The keyword “are exothermic reactions increasing entropy” is answered by separating two different entropy changes: the entropy change of the reacting system and the entropy change of the surroundings. Exothermicity (\(\Delta H < 0\)) concerns heat flow and does not, by itself, force the system’s entropy to increase.
1) Define the entropy bookkeeping clearly
For a reaction occurring at approximately constant temperature \(T\) and pressure \(P\), the Second Law is applied to the universe: \[ \Delta S_{\text{total}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}} \] where \(\Delta S_{\text{sys}}\) is the entropy change of the reacting mixture and \(\Delta S_{\text{surr}}\) is the entropy change of everything outside it (the environment that absorbs or provides heat).
2) What exothermicity guarantees (and what it does not)
Under constant \(T\), the surroundings entropy change is related to the heat released/absorbed by the system: \[ \Delta S_{\text{surr}} = -\frac{\Delta H_{\text{sys}}}{T} \]
- If a reaction is exothermic, then \(\Delta H_{\text{sys}} < 0\), so \(\Delta S_{\text{surr}} > 0\).
- \(\Delta S_{\text{sys}}\) can be positive, negative, or near zero, depending on how the molecular disorder and number of accessible microstates change (phase changes, gas moles, mixing, etc.).
Exothermic reactions increase the entropy of the surroundings, but they do not necessarily increase the entropy of the system. The sign of \(\Delta S_{\text{sys}}\) must be evaluated from the reaction’s physical/chemical changes.
3) Connect the entropy statement to Gibbs free energy
At constant \(T\) and \(P\), spontaneity is equivalently tested with Gibbs free energy: \[ \Delta G = \Delta H - T\Delta S_{\text{sys}} \] The criteria match: \[ \Delta G < 0 \quad \Longleftrightarrow \quad \Delta S_{\text{total}} > 0 \]
Exothermicity (\(\Delta H < 0\)) pushes \(\Delta G\) downward, favoring spontaneity, but the \( -T\Delta S_{\text{sys}}\) term can either help or oppose it depending on the sign of \(\Delta S_{\text{sys}}\).
4) Temperature dependence summarized
| Case | \(\Delta H\) | \(\Delta S_{\text{sys}}\) | Implication for \(\Delta G = \Delta H - T\Delta S_{\text{sys}}\) | Spontaneous when |
|---|---|---|---|---|
| Exothermic, entropy increases | \(< 0\) | \(> 0\) | Both terms favor \(\Delta G < 0\) | All \(T\) (typical) |
| Exothermic, entropy decreases | \(< 0\) | \(< 0\) | Competition between \(\Delta H\) and \(+T|\Delta S_{\text{sys}}|\) | Low \(T\) |
| Endothermic, entropy increases | \(> 0\) | \(> 0\) | Competition between \(+\Delta H\) and \(-T\Delta S_{\text{sys}}\) | High \(T\) |
| Endothermic, entropy decreases | \(> 0\) | \(< 0\) | Both terms oppose \(\Delta G < 0\) | Never (at constant \(T,P\)) |
5) A visual check: exothermic does not imply the same entropy behavior
6) Final conclusion
Exothermic reactions do not automatically mean “entropy increases.” The system entropy \(\Delta S_{\text{sys}}\) may increase or decrease, while exothermicity guarantees \(\Delta S_{\text{surr}} > 0\) under constant \(T\). Spontaneity is determined by the total entropy change \(\Delta S_{\text{total}}\) or, equivalently at constant \(T,P\), by whether \(\Delta G = \Delta H - T\Delta S_{\text{sys}}\) is negative.