Chemical Kinetics and Equilibrium Explained

Chemical Kinetics

Reaction Rate: The change in the concentration of reactants or products per unit time.

For a reaction aA + bB → cC + dD, the rate (v) can be expressed as:

v = -1/a * Δ[A]/Δt = -1/b * Δ[B]/Δt = 1/c * Δ[C]/Δt = 1/d * Δ[D]/Δt

Rate Law: The relationship between the reaction rate and the concentrations of reactants.

v = k [A]^m[B]ⁿ

Where k is the rate constant, and m and n are the reaction orders with respect to A and B, respectively.

Factors Influencing Reaction Rate

• Nature of Reactants: The physical state and chemical properties of reactants affect the rate. Homogeneous reactions (same phase) are often faster than heterogeneous reactions (different phases). In heterogeneous reactions, increasing the surface area increases the rate.
• Concentration of Reactants: Increasing the concentration of reactants generally increases the reaction rate due to more frequent collisions.
• Temperature: Increasing temperature increases the kinetic energy of molecules, leading to more frequent and energetic collisions, thus increasing the rate. The relationship is described by the Arrhenius equation: k = A * e^-Ea/RT, where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the absolute temperature.
• Catalysts: Substances that increase the reaction rate without being consumed. Positive catalysts speed up the reaction by lowering the activation energy (Ea). They do not affect the position of equilibrium.

Chemical Equilibrium

Chemical equilibrium is a state where the rates of the forward and reverse reactions are equal, resulting in no net change in the concentrations of reactants and products.

Equilibrium Constant (K_c)

For a reversible reaction aA + bB ⇌ cC + dD, the equilibrium constant K_c is defined as:

K_c = [C]^c[D]^d / [A]^a[B]^b

Where [A], [B], [C], and [D] are the equilibrium concentrations.

Reaction Quotient (Q)

The reaction quotient (Q) is calculated using current concentrations (not necessarily at equilibrium):

Q = [C]^c[D]^d / [A]^a[B]^b

Comparing Q to K_c indicates the direction the reaction will shift to reach equilibrium:

• If Q < K_c, the reaction shifts right (towards products).
• If Q = K_c, the system is at equilibrium.
• If Q > K_c, the reaction shifts left (towards reactants).

Equilibrium Constant (K_p)

For reactions involving gases, the equilibrium constant K_p is expressed in terms of partial pressures:

K_p = P_C^c P_D^d / P_A^a P_B^b

Relationship between K_p and K_c

K_p = K_c(RT)^Δn

Where R is the ideal gas constant, T is the absolute temperature, and Δn is the change in the number of moles of gas in the reaction (moles of gaseous products - moles of gaseous reactants).

Le Chatelier's Principle

When a system at chemical equilibrium is subjected to a stress (change in temperature, pressure, or concentration), the system will shift in a direction that relieves the stress and re-establishes equilibrium.

Effect of Changes

• Temperature:
  • For an exothermic reaction (ΔH < 0), increasing temperature shifts equilibrium left; decreasing temperature shifts equilibrium right.
  • For an endothermic reaction (ΔH > 0), increasing temperature shifts equilibrium right; decreasing temperature shifts equilibrium left.
• Pressure: (For gaseous systems)
  • Increasing pressure (decreasing volume) shifts equilibrium towards the side with fewer moles of gas.
  • Decreasing pressure (increasing volume) shifts equilibrium towards the side with more moles of gas.
  • Adding an inert gas at constant volume does not shift the equilibrium.
• Concentration:
  • Increasing the concentration of a reactant shifts equilibrium towards the products.
  • Increasing the concentration of a product shifts equilibrium towards the reactants.
  • Decreasing concentration has the opposite effect.
• Catalyst: A catalyst does not affect the position of equilibrium; it only speeds up the rate at which equilibrium is reached.