Explain why spontaneity depends on temperature?
1 Answer
Spontaneity is most easily defined by a thermodynamic equation you've probably seen before:
\mathbf(DeltaG = DeltaH - TDeltaS) where:
DeltaG is the Gibbs' free energy, which tells you when a reaction is spontaneous, non-spontaneous, or at equilibrium.DeltaH is the enthalpy, which is the heat flowq at a constant pressure.DeltaS is the entropy, which is directly proportional to the number of microstates that can pertain to a system, i.e. loosely speaking, a measure of "disorder".
Since
EXAMPLE: ENTROPY
For example, let's consider this reaction:
2"Al"(s) + 6"HCl"(aq) -> 2"AlCl"_3(aq) + 3"H"_2(g)
You can see that there are more
So significant that in many General Chemistry classes, a general rule of thumb is used where the sign of the entropy can often be found from the
EXAMPLE: ENTHALPY
The following bonds were broken:
6xx("H"-"Cl") ,DeltaH_"bond" ~~ "431 kJ/mol"
The following bonds were made:
2xx("Al"-"Cl" xx 3) ,DeltaH_"bond" ~~ "502 kJ/mol" 3xx("H"-"H") DeltaH_"bond" ~~ "436 kJ/mol"
Therefore, the total enthalpy of the reaction is approximately:
color(green)(DeltaH_"rxn") = sum_i DeltaH_("broken",i) - sum_j DeltaH_("made",j)
= ("431 kJ/mol") - ("436 kJ/mol" + "502 kJ/mol")
= color(green)(-"507 kJ/mol")
EXAMPLE: GIBBS' FREE ENERGY
Interestingly enough, since
Remember that
color(blue)(DeltaG = -|DeltaH| - |T|*|DeltaS| < 0)
Therefore, this reaction is spontaneous for all temperatures.
However, had
- If
T is high enough, the reaction is spontaneous because|DeltaH| < |T|*|DeltaS| and thusDeltaG < 0 . - If
T is low enough, then the reaction is nonspontaneous because|DeltaH| > |T|*|DeltaS| and thusDeltaG > 0 . - If
DeltaH = TDeltaS , the reaction is at equilibrium becauseDeltaG = 0 .