Chemical Kinetics — MHT-CET Chemistry

Formulas (2)

• Converting One Species' Rate to Another's: Multiply by the Coefficient Ratio · Rate of reaction
  $$\text{rate} = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt} = \frac{1}{d}\frac{d[D]}{dt}$$
• Writing the Rate Expression, and Reading the Equation Back From It · Signs and reciprocals
  $$\text{reactant: } -\frac{1}{\text{coeff}}\frac{d[\cdot]}{dt} \qquad \text{product: } +\frac{1}{\text{coeff}}\frac{d[\cdot]}{dt}$$

Watch out for (2)

• Multiplying when you should divide
  → Converting One Species' Rate to Another's: Multiply by the Coefficient Ratio
• Coefficient in front instead of as a reciprocal
  → Writing the Rate Expression, and Reading the Equation Back From It

Formulas (4)

• The Rate Law and the Order: Exponents Come From Experiment, Not From the Equation · Rate law
  $$r = k[A]^x[B]^y,\qquad \text{order} = x + y \ (\text{experimental; may be } 0, \text{ fractional})$$
• The Rate Constant: k = rate/([A]ˣ[B]ʸ), Its Units and Its Properties · Rate constant
  $$k = \frac{r}{[A]^x[B]^y},\qquad [k] = (\text{mol dm}^{-3})^{1-n}\,\text{s}^{-1}$$
• How the Rate Changes When Concentrations Change: Multiply the Factors · Rate factor
  $$\frac{r'}{r} = \left(\frac{[A]'}{[A]}\right)^x\left(\frac{[B]'}{[B]}\right)^y$$
• Order Versus Molecularity · The contrast
  $$\text{molecularity} \in \{1, 2, 3\} \text{ (theoretical, per step)};\qquad \text{order} \in \mathbb{R}_{\ge 0} \text{ (experimental)}$$

Watch out for (4)

• Reading the order off the balanced equation
  → The Rate Law and the Order: Exponents Come From Experiment, Not From the Equation
• Squaring the wrong concentration
  → The Rate Constant: k = rate/([A]ˣ[B]ʸ), Its Units and Its Properties
• Adding the factors
  → How the Rate Changes When Concentrations Change: Multiply the Factors
• Calling H₂ + Br₂ 'monomolecular' because the order is fractional
  → Order Versus Molecularity

Formulas (2)

• [A]ₜ = [A]₀ − kt: Constant Rate, k in Concentration per Time · Zero order
  $$[A]_t = [A]_0 - kt,\qquad k = \frac{[A]_0 - [A]_t}{t}\ \ (\text{mol dm}^{-3}\,\text{s}^{-1})$$
• Zero-Order Half-Life: t½ = [A]₀/2k, Proportional to the Initial Concentration · Zero-order half-life
  $$t_{1/2} = \frac{[A]_0}{2k}$$

Watch out for (2)

• Forgetting the seconds-to-minutes conversion
  → [A]ₜ = [A]₀ − kt: Constant Rate, k in Concentration per Time
• Using 0.693/k
  → Zero-Order Half-Life: t½ = [A]₀/2k, Proportional to the Initial Concentration

Formulas (3)

• k = 0.693/t½ and k = rate/[A]: the Half-Life Is Fixed, the Unit Is time⁻¹ · First-order constant
  $$t_{1/2} = \frac{0.693}{k},\qquad k = \frac{r}{[A]}\ \ (\text{s}^{-1}),\qquad \text{slope of } \log[A]_t \text{ vs } t = -\frac{k}{2.303}$$
• k = (2.303/t) log([A]₀/[A]ₜ): Percent Decomposed, and the Time to 90%, 99%, 99.9% · Integrated first-order law
  $$k = \frac{2.303}{t}\log_{10}\frac{[A]_0}{[A]_t} \qquad t_{90\%} = \frac{2.303}{k},\ t_{99\%} = \frac{4.606}{k},\ t_{99.9\%} = \frac{6.909}{k}$$
• Counting Half-Lives: Fraction Left After n Half-Lives Is (1/2)^n · Half-life counting
  $$\frac{[A]_t}{[A]_0} = \left(\frac12\right)^{n},\qquad t = n\,t_{1/2}$$

Watch out for (3)

• Hours left as hours
  → k = 0.693/t½ and k = rate/[A]: the Half-Life Is Fixed, the Unit Is time⁻¹
• Using the percent decomposed as [A]ₜ
  → k = (2.303/t) log([A]₀/[A]ₜ): Percent Decomposed, and the Time to 90%, 99%, 99.9%
• Scaling the time with the concentration
  → Counting Half-Lives: Fraction Left After n Half-Lives Is (1/2)^n

Formulas (2)

• The Rate-Determining Step Writes the Rate Law · Rate from the slow step
  $$\text{slow step } aA + bB \to \dots \ \Rightarrow\ r = k[A]^a[B]^b$$
• Intermediates: Made in One Step, Used in the Next; Catalysts: Used, Then Regenerated · Cancelling species
  $$\text{intermediate: produced then consumed;}\qquad \text{catalyst: consumed then regenerated}$$

Watch out for (2)

• Writing the rate law from the overall equation
  → The Rate-Determining Step Writes the Rate Law
• Picking the product that appears in both steps
  → Intermediates: Made in One Step, Used in the Next; Catalysts: Used, Then Regenerated

Formulas (3)

• The Arrhenius Equation and Its Plot: Slope −Ea/2.303R, Intercept log A · Arrhenius
  $$k = A\,e^{-E_a/RT},\qquad \log_{10}k = \log_{10}A - \frac{E_a}{2.303R}\cdot\frac{1}{T}$$
• Two Temperatures: log(k₂/k₁) = (Ea/2.303R)·(T₂ − T₁)/(T₁T₂) · Two-temperature Arrhenius
  $$\log_{10}\frac{k_2}{k_1} = \frac{E_a}{2.303R}\left(\frac{T_2 - T_1}{T_1 T_2}\right)$$
• Collision Theory: Only Effective Collisions Count · Effective collisions
  $$\text{rate} = Z \cdot e^{-E_a/RT} \cdot P \qquad (Z \text{ collision frequency, } P \text{ orientation factor})$$

Watch out for (3)

• Dropping the 2.303 with a base-10 plot
  → The Arrhenius Equation and Its Plot: Slope −Ea/2.303R, Intercept log A
• Dividing the half-life by the ratio at the LOWER temperature
  → Two Temperatures: log(k₂/k₁) = (Ea/2.303R)·(T₂ − T₁)/(T₁T₂)
• 'Collisions are fewer than the observed rate'
  → Collision Theory: Only Effective Collisions Count