Problem 9 - Chemistry An Atoms First Approach

Question

The rate constant \((k)\) depends on which of the following (there may be more than one answer)? a. the concentration of the reactants b. the nature of the reactants c. the temperature d. the order of the reaction Explain.

Step-by-Step Solution

Answer

The rate constant (k) depends on the nature of the reactants (b) and the temperature (c). The nature of the reactants affects the rate constant because different reactions have different rate constants depending on the reactants involved and the mechanism of the reaction. The temperature affects the rate constant, as the reactant molecules have more kinetic energy at higher temperatures, making it more likely that they will collide with sufficient energy to overcome the activation energy barrier. This is described by the Arrhenius equation: \(k(T) = Ae^{(-Ea/RT)}\).

Step 1: Factor a: Concentration of the Reactants

The rate constant (k) is a proportionality constant that relates the rate of a reaction to the concentrations of the reactants. However, the rate constant itself doesn't change with the concentration of the reactants. So, (a) is not a factor affecting the rate constant.

Step 2: Factor b: Nature of the Reactants

The nature of the reactants affects the rate constant. Different reactions have different rate constants depending on the reactants involved and the mechanism of the reaction. For example, reactions involving ionic species usually have larger rate constants compared to those involving covalent species. So, (b) is a factor affecting the rate constant.

Step 3: Factor c: Temperature

The temperature affects the rate constant. As the temperature increases, the rate constant increases as well, because the reactant molecules have more kinetic energy, making it more likely that they will collide with sufficient energy to overcome the activation energy barrier. This is described by the Arrhenius equation: \[k(T) = Ae^{(-Ea/RT)}\] where \(k(T)\) = rate constant at temperature T, A = pre-exponential factor, Ea = activation energy, R = gas constant, and T = temperature in Kelvin. So, (c) is a factor affecting the rate constant.

Step 4: Factor d: Order of the Reaction

The order of the reaction affects the relationship between the rate of the reaction and the concentrations of the reactants, but it doesn't affect the rate constant itself. The rate constant is the proportionality constant in the rate law expression, and its value remains the same for a given reaction at a fixed temperature, regardless of the order of the reaction. So, (d) is not a factor affecting the rate constant. In conclusion, the rate constant (k) depends on the nature of the reactants (b) and the temperature (c).