Question

The rate equation for a chemical reaction is Rate of reaction \(=\mathrm{k}[\mathrm{X}][\mathrm{Y}]\) Consider the following statements in this regard (1) The order of reaction is one (2) The molecularity of reaction is two (3) The rate constant depends upon temperature Of these statements: a. 1 and 3 are correct b. 1 and 2 are correct c. 2 and 3 are correct d. 1,2 and 3 are correct

Short answer

The correct statements are 2 and 3 (Option c).

Step-by-step solution

Understand Order of Reaction

The order of a reaction indicates how the rate depends on the concentration of the reactants. Here, the rate equation is given by: \(\text{Rate} = k[X][Y]\). This suggests that the rate depends on the concentration of X and the concentration Y each raised to the first power. Therefore, the overall order of the reaction is the sum of the exponents, which is \(1 + 1 = 2\).

Analyze Molecularity of Reaction

Molecularity refers to the number of molecules or atoms involved in the elementary reaction step. Here, the reaction involves one molecule of X and one molecule of Y interacting as described in the rate equation. Thus, the molecularity is two, as two species are involved in the interaction.

Assess Dependence of Rate Constant on Temperature

The rate constant \(k\) in a chemical reaction does not depend on the concentrations of the reactants or products but does depend on temperature. Generally, an increase in temperature leads to an increase in the rate constant, following the Arrhenius equation. Therefore, statement 3 is correct, as \(k\) is dependent on temperature.

Evaluate Statements

Based on the explanations: - Statement 1 (Order is one) is incorrect; the reaction order is two. - Statement 2 (Molecularity is two) is correct. - Statement 3 (Rate constant depends on temperature) is correct. Thus, statements 2 and 3 are correct.

Key concepts

Order of Reaction

Understanding the order of a reaction is essential, as it tells us how a reaction rate is affected by the concentration of the reactants. For a given chemical reaction with a rate equation \[ \text{Rate} = k[X][Y] \]we consider the exponents of the reactants. Each reactant, \([X]\) and \([Y]\), appears to the power of one (i.e., the exponent is 1 for both X and Y). The overall order of reaction is determined by summing these exponents. In this case, the sum is \(1 + 1 = 2\). Therefore, the order of the reaction is two. - The order indicates how sensitive the reaction rate is to changes in reactant concentrations.- It is a common misconception to confuse order with molecularity. They are fundamentally different. Reading and interpreting the rate equation correctly helps you understand the dynamics of the reaction.

Molecularity

Molecularity refers to the number of reactant particles involved in an elementary reaction step. For the reaction given by the equation \[ \text{Rate} = k[X][Y] \] one molecule of X and one molecule of Y interact in a single step to produce products. Thus, two molecules are involved in the process. - Since molecularity involves counting reactant molecules, it is always a clear whole number.- It is vital to recognize that molecularity only applies to elementary reactions, not complex reactions.- Molecularity is intrinsically linked to the reaction mechanism and is indicative of the simplest form of a reaction step happening at the molecular level.Remembering this distinction and method of counting reactant molecules will guide you in identifying the molecularity of any elementary step correctly.

Rate Constant

The rate constant \(k\) is integral to the calculation of reaction rates. It is a unique value for each reaction under given conditions. - Importantly, the rate constant is independent of the concentrations of reactants and products.- The primary factor affecting \(k\) is temperature. The Arrhenius equation describes the influence of temperature on the rate constant: \[ k = A e^{-\frac{E_a}{RT}} \]where \(A\) is the pre-exponential factor, \(E_a\) is the activation energy, \(R\) is the gas constant, and \(T\) is the temperature in Kelvin.- Increasing temperature typically increases the rate constant, leading to a faster reaction rate.- A high activation energy typically means a more dramatic increase in rate with temperature.Understanding \(k\) and its dependencies is crucial for controlling and predicting chemical reaction rates in various conditions.

Temperature Dependence

Temperature plays a key role in chemical reaction kinetics by affecting the rate constant \(k\). According to the Arrhenius equation, as temperature increases, molecules acquire more kinetic energy, thus overcoming the activation energy barrier more quickly.- Higher temperatures mean more energetic collisions and hence a faster reaction.- Many reactions exhibit a temperature coefficient, where a 10°C rise roughly doubles the rate.This sensitivity of reaction rates to temperature changes is why reactions are often carried out at controlled temperatures in industrial and laboratory settings.- It's also why refrigeration can slow reaction rates, extending the shelf life of perishable goods. Grasping how temperature influences reaction rates enables better manipulation and optimization of chemical processes.