Spontaneity Conditions

When enthalpy and entropy fight, temperature decides the winner.

The Four Scenarios

Based on $\Delta G = \Delta H - T\Delta S$

$\Delta H$	$\Delta S$	$-T\Delta S$	Result ( $\Delta G$ )	Spontaneity
Exo (-)	Positive (+)	Calculates (-)	ALWAYS Negative	Always Spontaneous
Endo (+)	Negative (-)	Calculates (+)	ALWAYS Positive	Never Spontaneous
Exo (-)	Negative (-)	Calculates (+)	Depends on T	Spontaneous at LOW T
Endo (+)	Positive (+)	Calculates (-)	Depends on T	Spontaneous at HIGH T

Calculating the Switch-Over Temperature

When does a reaction become spontaneous? It happens when $\Delta G$ switches from positive to negative.
This "tipping point" is when $\Delta G = 0$ .

0 = \Delta H - T\Delta S

\therefore T = \frac{\Delta H}{\Delta S}

(Remember to convert units so both are in J or both in kJ!)

Putting it into Practice

Calculating the Tipping Point

Paper 2 Style

Estimate the temperature (in Kelvin) above which the decomposition of limestone becomes spontaneous.

$\Delta H = +178 \: kJ \: mol^{-1}$
$\Delta S = +160 \: J \: K^{-1} \: mol^{-1}$

Practice: Impossible Reactions

[2 Marks]

Explain why a reaction with $\Delta H > 0$ and $\Delta S < 0$ can never be spontaneous, regardless of temperature.

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