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# Free Energy

## Defines free energy and how entropy and enthalpy affect its value.

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Free Energy

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#### Free Energy

Free energy (G) is energy that is available, or free, to do work! Spontaneous reactions release free energy as they proceed. The formula to find the free energy change of a reaction involves the change in enthalpy (∆H) and entropy (∆S):

ΔG=ΔHTΔS\begin{align*}\Delta G^\circ=\Delta H^\circ - T \Delta S^\circ\end{align*}

Note: the T in this equation is the temperature in Kelvin, which is always positive.

What are the units for the calculation of ∆G?

Keeping in mind that a spontaneous reaction is one that releases free energy, making the sign of ∆G negative, fill out the following chart to help you remember the different outcomes of ∆G:

 ΔH\begin{align*}\Delta H\end{align*} ΔS\begin{align*}\Delta S\end{align*} ΔG\begin{align*}\Delta G\end{align*} − value (exothermic) + value (disordering) always negative - never positive + value (endothermic) + value (disordering) negative at higher temperatures − value (exothermic) − value (ordering) negative at lower temperatures + value (endothermic) − value (ordering) never negative - always positive

Why does the temperature matter for the second and third combinations above?

#### Free Energy Change

Based on the following equation:

CH4(g)+H2O(g)CO(g)+3H2(g)\begin{align*}\text{CH}_4(g)+\text{H}_2\text{O}(g) \rightarrow \text{CO}(g)+3\text{H}_2(g)\end{align*}

If the ∆H˚ is +206.1 kJ/mol and the ∆S˚ is +215 J/K • mol, calculate the ∆G˚ at 25˚C. Is the reaction spontaneous?

Remember: the ˚ refers to the use of standard conditions when calculating the free energy.