   Chapter 14, Problem 16PS

Chapter
Section
Textbook Problem

The decomposition of N2O5 in CCl4 is a first-order reaction. If 2.56 mg of N2O5 is present initially and 2.50 mg is present after 4.26 minutes at 55 °C, what is the value of the rate constant, k?

Interpretation Introduction

Interpretation: The rate constant of the reaction has to be found.

Concept introduction:

Rate law or rate equation: The relationship between the reactant concentrations and reaction rate is expressed by an equation.

aA + bBxXRate of reaction = k [A]m[B]n

Order of a reaction: The order of a reaction with respect to a particular reactant is the exponent of its concentration term in the rate law expression, and the overall reaction order is the sum of the exponents on all concentration terms.

Rate constant, k: It is a proportionality constant that relates rate and concentration at a given temperature.

Explanation

The reaction rate of the chemical reaction is calculated as,

Given:The reaction is first order reaction,rate law is , ln[N2O5]t=-kt+ln[N2O5]0time = 27minsTherefore,ln[N2O5]t=-kt+ ln[N2O5]0ln (2.50 mg) = (k)(4.26mins)+ ln(2

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