Question

When the reactants are \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) at one mole per litre each the rate equation is, rate \(=\mathrm{k}[\mathrm{A}]^{\mathrm{x}}[\mathrm{B}]^{1 / \mathrm{Y}}\) \([\mathrm{C}]^{\mathrm{X} / \mathrm{Y}}\). The order of the reaction is a. \(X+\frac{(1+X)}{Y}\) b. \(\mathrm{X}-\mathrm{Y}+\frac{\mathrm{X}}{\mathrm{Y}}\) c. \(\mathrm{X}+\mathrm{Y}+\frac{\mathrm{X}}{\mathrm{Y}}\) d. \(2(X+Y)\)

Short answer

The order of the reaction is option a: \(X + \frac{1+X}{Y}\).

Step-by-step solution

Identify Reaction Order Formula

The reaction order is determined by the sum of the exponents of the concentrations of the reactants in the rate equation. The rate in relation to each reactant is described by its power in the rate equation.

Substitute from Rate Equation

The rate equation provides us with the details: \\(\text{rate} = k[A]^X[B]^{1/Y}[C]^{X/Y}\). Thus, the exponents for A, B, and C are \(X\), \(1/Y\), and \(X/Y\), respectively.

Add the Exponents

To find the order of the reaction, add the exponents of A, B, and C. This gives: \(X + \frac{1}{Y} + \frac{X}{Y}\).

Simplify the Expression

Combine the terms to simplify: \(X + \frac{1+X}{Y}\).

Match with Choices

Compare the simplified expression \(X + \frac{1+X}{Y}\) with the provided options to find the correct match.

Key concepts

Rate Equation

In the realm of chemical kinetics, the Rate Equation is a fundamental concept. It describes how the rate of a chemical reaction depends on the concentration of its reactants. The rate equation is typically expressed in the form:

• rate = k[A]^x[B]^y[C]^z

Here,

• k is the rate constant,
• [A], [B], and [C] are the concentrations of the reactants,
• x, y, and z are the exponents representing the contribution of each reactant to the reaction's rate.

This equation helps chemists understand how changes in concentration can impact the speed of the reaction. A simple increase or decrease in the concentration of a reactant can significantly affect how fast the reaction proceeds. By carefully examining this equation, one can determine the reaction order, a crucial piece of information when predicting or controlling reaction processes.

Reaction Order

The Reaction Order is a vital descriptor in chemical kinetics. It indicates how sensitive the reaction rate is to changes in concentrations of the reactants. The overall order of a reaction is the sum of all the exponents of the concentration terms in the rate equation. For example, in the original exercise:

• the reaction order is calculated as: \(X + \frac{1}{Y} + \frac{X}{Y}\)

This sum describes the dependence of the reaction rate on the concentration of each reactant.

Importance of Reaction Order

• Determines how the reaction rate changes as reactant concentrations change.
• Helps predict how long it will take for a reaction to reach completion under different conditions.
• Can provide insights into the reaction mechanism.

Knowing the reaction order is crucial for anyone looking to manipulate or optimize chemical reactions, such as in industrial processes or laboratory experiments.

Exponents in Rate Law

Exponents in Rate Law are critical as they define the effect that the concentration of each reactant has on the rate of reaction. In the rate equation, these exponents emerge from experimental data and not from the stoichiometric coefficients of the chemical equation.

Understanding the Exponents

• The exponent indicates the order with respect to a reactant. For example, in \([A]^x\), x is the order of the reaction concerning reactant A.
• A zero-order reactant means the reaction rate is unaffected by changes in that reactant’s concentration.
• A first-order reactant means the reaction rate is directly proportional to that reactant's concentration.
• A second-order reactant means the reaction rate is proportional to the square of that reactant's concentration.

These subtleties allow chemists to model how the speed of a reaction will change as reagent quantities are altered. Studying these exponents provides invaluable insights into the reaction’s dynamics and complexities, thus aiding in the prediction and control of chemical behavior.