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Chemistry

9th Edition
Steven S. Zumdahl
ISBN: 9781133611097

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Chemistry

9th Edition
Steven S. Zumdahl
ISBN: 9781133611097
Textbook Problem

One experimental procedure that can be used to determine the rate law of a reaction is the method of initial rates. What data are gathered in the method of initial rates, and how are these data manipulated to determine k and the orders of the species in the rate law? Are the units for k. the rate constant, the same for all rate laws? Explain. If a reaction is first order in A, what happens to the rate if [A] is tripled? If the initial rate for a reaction increases by a factor of 16 when [A] is quadrupled, what is the order of n? If a reaction is third order in A and [A] is doubled, what happens to the initial rate? If a reaction is zero order, what effect does [A] have on the initial rate of a reaction?

Interpretation Introduction

Interpretation: An explanation regarding the various questions related to the method of initial rates, a procedure used to determine the rate law of a reaction is to be stated.

Concept introduction: The differential rate law provides the rate of a reaction at specific reaction concentrations. The instantaneous rate of a reaction that is measured initially or at t=0 is known as the initial rate of the reaction. The unit of the rate constant k is different for all the rate laws

To determine: An explanation regarding the various questions related to the method of initial rates.

Explanation

To determine: An explanation regarding the data gathered in the method of initial rates and the manipulation of this data to obtain the value of k .

The instantaneous rate of a reaction that is measured initially or at t=0 is known as the initial rate of the reaction.

In the stated method, the initial concentration of the reactants and the initial rate of the reaction are obtained. A rate equation is assumed using variables like m and n . These determine the order of the reaction.

For a reaction,

aA+ bBcC + dD

Rate=k[A]m[B]n

Where,

  • [A] and [B] are the molar concentrations of the reactants ‘A’ and ‘B’ respectively.
  • k ’ is the rate constant.
  • m and n are the reaction orders.

A rate law equation is written for every initial rate. The correct value of the variables is determined by solving these equations.

Therefore, the orders of the stated reactants are found (with respect to the individual reactants). The value of the rate constant, k , is determined by substitution of the initial concentration and the initial rate value in the rate law equation.

To determine: If the unit of k is different for all rate laws.

Solution: The unit of k is different for all the rate laws.

The rate constant is denoted by the symbol ‘ k ’. The general formula for calculating the units of the rate constant is expressed as,

Unit of the rate constant =mol1(n)L(n)1s1 .

Where,

  • n ’ is the order of the reaction.

Therefore, the unit of k is different for different order of a reaction

To determine: The effect on the rate of a reaction for a reaction of first order in A if the [A] is tripled.

For a reaction,

AProducts

Rate=k[A]1

Where,

  • [A] is the molar concentrations of the reactant ‘A’.
  • k ’ is the rate constant.
  • 1 is the order of the reaction.

If [A] is tripled,

Rate=k[3A]1=3k[A]

Therefore, the rate of the reaction is tripled.

To determine: The order of the reaction if the initial rate of a reaction increases by a factor of 16 when [A] is quadrupled

For a reaction,

AProducts

Rate=k[A]n

Where,

  • [A] is the molar concentrations of the reactant ‘A’

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