Question

The rate of the reaction, 2NO + Cl$_2$ $\rightarrow$ 2NOCl is given by the rate equation, rate = k[NO]$^2$[Cl$_2$]. The value of the rate constant can be increased by

• A. increasing the concentration of NO.
• B. increasing the temperature.
• C. increasing the concentration of the Cl$_2$.
• D. doing all of these.

Hint:

Key Exam Tip:
Remember the distinction between factors affecting the reaction rate and factors affecting the rate constant (k):
• Concentrations of Reactants: Affects the rate directly but does not change the rate constant (k).
• Temperature: Affects both the rate and the rate constant (k). An increase in temperature generally leads to a higher rate constant.
• Catalyst: Speeds up the reaction by increasing the rate constant (k) by lowering the activation energy ($E_a$).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The rate constant (\( k \)) is a fundamental parameter of a chemical reaction.
Crucially, \( k \) is independent of the concentration of reactants and products. It depends only on the nature of the reaction, the presence of a catalyst, and the temperature.
Step 2: Key Formula or Approach:
The relationship between the rate constant and temperature is defined by the Arrhenius Equation:
\[ k = A \cdot e^{-E_a/RT} \]
where \( T \) is the absolute temperature.
Step 3: Detailed Explanation:
According to the Arrhenius equation, as the temperature (\( T \)) increases, the magnitude of the negative exponent (\( -E_a/RT \)) becomes smaller (closer to zero).
This causes the term \( e^{-E_a/RT} \) to increase significantly.
Consequently, the value of the rate constant \( k \) increases as temperature rises.
Increasing concentration only increases the rate of the reaction, not the rate constant.
Step 4: Final Answer:
Only an increase in temperature or the addition of a catalyst can increase the value of \( k \).