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

The given rate equation for the reaction 2NO + Cl$_2$ $\rightarrow$ 2NOCl is: rate = k[NO]$^2$[Cl$_2$] This equation describes how the rate of the reaction is dependent on the concentrations of the reactants NO and Cl$_2$, and the rate constant, k. The rate constant (k) is a proportionality factor that is specific to a particular reaction at a particular temperature. Let's analyze the effect of each option on the rate constant (k): 1) Increasing the concentration of NO: The rate equation shows that the reaction rate is proportional to the square of the concentration of NO ([NO]$^2$). If the concentration of NO increases, the rate of the reaction will increase. However, the rate constant (k) is defined as the rate of reaction when all reactant concentrations are unity. Thus, 'k' is fundamentally independent of reactant concentrations at a constant temperature. Increasing [NO] increases the overall rate, but does not change the rate constant. 2) Increasing the temperature: The rate constant (k) is strongly dependent on temperature. This relationship is described by the Arrhenius equation: $k = Ae^{-E_a/RT}$ where:
• k is the rate constant
• A is the pre-exponential factor (frequency of collisions)
• $E_a$ is the activation energy (minimum energy required for a reaction to occur)
• R is the ideal gas constant
• T is the absolute temperature (in Kelvin) From the Arrhenius equation, as temperature (T) increases, the term $e^{-E_a/RT}$ increases because the exponent becomes less negative. This leads to a higher value of the rate constant (k). Therefore, increasing the temperature directly increases the rate constant. 3) Increasing the concentration of Cl$_2$: Similar to NO, the rate equation shows that the rate is directly proportional to the concentration of Cl$_2$ ([Cl$_2$]). Increasing [Cl$_2$] will increase the rate of the reaction. However, the rate constant (k) is independent of reactant concentrations at a constant temperature. Thus, increasing [Cl$_2$] increases the rate, but not the rate constant. 4) Doing all of these: Since only increasing the temperature affects the rate constant, this option is incorrect. The question specifically asks what can increase the *value of the rate constant*. Based on chemical kinetics principles, only temperature (and catalysts, which are not options here) affects the rate constant. Final Answer: \(\boxed{2}\)