Thermochemistry and Chemical Equilibrium

Posted on Feb 25, 2025 in Chemistry

Work and Heat

Reversible processes are those in which the system and surroundings are in constant equilibrium; involves infinitesimal changes to some property:

  • Slow heating
  • Slow expansion

Irreversible processes are those in which the system and surroundings are not in equilibrium:

  • Expansion against constant pressure
  • Phase change at non-standard transition temperature

Internal Energy

For isothermal processes where ΔT = 0, ΔU = 0 and therefore q = -w.

At constant volume, ΔU = q.

Enthalpy

At constant pressure, ΔH = q.

The enthalpy of vaporization should always be positive.

The enthalpy of fusion is the enthalpy of melting.

-ΔHfus = -ΔHfreezing

Temperature remains constant through phase transitions on heating curves.

-The slope of the heating curve is the increase of heat capacity.

Entropy

Spontaneous processes always increase the entropy of an isolated system (even if the system is the entire universe).

-Energy transfer creates larger entropy changes at lower temperatures.

A higher heat capacity means a greater entropy change.

For reversible phase changes at constant transition temperature, the entropy can be calculated by dividing the ΔHtransition by T.

Thermochemistry

Because enthalpy is a state function, ΔHforward = -ΔHreverse.

When determining reaction enthalpy at different temperatures, it is important to construct a path:

  1. Heat/cool the system from the desired temperature to reference temperature.
  2. (a) ΔH = CΔT or ΔS varies with temp eqn.
  3. Use tabulated values at reference temperatures (normally a phase transition).
  4. (a) ΔH = ΔHgiven or ΔS = ΔH/T
  5. Heat/cool system back to desired temperature.
  6. (a) ΔH = CΔT or ΔS varies with temp.

Molecular Interpretation of Entropy

A microstate is a particular arrangement of particles in a system.

-If different microstates have the same energy, then they have the same probability of occurring.

When a system has more thermal energy, more microstates become available to it, increasing the entropy.

Absolute Entropies

Can interpret higher levels of entropy for substances as being related to the increased degrees of freedom they possess.

Absolute entropies of substances are calculated experimentally and can be summed to get entropy of reaction.

Global Changes in Entropy

Must consider the system and the surroundings to create a composite isolated environment (the universe).

As long as the sum ΔSsys + ΔSsurr > 0, then the process is spontaneous.

Exothermic reactions will have ΔSsurr > 0 because heat is released to surroundings.

Assuming reversible process, ΔSsurr = qsurr/T or -ΔHsys/T.

Systems at equilibrium experience ΔStot = 0.

Gibbs Free Energy

Gibbs free energy equals the enthalpy minus the product of the temperature and the entropy.

Another way to define GFE is ΔStot= -ΔG/T.

ΔG is always zero at equilibrium.

ΔG represents non-expansion work.

GFE varies with temperature:

  • Exothermic and entropy-increasing processes will always be spontaneous.
  • Endothermic and entropy-increasing processes will be spontaneous at high temperatures.
  • Exothermic and entropy-decreasing processes will be spontaneous at low temperatures.
  • Endothermic and entropy-decreasing processes will never be spontaneous.

Vapor Pressure

Liquids will exert a vapor pressure at a given temperature, which is the partial pressure of the equilibrium gaseous phase produced by the liquid.

Volatile (low boiling) liquids exert high vapor pressure.

Intermolecular forces make liquids less volatile.

At higher temperatures, the equilibrium position between liquid and gas shifts right, and vapor pressure increases.

The boiling point is defined to be where the vapor pressure is equal to atmospheric pressure.

-Normal boiling point is at 1 atm.

Can use the Clausius-Clapeyron equation to find nonstandard boiling points by determining the temperature at which the vapor pressure is equal to the external pressure.

Phase Equilibria

Phase diagrams plot the phase transition temperatures as pressure changes.

-Show the thermodynamically favored phase for a given temperature and pressure.

Along phase boundaries, both phases are observed in equilibrium.

For most substances, increased pressure increases the melting point.

At the triple point, the solid, liquid, and gaseous phases coexist in equilibrium (VPs equal each other).

Above the critical temperature, a gas cannot be condensed, and similarly, above the critical pressure, a liquid cannot be vaporized.

Phase Equilibria in Two-Component Systems

Raoult’s law states that the vapor pressure of a liquid in an ideal solution is equal to the mole fraction times the vapor pressure of the pure liquid.

The total vapor pressure of an ideal solution is the sum of partial pressures for each liquid.

-Is less than the vapor pressure of either pure liquid, so the boiling point is elevated.

The vapor phase of a solution will be enriched in the more volatile species.

-Reason for which fractional distillation can be used to purify a specific liquid.

Azeotropes are liquids that, at specific ratios, have identical vapor pressure; makes them hard to distill.

Chemical Equilibrium

All reactions occur reversibly in theory.

At equilibrium, the amount of products and reactants form a stable ratio.

ΔGm = ΔGo + RTlnQ

When Q = 1, ΔGm = ΔGom

When Q = K and ΔGm = 0, ΔGom = -RTlnK

Alternative Forms of the Equilibrium Constant

Reversing an equation requires you to reciprocate the equilibrium constant.

If a chemical equation is multiplied by a coefficient, one must raise K to the power equal to that coefficient.

If adding several equations together, multiply the equilibrium constants.

Any thermodynamic equations you want to apply to the equilibrium constant must be done on the form written in Bar.

One can convert between KC and KP using KP = (RT)ΔnKC.

Equilibrium Calculations

Large K values indicate the reaction goes to completion, whereas small K values indicate the reaction favors the reactants.

Can relate Q and K:

  • If Q = K, the reaction is at equilibrium.
  • If Q < K, the reaction will move to the products.
  • If Q > K, the reaction will move to the reactants.

When performing calculations, one should compute Q and compare it to K to determine whether to add variables (Q < K) or subtract variables (Q > K).

The Response of Equilibria to Changes in Conditions

Le Chatelier’s Principle has three main ramifications:

  • Adding or removing species will cause the reaction to shift in the direction to consume those species.
  • Increasing the temperature will shift the reaction to the reactants if it is exothermic or to the products if it is endothermic.
  • Increasing or decreasing the volume will change the total pressure; will shift to the side with more or fewer moles of gas to resist the change in pressure.

The Van’t Hoff equation relates the change in equilibrium constant with temperature.