Distinguish between the following: a) Instantaneous and initial rates b) Order and molecularity of reaction

Compare Experiment II and Experiment III, where $[A]$ is constant:
$$
\frac{\text{Rate}_3}{\text{Rate}_2} = \frac{k[A]_3^x[B]_3^y}{k[A]_2^x[B]_2^y}
$$
$$
\frac{0.40}{0.10} = \frac{k[0.01]^x[0.40]^y}{k[0.01]^x[0.20]^y}
$$
$$
4 = \left(\frac{0.40}{0.20}\right)^y
$$
$$
4 = (2)^y
$$
$$
y = 2
$$
The reaction is **second order** with respect to B.

• ii) What is the overall order of reaction?

Overall order $= x + y = 1 + 2 = 3$.  
The overall order of the reaction is **third order**.

3c) Match the statements given in Column I and Column II:

• (i) Catalyst alters the rate of reaction $\longrightarrow$ (c) By lowering the activation energy
• (ii) Molecularity $\longrightarrow$ (a) cannot be fraction or zero
• (iii) Second half-life of first order reaction $\longrightarrow$ (d) is same as the first
• (iv) Energetically favourable reactions are sometimes slow $\longrightarrow$ (b) proper orientation is not the only factor
• (v) Mathematical expression for rate of reaction $\longrightarrow$ (f) rate law
• (vi) Rate of reaction for zero order reaction is equal to $\longrightarrow$ (e) rate constant
• (vii) Units of rate constant for zero order reaction is same as $\longrightarrow$ (h) rate of a reaction
• (viii) Order of a complex reaction is determined by $\longrightarrow$ (g) order of slowest step

3d)

• i) List three (3) physical parameters that can be used to monitor rate of reaction.

  1. Change in concentration (e.g., using spectroscopy or titration)
  2. Change in pressure (for gas-phase reactions)
  3. Change in color (if a reactant or product is colored)

• ii) Write the Arrhenius equation and define the terms in it. The Arrhenius equation is:

  $$k = A e^{-E_a/RT}$$

  Where:

  • $k$ is the rate constant.
  • $A$ is the Arrhenius pre-exponential factor (or frequency factor), representing the frequency of collisions with proper orientation.
  • $E_a$ is the activation energy, the minimum energy required for a reaction to occur.
  • $R$ is the ideal gas constant.
  • $T$ is the absolute temperature in Kelvin.

• iii) How does a catalyst work? A catalyst works by providing an alternative reaction pathway with a lower activation energy ($E_a$). This allows a larger fraction of reactant molecules to have sufficient energy to react, thereby increasing the rate of the reaction without being consumed in the process.

• iv) If the rate constant of a reaction is $k = 3 \times 10^{-4} s^{-1}$, then identify the order of the reaction. The unit of the rate constant ($k$) is $s^{-1}$. For a reaction of order $n$, the general unit of the rate constant is $(\text{concentration})^{1-n} \text{time}^{-1}$. Comparing $s^{-1}$ with $(\text{concentration})^{1-n} \text{time}^{-1}$, we see that the concentration term must be dimensionless, meaning $1-n = 0$. Therefore, $n = 1$. The reaction is a first-order reaction.