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Chapter 8: Problem 184

Match the following: List I List II 1\. zero order reaction (p) mole- \({ }^{1} \mathrm{Lt} \sec -1\) 2\. first order reaction (q) \(\mathrm{mole}-{ }^{2}\) Lt2 \(\mathrm{sec}-1\) 3\. second order reaction (r) mole Lt- \({ }^{-1} \sec -1\) 4\. third order reaction (s) \(\sec -1\)

Short Answer

Expert verified
1-p, 2-s, 3-r, 4-q.

Step by step solution

01

Interpretation of Matching Rules

To solve this match-the-following exercise, we need to first understand the rate laws of each order of reaction and match them to the correct units in List II.
02

Rate Law for Zero Order Reaction

A zero order reaction has a rate law: \( \text{Rate} = k \). The rate constant \( k \) here has units that result in the rate of reaction units \( \text{mole} \, \text{L}^{-1} \, \text{sec}^{-1} \). Hence the unit that matches is \( \text{mole}-^{1} \text{Lt} \sec^{-1} \) which corresponds to list item (p).
03

Rate Law for First Order Reaction

A first order reaction has a rate law: \( \text{Rate} = k[A] \). The rate constant \( k \) has units \( \sec^{-1} \) to ensure the resultant rate has units \( \text{mole} \, \text{L}^{-1} \, \text{sec}^{-1} \). This corresponds to list item (s).
04

Rate Law for Second Order Reaction

A second order reaction can be written as \( \text{Rate} = k[A][B] \) or \( \text{Rate} = k[A]^2 \). The rate constant \( k \) has units \( \text{mole}^{-1} \text{L} \sec^{-1} \), thereby producing rate units of \( \text{mole} \, \text{L}^{-1} \, \text{sec}^{-1} \). Therefore, it should match with item (r).
05

Rate Law for Third Order Reaction

A third order reaction typically written as \( \text{Rate}=k[A]^2[B] \) or similar combinations. Its rate constant \( k \) will have units \( \text{mole}^{-2} \text{L}^2 \sec^{-1} \), ensuring the expression remains dimensionally consistent. This matches with item (q).
06

Final Matched Results

Based on the calculated rate law units for each order, the matches are: 1. Zero order reaction matches with (p) 2. First order reaction matches with (s) 3. Second order reaction matches with (r) 4. Third order reaction matches with (q).

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Key Concepts

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

Rate Law
Understanding the rate law of a reaction is essential for grasping the concept of reaction order and rates. The rate law expresses the rate of a chemical reaction as a function of the concentration of its reactants. In simpler terms, it shows how the speed of a reaction depends on the substances involved.

  • **Zero-order reactions**: The rate is independent of the concentration of the reactant(s). The rate law is expressed as: \( \text{Rate} = k \). Here, \( k \) is the rate constant with units of \( \text{mole}^-1 \text{Lt} \sec^{-1} \).

  • **First-order reactions**: The rate is directly proportional to the concentration of one reactant. It follows the law: \( \text{Rate} = k[A] \). The unit for \( k \) is \( \sec^{-1} \), ensuring the rate has units of \( \text{mole} \, \text{L}^{-1} \, \text{sec}^{-1} \).

  • **Second-order reactions**: These reactions depend on the concentration of one reactant squared, or two reactants. The rate law is: \( \text{Rate} = k[A]^2 \) or \( \text{Rate} = k[A][B] \). Here, the unit for \( k \) is \( \text{mole}^{-1} \text{Lt} \sec^{-1} \).

  • **Third-order reactions**: Dependent on either the concentration tripled or combinations like \( A^2[B] \). The rate law defines \( k \) with units of \( \text{mole}^{-2} \text{Lt}^2 \sec^{-1} \).
Reaction Kinetics
Reaction kinetics explores the rate at which a reaction progresses and the factors impacting this rate. It delves into the pathways and steps within a chemical reaction. Knowing the kinetics is crucial for predicting how a reaction behaves over time.

Several factors affect reaction kinetics, including:
  • **Concentration of reactants**: Higher concentrations generally increase the rate of reaction due to more frequent collisions between molecules.

  • **Temperature**: Raising the temperature speeds up reactions by providing more energy, which increases the frequency and intensity of collisions.

  • **Catalysts**: These substances lower the activation energy needed for a reaction, increasing the rate without being consumed in the process.

  • **Surface area**: More surface area allows more collisions and, as a result, a faster reaction rate.
Understanding these factors helps chemists to control and optimize reactions for desired outcomes.
Reaction Order Units
Reaction order is a classification of reactions based on how the concentration of reactants affects the rate. For each order, the rate law is different and has specific units for the rate constant to maintain consistency.

The units of the rate constant (\( k \)) vary depending on the reaction order:
  • **Zero-order**: Units of \( k \) are \( \text{mole}^1 \text{Lt}^{-1} \sec^{-1} \). This indicates that the rate is independent of the concentration of reactants.

  • **First-order**: The units are \( \sec^{-1} \), reflecting a direct proportionality to a single reactant's concentration.

  • **Second-order**: For these reactions, \( k \)'s units are \( \text{mole}^{-1} \text{Lt} \sec^{-1} \). This accounts for either a single reactant squared or two reactants.

  • **Third-order**: Here, the units are \( \text{mole}^{-2} \text{Lt}^2 \sec^{-1} \), accounting for reactant combinations such as \( [A]^2[B] \).
By understanding the units of the rate constant, chemists can deduce the order of the reaction and predict the reaction's behavior under various conditions.

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Most popular questions from this chapter

Which of the following is incorrect about order of reaction? a. it is calculated experimentally b. it is sum of powers of concentration in rate law expression c. the order of reaction cannot be fractional d. there is not necessarily a connection between order and stoichiometry of a reaction.

The equation of tris(1,10-phenanthroline) iron(II) in acid solution takes place according to the equation: \(\mathrm{Fe}(\text { phen })_{3}^{2+}+3 \mathrm{H}_{3} \mathrm{O}^{+}+3 \mathrm{H}_{2} \mathrm{O} \rightarrow\) \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}+3\) (phen) \(\mathrm{H}^{+}\) If the activation energy (Ea) is \(126 \mathrm{~kJ} / \mathrm{mol}\) and the rate constant at \(30^{\circ} \mathrm{C}\) is \(9.8 \times 10^{-3} \mathrm{~min}^{-1}\), what is the rate constant at \(50^{\circ} \mathrm{C}\) ? a. \(2.2 \times 10^{-1} \mathrm{~min}^{-1}\) b. \(3.4 \times 10^{-2} \mathrm{~min}^{-1}\) c. \(0.23 \times 10^{-1} \mathrm{~min}^{-1}\) d. \(1.2 \times 10^{-1} \min ^{-1}\)

For a first order reaction, a. The degree of dissociation is equal to \(\left(1-\mathrm{e}^{-\mathrm{k}} \mathrm{t}\right)\) b. The pre-exponential factor in the Arrhenius equation has the dimensions of time \(\mathrm{T}^{-1}\). c. The time taken for the completion of \(75 \%\) reaction is thrice the \(t 1 / 2\) of the reaction. d. both (a) and (b)

Which of the following statement(s) is/are incorrect? a. A plot of \(\mathrm{P}\) versus \(\mathrm{l} / \mathrm{V}\) is linear at constant temperature. b. A plot of P versus \(1 / \mathrm{T}\) is linear at constant volume. c. A plot of \(\log \mathrm{K}_{\mathrm{p}}\) versus \(1 / \mathrm{T}\) is linear d. A plot of \(\log [x]\) versus time is linear for zero order reaction.

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
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