Chemical Principles: Thermo, Kinetics, Eq

Posted on May 3, 2025 in Chemistry

Work

  • Isobaric Process: At constant pressure (P = cte)
    W1→2 = -PΔV
  • Isothermal Process: At constant temperature (T = constant)
    W1→2 = -nRT ln(P1/P2)
  • Isochoric Process: At constant volume (V = constant)
    W1→2 = 0

Heat

  • Specific Heat: c = dQ / (mΔT)
    Q = c · m · ΔT
    If ΔT > 0, heat is absorbed.
    If ΔT < 0, heat is ceded (released).
  • Latent Heat of Change of State (L): At constant temperature
    From solid to liquid: Qf = m · Lf
    From liquid to gas: Qv = m · Lv

First Law of Thermodynamics

ΔU = Q + W

Calculating Qv

At constant volume (ΔV = 0), W = 0, so ΔU = Qv.
ΔU = Uproducts – Ureactants
If Uproducts > Ureactants, Qv > 0 (endothermic).
If Uproducts < Ureactants, Qv < 0 (exothermic).

Enthalpy Calculations (ΔHr)

ΔH = Qp (at constant pressure)
ΔH = Hproducts – Hreactants
If Hproducts > Hreactants, ΔH > 0 (endothermic).
If Hproducts < Hreactants, ΔH < 0 (exothermic).

ΔHr = Σ(ΔHf, products) – Σ(ΔHf, reactants)

According to Hess’s Law, if a chemical equation can be obtained by summing other equations with known ΔH values, the ΔHr for the overall reaction will be the algebraic sum of those ΔH values.

ΔHr = Σ(Bond Enthalpiesbroken) – Σ(Bond Enthalpiesformed)

Spontaneous Chemical Reactions

  • In an isolated system: Spontaneity depends on entropy (ΔS).
    ΔS at constant pressure = m · Cp · ln(T2/T1)
    ΔS at constant temperature = m · L / T
    For a spontaneous process, ΔS > 0.
  • In a system that exchanges energy: Spontaneity depends on Gibbs Free Energy (ΔG).
    ΔG = ΔH – TΔS
    For a spontaneous process, ΔG < 0.

Average Reaction Rate

Rate = + Δ[C] / Δt or – Δ[A] / Δt

Instantaneous Reaction Rate

Rate = -d[A] / dt

Factors Affecting Reaction Rate

  • Nature of Reactants:
    • Covalent reactions are often very slow (difficult to break bonds).
    • Ionic reactions are often very fast (bonds are partly broken or ions are already formed).
    • For gases and solids, the rate depends on the number of bonds and the degree of division (e.g., powder reacts faster than solid blocks).
  • Concentration of Reactants:
    • Qualitatively: Increasing concentration (Moles/volume) increases the frequency of collisions, increasing the probability of effective collisions, thus increasing the speed.
    • Quantitatively: Rate = k[A]x[B]y (for A + B → Products)
      x + y = total order of the reaction.
  • Temperature:
    • Qualitatively: Increasing temperature increases the average kinetic energy of molecules, increasing the frequency of collisions and the probability of effective collisions, thus increasing the speed.
    • Quantitatively: k = A · exp(-Ea/RT) (Arrhenius equation).
      When Ea is constant, increasing T increases k and thus the rate.
      When T is constant, increasing Ea decreases k and thus the rate.
  • Catalyst: Reduces the activation energy (Ea) and does NOT change ΔH, ΔG, or ΔS.

Le Chatelier’s Principle

If a change of condition (like temperature, pressure, or concentration) is applied to a system in equilibrium, the system will shift in a direction that relieves the stress.

  • Pressure/Volume (for gas phase reactions):
    • If total pressure increases (or volume decreases), the system shifts towards the side with fewer moles of gas.
    • If total pressure decreases (or volume increases), the system shifts towards the side with more moles of gas.
  • Concentration:
    • Increasing the concentration of reactants or decreasing the concentration of products shifts the equilibrium to the right (towards products).
    • Decreasing the concentration of reactants or increasing the concentration of products shifts the equilibrium to the left (towards reactants).
  • Temperature:
    • Increasing temperature favors the endothermic reaction.
    • Decreasing temperature favors the exothermic reaction.

Homogeneous Equilibria & Mass Action

For the reaction aA + bB ⇌ cC + dD

Law of Mass Action

Equilibrium Constant: Kc = ([C]c[D]d) / ([A]a[B]b)

Reaction Quotient

Qc = ([C]0c[D]0d) / ([A]0a[B]0b)
(where [ ]0 represents initial concentrations)

  • If Qc > Kc: The system is not at equilibrium. The ratio of products to reactants is too high. To reach equilibrium, the system shifts to the left (towards reactants), consuming products and forming reactants.
  • If Qc = Kc: The system is at equilibrium.
  • If Qc < Kc: The system is not at equilibrium. The ratio of products to reactants is too low. To reach equilibrium, the system shifts to the right (towards products), consuming reactants and forming products.

Equilibrium Constant Kp

For gas phase reactions, Kp is based on partial pressures.
Kp = (PCc · PDd) / (PAa · PBb)
Partial Pressure PA = xA · PTotal (where xA is the mole fraction of A)

Relationship between Kc and Kp:
Kp = Kc (RT)Δn
Kc = Kp (RT)-Δn
where Δn = (moles of gaseous products) – (moles of gaseous reactants) = (c + d) – (a + b).