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Chapter 8: Problem 177

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, the exponents for concentration do not necessarily match the stoichiometric coefficients. \((\mathbf{R})\) : It is the mechanism and not the balanced chemical equation for the overall change that governs the reaction rate.

Short Answer

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

Step by step solution

01

Understanding the Assertion

The Assertion (A) states that in rate laws, the exponents for concentration do not necessarily match the stoichiometric coefficients. This is true because rate laws are determined experimentally and can vary based on reaction mechanism, not just the balanced equation.
02

Analyzing the Reason

The Reason (R) states that it is the mechanism and not the balanced chemical equation for the overall change that governs the reaction rate. This is also true because the reaction rate depends on the sequence of elementary steps (mechanism), which can differ from the overall balanced equation.
03

Evaluating the Relationship

Both the Assertion and the Reason are true. The Reason correctly explains why the exponents in rate laws may not match the stoichiometric coefficients, as they are determined by the reaction mechanism.
04

Making the Decision

Since both A and R are true and R is the correct explanation for A, the correct answer is option (a).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Rate Laws
Rate laws describe how the concentration of reactants affects the rate of a chemical reaction. A rate law is typically expressed as:
  • Rate = k[A]^m[B]^n
Here, \(A\) and \(B\) are reactants; \(m\) and \(n\) are the exponents, which are determined experimentally. These exponents indicate the order of the reaction with respect to each reactant.
The rate constant, \(k\), is a proportionality factor that changes with temperature but is constant for a given set of conditions.
It鈥檚 important to note that these exponents in the rate law are not necessarily related to the stoichiometric coefficients from the balanced chemical equation. This is because they are derived from the reaction鈥檚 mechanism rather than the stoichiometric balance. Thus, measuring reaction rates and conducting experiments is crucial to accurately determine the rate law.
Reaction Mechanisms
To fully understand how a reaction proceeds, studying the reaction mechanism is crucial. A reaction mechanism provides a detailed step-by-step pathway of how reactants transform into products. It often involves multiple elementary steps, which are simple reactions that make up the overall reaction.
The mechanism gives insights into the transition states and intermediates that are formed during the reaction. Unlike the overall balanced equation, the mechanism reveals the details that dictate the reaction rate. Each elementary step has its own rate law, and the slowest step (rate-determining step) usually determines the overall reaction rate.
Understanding the reaction mechanism helps chemists control and optimize reactions in industrial settings and research.
Stoichiometric Coefficients
Stoichiometric coefficients are numbers in a balanced chemical equation that indicate the molar ratio in which reactants combine to form products. For example, in the equation \(2 H_2 + O_2 \rightarrow 2 H_2O\), the coefficients suggest that two moles of hydrogen react with one mole of oxygen to produce two moles of water.These coefficients tell us the proportions necessary for a complete reaction without any leftover reactants. However, they do not provide information about the speed or rate of the reaction.
In the context of rate laws, stoichiometric coefficients should not be confused with the reaction orders (exponents) in the rate equation. Reaction orders must be determined through experiments, despite the seeming simplicity offered by stoichiometric coefficients in balanced equations.

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Most popular questions from this chapter

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 first order reaction \(t_{1 / 2}\) is independent of initial concentration. \((\mathbf{R})\) : The unit of \(\mathrm{K}\) is time \(^{-1}\).

Which of the following statements are true about reaction mechanisms? (I) A rate law can be written from the molecularity of the slowest elementary step. (II) The final rate law can include intermediates. (III) The rate of the reaction is dependent on the fastest step in the mechanism. (IV) A mechanism can never be proven to be the correct pathway for a reaction. a. I and II b. I and IV c. II and III d. I, II and III

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): For the hydrogen halogen photochemical reaction, the quantum yield for the formation of \(\mathrm{HBr}\), is lower than that of \(\mathrm{HCl}\). (R): \(\mathrm{Br}+\mathrm{H}_{2} \rightarrow \mathrm{HBr}+\mathrm{H}\) has higher activation energy than \(\mathrm{Cl}+\mathrm{H}_{2} \rightarrow \mathrm{HCl}+\mathrm{H}\)

Two reactions \(\mathrm{X} \rightarrow\) Products and \(\mathrm{Y} \rightarrow\) products have rate constant \(\mathrm{k}_{\mathrm{x}}\) and \(\mathrm{k}_{\mathrm{Y}}\) at temperature \(\mathrm{T}\) and activation energies \(\mathrm{E}_{\mathrm{x}}\) and \(\mathrm{E}_{\mathrm{Y}}\) respectively. If \(\mathrm{k}_{\mathrm{x}}>\) \(\mathrm{k}_{\mathrm{r}}\) and \(\mathrm{E}_{\mathrm{x}}<\mathrm{E}_{\mathrm{Y}}\) and assuming that for both the reaction is same, then a. At lower temperature \(\mathrm{k}_{\mathrm{Y}}>\mathrm{k}_{\mathrm{x}}\) b. At higher temperature \(\mathrm{k}_{\mathrm{x}}\) will be greater than \(\mathrm{k}_{\mathrm{y}}\) c. At lower temperature \(\mathrm{k}_{\mathrm{x}}\) and \(\mathrm{k}_{\mathrm{Y}}\) will be close to each other in magnitude d. At temperature rises, \(\mathrm{k}_{\mathrm{x}}\) and \(\mathrm{k}_{\mathrm{Y}}\) will be close to each other in magnitude

The first order isomerisation reaction: Cyclopropane \(\rightarrow\) propene, has a rate constant of \(1.10 \times 10^{-4} \mathrm{~s}^{-1}\) at \(470^{\circ} \mathrm{C}\) and an activation energy of \(264 \mathrm{~kJ} / \mathrm{mol}\). What is the temperature of the reaction when the rate constant is equal to \(4.36 \times 10^{-3} \mathrm{~s}^{-1}\) ? a. \(240^{\circ} \mathrm{C}\) b. \(150^{\circ} \mathrm{C}\) c. \(540^{\circ} \mathrm{C}\) d. \(450^{\circ} \mathrm{C}\)
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