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Chapter 7: Problem 156

For the reaction \(\mathrm{W}+\mathrm{X} \rightarrow \mathrm{Y}+\mathrm{Z}\), the rate \((\mathrm{dx} / \mathrm{dt})\) when plotted against time ' \(\mathrm{t}\) ' gives a straight line parallel to time axis. The order and rate for this reaction are a. \(\mathrm{O}, \mathrm{K}\) b. \(1, \mathrm{~K}+1\) b. II, \(\mathrm{K}+1\) d. \(\mathrm{K}, \mathrm{K}+1\)

Short Answer

Expert verified
The order is 0, and the rate is K (option a).

Step by step solution

01

Understanding the Problem

The question involves a chemical reaction where the rate of change in concentration with respect to time is plotted, and it gives a straight line parallel to the time axis. We need to find the order and the rate constant of this reaction.
02

Interpreting the Graph

A straight line parallel to the time axis indicates that the rate of the reaction does not change over time. This behavior is characteristic of a zero-order reaction.
03

Identify Reaction Order

In a zero-order reaction, the rate of reaction is constant and does not depend on the concentration of the reactants. Hence, the order of this reaction is 0.
04

Determine Rate

Since the rate of a zero-order reaction is constant, it is equal to the rate constant, denoted by 'K'. Thus, the rate of reaction is also given by the rate constant K.
05

Choose the Correct Option

From the options provided, the correct match for a zero-order reaction rate and order is option 'a', where the order is 0 and the rate is K.

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Key Concepts

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

Rate Constant in Zero-Order Reactions
When talking about zero-order reactions, one of the key attributes is the rate constant, typically denoted by the letter "K". In these reactions, the rate constant represents the speed at which the reaction proceeds over time. Unlike reactions that are dependent on the concentration of reactants, zero-order reactions progress at a constant rate. This means that instead of accelerating or slowing down, they simply proceed at a steady pace until depletion of the reactants or other limiting factors.
  • The rate constant in zero-order reactions is unique because it equates directly to the reaction rate. This constancy turns the equation into a simple expression where the rate equals "K".
  • This makes zero-order kinetics stand out as they are much simpler to model and predict over time compared to reactions of higher orders.
  • Typical scenarios where zero-order reactions occur include reactions on surfaces or catalytic processes where the reactant saturation level reaches a maximum and doesn't increase despite an increase in concentration.
Understanding Reaction Rate in Zero-Order Reactions
In any chemical reaction, the reaction rate tells us how quickly the reactants are transformed into products. For a typical zero-order reaction, the reaction rate remains constant over time, which is different from most other reactions where the rate changes as the concentrations of reactants decrease. This is because, in a zero-order reaction, the reaction rate is not influenced by changes in concentrations.
  • Because the rate is constant, it creates a simple linear plot when graphing the concentration of reactants versus time, resulting in a straight line parallel to the time axis.
  • This constant reaction rate simplifies calculations as it allows us to easily predict how long the reaction will take to reach completion under the given conditions.
  • It also implies that the same amount of reactant is used up in equal intervals of time until the reactants are exhausted.
Order of Reaction: Zero-Order Explained
The concept of the order of reaction is fundamental in understanding how different reactant concentrations affect the rate of a chemical reaction. In zero-order reactions, something quite unique occurs: the reaction rate does not depend on the concentration of the reactants. This means that even if you increase the concentration of the reactants, the reaction still proceeds at the same rate.
  • The order of a reaction is 0 when changes in the reactant concentrations have no effect on the rate. This is because the rate is already dictated by other factors, such as a surface or enzyme being saturated with the reactant.
  • Zero-order kinetics are usually observed in reactions where an external factor, rather than reactant concentration, governs the speed, such as light intensity in photochemical reactions or surface area in catalytic reactions.
  • Identifying that a reaction is zero-order helps in simplifying the mathematical descriptions to predict the behavior of the reaction over time.

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Most popular questions from this chapter

The reaction: \(2 \mathrm{HI} \rightarrow \mathrm{H}_{2}+\mathrm{I}_{2}\), is second order and the rate constant at \(800 \mathrm{~K}\) is \(9.70 \times 10^{-2} \mathrm{M}^{-1} \mathrm{~s}^{-1}\). How long will it take for \(8.00 \times 10^{-2}\) mol/litre of HI to decrease to one-fourth of its initial concentration? a. \(587 \mathrm{~s}\) b. \(387 \mathrm{~s}\) c. \(148 \mathrm{~s}\) d. \(687 \mathrm{~s}\)

The calculation of the Arrhenius factor is based on the a. Idea that the reactant species must come together, leading to the formation of the transition state which then transforms into the products b. Idea that, for a reaction to take place, the reactant species must come together c. Calculation of the order of thereaction d. Calculation of the molecularity of the 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

A three-step mechanism has been suggested for the formation of carbonyl chloride: Step I: \(\mathrm{Cl}_{2} \rightarrow 2 \mathrm{Cl}\) Step II: \(\mathrm{Cl}+\mathrm{CO} \rightarrow \mathrm{COCl}\) Step III: \(\mathrm{COCl}+\mathrm{Cl}_{2} \rightarrow \mathrm{COCl}_{2}+\mathrm{Cl}\) Which species is an intermediate in the mechanism? a. \(\mathrm{COCl}_{2}\) b. \(\mathrm{COCl}\) c. \(\mathrm{Cl}\) d

The reaction of hydrogen and iodine monochloride is given as:\(\mathrm{H}_{2}(\mathrm{~g})+2 \mathrm{ICl}(\mathrm{g}) \rightarrow 2 \mathrm{HCl}(\mathrm{g})+\mathrm{I}_{2}(\mathrm{~g})\) This reaction is of first order with respect to \(\mathrm{H}_{2}(\mathrm{~g})\) and ICl (g), following mechanisms were proposed: Mechanism (1): \(\mathrm{H}_{2}(\mathrm{~g})+2 \mathrm{ICl}(\mathrm{g}) \rightarrow 2 \mathrm{HCl}(\mathrm{g})+\mathrm{I}_{2}(\mathrm{~g})\) Mechanism (2): \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{ICl}(\mathrm{g}) \rightarrow \mathrm{HCl}(\mathrm{g})+\mathrm{HI}_{2}(\mathrm{~g}) ;\) slow \(\mathrm{HI}(\mathrm{g})+\mathrm{ICl}(\mathrm{g}) \rightarrow \mathrm{HCl}(\mathrm{g})+\mathrm{I}_{2}(\mathrm{~g}) ;\) fast Which of the above mechanism(s) can be consistent with the given information about the reaction? a. 2 only b. Both 1 and 2 c. Neither 1 nor 2 d. I only
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