Chemical Kinetics - Formula Sheet

Reaction Rates and Order

• Average Rate: \(Rate = -\frac{\Delta [R]}{\Delta t} = \frac{\Delta [P]}{\Delta t}\)
• General Rate Law: \(Rate = k [A]^m [B]^n\)
• Overall Order: \(n = m + n\)

Integrated Rate Equations

• Zero Order: \(k = \frac{[A_0] - [A]}{t}\)
• First Order: \(k = \frac{2.303}{t} \log \frac{[A_0]}{[A]}\)
• General nth Order (\(n \neq 1\)): \(\frac{1}{[A]^{n-1}} - \frac{1}{[A_0]^{n-1}} = (n-1)kt\)

Half-Life Formulas

• Zero Order: \(t_{1/2} = \frac{[A_0]}{2k}\)
• First Order: \(t_{1/2} = \frac{0.693}{k}\)
• General nth Order (\(n \neq 1\)): \(t_{1/2} \propto \frac{1}{[A_0]^{n-1}}\)

Arrhenius Equation and Activation Energy

• Arrhenius Equation: \(k = A e^{-\frac{E_a}{RT}}\)
• Logarithmic Form: \(\log k = \log A - \frac{E_a}{2.303RT}\)
• Two-Temperature Form: \(\log \frac{k_2}{k_1} = \frac{E_a}{2.303R} \left( \frac{T_2 - T_1}{T_1 T_2} \right)\)

Symbol Definitions

• \(k\): Rate constant
• \([A_0]\): Initial concentration of reactant
• \([A]\): Concentration of reactant at time \(t\)
• \(t_{1/2}\): Half-life period
• \(E_a\): Activation energy (\(J \, mol^{-1}\))
• \(R\): Gas constant (\(8.314 \, J \, K^{-1} \, mol^{-1}\))
• \(T\): Absolute temperature (Kelvin)
• \(A\): Frequency factor or Arrhenius pre-exponential factor