Chemical Kinetics — JEE Mains Chemistry

Formulas (2)

• Average rate from a change in concentration · Average rate
  $$r_{\text{av}} = -\frac{\Delta[\text{R}]}{\Delta t} = +\frac{\Delta[\text{P}]}{\Delta t}$$
• Rates of different species through the coefficients · Rate of reaction
  $$r = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt} = \frac{1}{d}\frac{d[D]}{dt}$$

Watch out for (4)

• Clock reaction: the time and the thiosulphate
  → Average rate from a change in concentration
• Minutes divided as if they were hours
  → Average rate from a change in concentration
• Two species' rates taken as equal
  → Rates of different species through the coefficients
• A species' rate reported as the rate of reaction
  → Rates of different species through the coefficients

Formulas (2)

• How the rate changes when concentrations change · Ratio of rates
  $$\frac{r_2}{r_1} = \left(\frac{[A]_2}{[A]_1}\right)^{m}\left(\frac{[B]_2}{[B]_1}\right)^{n}$$
• Order from a table of initial rates · Order in A from two runs
  $$m = \frac{\log(r_2/r_1)}{\log([A]_2/[A]_1)} \quad ([B]\ \text{fixed})$$

Reference tables (1)

Watch out for (5)

• Order read from the balanced equation
  → How the rate changes when concentrations change
• More solution taken as a faster reaction
  → How the rate changes when concentrations change
• Two runs where both concentrations changed
  → Order from a table of initial rates
• Rate and k given the same unit
  → Unit of the rate constant for each order, and order versus molecularity
• A fractional molecularity
  → Unit of the rate constant for each order, and order versus molecularity

Formulas (3)

• The integrated first-order law and the half-life · Integrated first-order law
  $$k = \frac{2.303}{t}\log\frac{[A]_0}{[A]}\qquad t_{1/2} = \frac{0.693}{k}$$
• Comparing the times to two levels of completion · Ratio of two completion times
  $$\frac{t_1}{t_2} = \frac{\log([A]_0/[A]_1)}{\log([A]_0/[A]_2)}$$
• Exponential form, straight-line plots and rate ratios · Exponential form
  $$[A] = [A]_0\,e^{-kt}\qquad \ln\frac{[A]}{[A]_0} = -kt$$

Watch out for (6)

• The percent decomposed used as [A]
  → The integrated first-order law and the half-life
• Expiry time of a drug
  → The integrated first-order law and the half-life
• 67% complete read as two-thirds left
  → Comparing the times to two levels of completion
• Times scaled like the percentages
  → Comparing the times to two levels of completion
• A first-order reaction that 'completes'
  → Exponential form, straight-line plots and rate ratios
• Rate ratio used for any order
  → Exponential form, straight-line plots and rate ratios

Formulas (2)

• Rate constant of a gas reaction from the total pressure · A(g) → B(g) + C(g)
  $$k = \frac{2.303}{t}\log\frac{p_i}{2p_i - P_t}$$
• Radioactive decay, carbon dating and bacterial growth · Radioactive decay
  $$\frac{N}{N_0} = e^{-\lambda t} = \left(\tfrac12\right)^{t/t_{1/2}},\qquad \lambda = \frac{0.693}{t_{1/2}}$$

Watch out for (4)

• The total pressure put into the log
  → Rate constant of a gas reaction from the total pressure
• P∞ taken as the initial pressure
  → Rate constant of a gas reaction from the total pressure
• Decay constant rising with temperature
  → Radioactive decay, carbon dating and bacterial growth
• Growth drawn as decay
  → Radioactive decay, carbon dating and bacterial growth

Formulas (2)

• The zero-order law and its half-life · Zero-order law
  $$[A] = [A]_0 - kt\qquad t_{1/2} = \frac{[A]_0}{2k}$$
• Order from how the half-life depends on the starting concentration · Half-life and order
  $$t_{1/2} \propto [A]_0^{\,1-n}\quad\Rightarrow\quad \frac{t_{1/2}'}{t_{1/2}} = \left(\frac{[A]_0'}{[A]_0}\right)^{1-n}$$

Reference tables (1)

Watch out for (6)

• One-quarter taken as two half-lives
  → The zero-order law and its half-life
• Zero-order half-life treated as fixed
  → The zero-order law and its half-life
• Seconds compared with minutes
  → Order from how the half-life depends on the starting concentration
• The order changing with concentration
  → Order from how the half-life depends on the starting concentration
• The sign of the slope
  → Identifying zero and first order from the shape of a graph
• A rate–time line read as a concentration–time line
  → Identifying zero and first order from the shape of a graph

Formulas (3)

• Reading Ea and A from the Arrhenius equation or its plot · Arrhenius equation
  $$k = A\,e^{-E_a/RT}\qquad \ln k = \ln A - \frac{E_a}{RT}\qquad \log k = \log A - \frac{E_a}{2.303RT}$$
• Two-temperature form of the Arrhenius equation · Two-temperature form
  $$\log\frac{k_2}{k_1} = \frac{E_a}{2.303R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)$$
• Ratio of rate constants for two reactions with the same A · Same A, different Ea
  $$\ln\frac{k_2}{k_1} = \frac{E_{a1} - E_{a2}}{RT}$$

Watch out for (6)

• The ln form read as the log form
  → Reading Ea and A from the Arrhenius equation or its plot
• Fraction BELOW the activation energy
  → Reading Ea and A from the Arrhenius equation or its plot
• Endothermic reactions slowing on heating
  → Reading Ea and A from the Arrhenius equation or its plot
• Celsius in the formula
  → Two-temperature form of the Arrhenius equation
• The reciprocals subtracted the wrong way round
  → Two-temperature form of the Arrhenius equation
• ln of the ratio given when log was asked
  → Ratio of rate constants for two reactions with the same A

Formulas (2)

• Rate law and activation energy from a mechanism · Composite activation energy
  $$k = \frac{k_1k_2}{k_3}\ \Rightarrow\ E_a = E_{a1} + E_{a2} - E_{a3}$$
• Reading energy profiles and the effect of a catalyst · Barriers and enthalpy
  $$\Delta H = E_{a,f} - E_{a,b}$$

Watch out for (5)

• An intermediate left in the rate law
  → Rate law and activation energy from a mechanism
• Rate law written from the overall equation
  → Rate law and activation energy from a mechanism
• A catalyst that changes ΔH
  → Reading energy profiles and the effect of a catalyst
• The sign of ΔH flipped
  → Reading energy profiles and the effect of a catalyst
• Valleys counted as activated complexes
  → Reading energy profiles and the effect of a catalyst