Question

In the following question two statements Assertion (A) and Reason (R) are given Mark. a. If \(\mathrm{A}\) and \(\mathrm{R}\) both are correct and \(\mathrm{R}\) is the correct explanation of \(\mathrm{A}\); b. If \(A\) and \(R\) both are correct but \(R\) is not the correct explanation of \(\mathrm{A}\); c. \(\mathrm{A}\) is true but \(\mathrm{R}\) is false; d. \(\mathrm{A}\) is false but \(\mathrm{R}\) is true, e. \(\mathrm{A}\) and \(\mathrm{R}\) both are false. (A): In rate laws, unlike in the expression for equilibrium constants, the exponents for concentrations do not necessarily match stoichiometric coefficients. (R): It is the mechanism and not the balanced chemical equation for the overall change the governs the reaction rate. Reaction rate is experimentally quantity and not necessary depends on stoichiometric coefficients

Short answer

Option (a): Both A and R are correct, and R is the correct explanation of A.

Step-by-step solution

Understanding the Assertion

The assertion (A) states that, in rate laws, the exponents for concentrations do not necessarily match the stoichiometric coefficients from the balanced chemical equation. This is true. Rate laws are determined experimentally and the exponents are related to the reaction mechanism, not the stoichiometry of the overall equation.

Understanding the Reason

The reason (R) states that the reaction mechanism governs the reaction rate, not the balanced chemical equation. This is also true, as the rate of reaction is determined by the slowest step in the reaction mechanism, known as the rate-determining step, and not directly by the stoichiometry of the reaction.

Checking if Reason Explains Assertion

Now, we need to determine if "It is the mechanism and not the balanced chemical equation that governs the reaction rate" (R) explains why "In rate laws, the exponents for concentrations do not necessarily match stoichiometric coefficients" (A). Yes, it does, because the exponents in the rate law come from the reaction mechanism steps, which may differ from the stoichiometric coefficients of the overall reaction.

Conclusion

Since both the Assertion (A) and the Reason (R) are true, and the Reason (R) correctly explains the Assertion (A), the answer is option (a).

Key concepts

Rate Laws

In chemical kinetics, rate laws are mathematical expressions that describe the dependence of reaction rates on the concentration of reactants. They are significant because they help us understand how fast a reaction occurs under specific conditions. Contrary to initial expectations, the rate law's exponents do not necessarily match the stoichiometric coefficients of the balanced chemical equation.

Rate laws are expressed in the general form: \[ ext{Rate} = k[ ext{A}]^m [ ext{B}]^n\]where \(k\) is the rate constant, and \([A]\) and \([B]\) are the molar concentrations of the reactants. The exponents \(m\) and \(n\) indicate the order of the reaction with respect to each reactant, and they are determined experimentally.

• Rate laws provide insights into the reaction mechanism.
• They highlight the role of concentration in influencing the rate.
• Unlike equilibrium constants, rate laws depend on the pathway of the reaction rather than just the initial and final states.

Understanding these concepts is essential for predicting how changes in concentration affect reaction rates.

Reaction Mechanism

A reaction mechanism is a series of elementary steps that describe the route taken by molecules as they transform from reactants to products. These steps give a more detailed view of how a chemical reaction proceeds.

Each step in a reaction mechanism can be considered a simple process involving collisions and transformations between molecules or atoms. Not all steps are created equal; one of the steps, known as the rate-determining step, generally controls the overall rate of the reaction.

• The mechanism reflects the actual path and intermediate states that reactants go through.
• It includes various species that appear temporarily and influence the progression.
• Each elementary step has its own rate and molecularity, which collectively contribute to the reaction's observed rate law.

By studying the reaction mechanism, chemists can better understand the details that affect the overall rate and predict conditions to optimize the reaction collision.

Stoichiometric Coefficients

Stoichiometric coefficients are part of balanced chemical equations and represent the proportions of molecules or moles required for the reaction to proceed according to the law of conservation of mass. These coefficients ensure that the number of each type of atom is equal on both the reactant and product sides of an equation.

However, these coefficients do not always reflect the reaction dynamics seen in kinetic studies. For instance, in a chemical equation: \[ ext{aA} + ext{bB} → ext{cC}\]The coefficients \(a, b,\) and \(c\) indicate how much of each reactant is theoretically needed and produced from the reaction, but they are not used directly to write the rate law.

• Changes in stoichiometric coefficients alter how much of each reactant is needed but not necessarily the rate law.
• In kinetic expressions, the emphasis is on experimental determinations rather than theoretical balanced equations.
• Understanding the difference between stoichiometric coefficients and kinetic expressions is key to mastering chemical kinetics.

Students often find understanding these distinctions crucial for effective analysis of chemical reactions in kinetic terms.