Chemical Energetics 2 - Notes

Direction of Chemical Change

• Chemists are interested in the direction of change to predict conditions for reactions.

Spontaneous Change

• A spontaneous process continues without external assistance once started.

• A non-spontaneous process requires continuous external assistance.

• Examples of spontaneous processes:

  • $H<em>2O(s) \longrightarrow H</em>2O(l)$ at 298 K and 1 atm

  • $NaOH(aq) + HCl(aq) \longrightarrow NaCl(aq) + H_2O(l)$

  • $CH<em>4(g) + 2O</em>2(g) \longrightarrow CO<em>2(g) + 2H</em>2O(l)$

• If a process is spontaneous, the reverse is non-spontaneous.

• "Spontaneous" does not indicate the rate of the process.

Criteria for Spontaneity

• Early thought: systems minimize energy (exothermic reactions are spontaneous).

• However, endothermic processes can also be spontaneous.

• Examples of spontaneous endothermic reactions:

  • $NH<em>4NO</em>3(s) + aq. \longrightarrow NH<em>4NO</em>3(aq) \qquad ΔH^\ominus = +26 kJ mol^{-1}$

  • $H<em>2O(s) \longrightarrow H</em>2O(l) \qquad ΔH^\ominus = +6.01 kJ mol^{-1}$

• Enthalpy alone cannot account for spontaneous change; entropy is also involved.

• Two tendencies:

  • Lower energy state

  • Greater entropy

Entropy and Entropy Change

What is Entropy?

• Entropy (S) measures disorder of matter and energy in a system.

• More ways matter and energy can be arranged/dispersed = higher entropy.

• Entropy increases as substance changes from solid to liquid to gas.

Some Entropy Values

• Absolute entropy values can be determined experimentally.

• Gases > Liquids > Solids in entropy values.

• Entropy increases with increasing molecular complexity in related compounds.

Entropy Change

• Entropy change ($\Delta$S) measures the change in disorder in a system.

• $\Delta S = S<em>{final} – S</em>{initial}$

• $\Delta$S > 0: final state more disordered.

• $\Delta$S < 0: final state less disordered.

• Qualitative idea of entropy change can be obtained by inspecting the reaction equation.

Factors Affecting Entropy

Change in Temperature

• Entropy increases as temperature increases.

• Higher temperature means more kinetic energy, more rapid random motion (liquids and gases).

• Broadening of Boltzmann energy distribution increases entropy.

• More energy states available at higher temperatures for particles to occupy.

Change in Phase

• Entropy increases in the order: S{solid} < S{liquid} << S_{gas}

• Solid to liquid: order is destroyed, particles more randomly arranged.

• Liquid to gas/solid to gas: larger entropy increase due to greater disorder and volume increase.

Change in Number of Particles

• Entropy increases as the number of particles increases.

• More particles = more ways to arrange and distribute energy.

• Increase in moles of gaseous particles significantly increases entropy.

• Examples:

  • $CaCO<em>3(s) \longrightarrow CaO(s) + CO</em>2(g)$

  • $N<em>2O(g) \longrightarrow N</em>2(g) + \frac{1}{2}O_2(g)$

  • $C<em>3H</em>8(g) + 5O<em>2(g) \longrightarrow 3CO</em>2(g) + 4H_2O(g)$

Entropy Changes When An Ionic Solid Dissolves in Water

• Dissolution can lead to net increase or decrease in disorder.

• Example 1: $NaCl(s) + aq. \longrightarrow Na^+(aq) + Cl^-(aq)$, \Delta S > 0

  • Disruption of crystal increases disorder; hydration decreases disorder.

  • Overall, net increase in disorder.

• Example 2: $CaSO<em>4(s) + aq. \longrightarrow Ca^{2+}(aq) + SO</em>4^{2-}(aq)$, \Delta S < 0

  • For salts with highly charged ions, hydration decreases entropy more.

Gibbs Free Energy Change

Standard Gibbs Free Energy Change

• Two tendencies: lower energy, greater entropy.

• Neither $\Delta$H nor $\Delta$S alone predicts spontaneity.

• Gibbs free energy (G) combines $\Delta$H and $\Delta$S.

• $\Delta G^\ominus = \Delta H^\ominus – T\Delta S^\ominus$

• Standard conditions: 1 bar, specified temperature (commonly 298 K).

• Reactants and products in standard states.

• $\Delta$H and $\Delta$S assumed constant unless phase change occurs.

• Similarly, at constant temperature and pressure: $\Delta G = \Delta H – T\Delta S$

Relationship between $\Delta G^\ominus$ and Spontaneity

• Sign of $\Delta G^\ominus$ indicates spontaneity under standard conditions.

• \Delta G^\ominus < 0: spontaneous (exergonic).

• \Delta G^\ominus > 0: non-spontaneous (endergonic).

• Similarly, the sign of $\Delta$G indicates spontaneity under non-standard conditions.

• \Delta G < 0: spontaneous (exergonic).

• \Delta G > 0: non-spontaneous (endergonic).

• $\Delta G = 0$: system at equilibrium.

Limitations of $\Delta G^\ominus$

• Indicates thermodynamic feasibility but not kinetic feasibility.

• Reaction with \Delta G^\ominus < 0 may not occur due to high activation energy.

Effect of Temperature on Spontaneity

• $\Delta G = \Delta H – T\Delta S$

• $\Delta$G depends on temperature.

• $\Delta$H and $\Delta$S relatively constant without phase changes.

The 4 Scenarios

• (a) \Delta H < 0 and \Delta S > 0: \Delta G < 0 at all temperatures (spontaneous).

  • Examples: decomposition of ozone and dinitrogen monoxide, organic combustion, combustion of explosives.

• (b) \Delta H > 0 and \Delta S < 0: \Delta G > 0 at all temperatures (non-spontaneous).

  • Examples: photosynthesis, formation of ozone from oxygen.

• (c) \Delta H > 0 and \Delta S > 0: \Delta G > 0 at low temperatures, \Delta G < 0 at high temperatures.

  • Examples: melting/boiling, most decomposition reactions, electrolysis, dissolving.

• (d) \Delta H < 0 and \Delta S < 0: \Delta G < 0 at low temperatures, \Delta G > 0 at high temperatures.

  • Examples: condensation/freezing, addition/combination reactions, electrochemical cells, precipitation.