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Chemistry

9th Edition
Steven S. Zumdahl
ISBN: 9781133611097

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BuyFindarrow_forward

Chemistry

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

A reaction of the form

aA Products

gives a plot of ln[A] versus time (in seconds), which is a straight line with a slope of −7.35 X 10−3. Assuming [A]0 = 0.0100 M, calculate the time (in seconds) required for the reaction to reach 22.9% completion.

Interpretation Introduction

Interpretation: For the given reaction the time required for the 22.9% completion of the reaction is to be calculated.

Concept introduction: Rate constant is a proportionality coefficient that relates the rate of any chemical reaction at a specific temperature to the concentration of the reactant or the concentration of the product.

Order of reaction is a part of reaction which present as a power of concentration of reactants.

To determine: The amount of time required for the reaction to reach 22.9% completion.

Explanation

Explanation

Given

The reaction is given as,

aAproducts

The plot of ln[A] Vs time (sec) is a straight line with a slop of 7.35×103 .

The initial concentration of the reactant (A) is 0.0100M .

The given straight line plot is a compulsory condition of first order reaction. Therefore, the given reaction is the first order reaction.

For the first order reaction the integrated rate law is given by the equation,

ln[A]=kt+ln[A0]

Where,

  • ln[A] is the concentration of the reactant.
  • ln[A0] is the initial concentration of the reactant.
  • k is the slop and is known as rate constant.
  • t is the time.
  • The negative sign shows the negative slop of the straight line.

The above exactly a form of equation of straight line that is given as,

y=mx+c

Where,

  • y is the vertical axis.
  • x is the horizontal axis.
  • m is the slope of the straight line.
  • c is the intercept on y -axis.

The first order reaction clearly indicates the straight line plot of ln[A] Vs time. The negative value of slope is 7.35×103 . Therefore, the value of k is 7.35×103

The half life of the first order reaction is given by the formula,

kt1/2=0.693

Where,

  • t1/2 is the half life.

Substitute the value of rate constant in the above equation.

kt1/2=0.693(7.35×103)t1/2=0.693t1/2=0.6937.35×103=94

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