when the temperature increases? Choose a hypothesis: a) Delta G will stay negative b) Delta G will change sign when T gets high enough

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### b) \( \Delta G \) will change sign when \( T \) gets high enough

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## Step 1: Understand Gibbs Free Energy (\(\Delta G\)) Relation<br />### Gibbs Free Energy (\(\Delta G\)) is given by the equation \(\Delta G = \Delta H - T\Delta S\), where \(\Delta H\) is the enthalpy change, \(T\) is the temperature, and \(\Delta S\) is the entropy change. For an exothermic reaction, \(\Delta H\) is negative.<br />## Step 2: Conditions for Spontaneity<br />### A reaction is spontaneous if \(\Delta G\) is negative. Initially, at \(T=0\), \(\Delta G\) depends primarily on \(\Delta H\), which is negative. As temperature increases, \(T\Delta S\) becomes more significant. Depending on the sign of \(\Delta S\), this can alter \(\Delta G\).<br />## Step 3: High Temperature Effect<br />### If \(\Delta S\) is positive, increasing \(T\) will make \(T\Delta S\) larger, potentially making \(\Delta G\) less negative or even positive. If \(\Delta S\) is negative, increasing \(T\) will make \(\Delta G\) more negative.
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