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:
Factors Affecting Reaction Rate vs. Rate Constant:
• Concentration of Reactants: Affects the rate of the reaction but not the rate constant (k).
• Temperature: Affects both the rate and the rate constant (k). Higher temperature generally leads to a higher rate constant.
• Catalyst: Affects the rate by lowering the activation energy, thus increasing the rate constant (k). In this question, only temperature and a catalyst (not provided as an option) affect the rate constant.

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 shows that the rate of the reaction depends on the rate constant (k) and the concentrations of the reactants NO and Cl$_2$. The rate constant (k) is a proportionality constant specific to a reaction at a given temperature. Let's analyze how each factor affects the rate and specifically the rate constant: 1) Increasing the concentration of NO: According to the rate equation, the rate is directly proportional to [NO]$^2$. If [NO] increases, the rate of the reaction will increase significantly. However, the rate constant 'k' is independent of reactant concentrations at a constant temperature. Increasing the concentration of NO will increase the rate of the reaction, but not the rate constant. 2) Increasing the temperature: The rate constant (k) is highly dependent on temperature. According to the Arrhenius equation, $k = Ae^{-E_a/RT}$, where:
• k is the rate constant.
• A is the pre-exponential factor (frequency factor).
• $E_a$ is the activation energy.
• R is the gas constant.
• T is the absolute temperature. As temperature (T) increases, the term $e^{-E_a/RT}$ increases (because the exponent becomes less negative), leading to an increase in the rate constant (k). Therefore, increasing the temperature will increase the value of the rate constant. 3) Increasing the concentration of Cl$_2$: The rate equation shows that the rate is directly proportional to [Cl$_2$]. If [Cl$_2$] increases, the rate of the reaction will increase. However, like concentration of NO, the rate constant 'k' is independent of reactant concentrations at a constant temperature. Increasing the concentration of Cl$_2$ will increase the rate of the reaction, 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*. Among the given options, only increasing the temperature affects the rate constant. Final Answer: \(\boxed{2}\)