   Chapter 14, Problem 17PS

Chapter
Section
Textbook Problem

The decomposition of SO2Cl2 is a first-order reaction:SO2Cl2(g) → SO2(g) + Cl2(g)The rate constant for the reaction is 2.8 × 10−3 min−1 at 600 K. If the initial concentration of SO2Cl2 is 1.24 ×10−3 mol/L, how long will it take for the concentration to drop to 0.31 × 10−3 mol/L?

Interpretation Introduction

Interpretation: The time required for the reaction has to be given.

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,

Reactionrate = k [SO2Cl2].Given:The reaction is first order reaction,rate law is , ln[SO2Cl2]t=-kt+ln[SO2Cl2]0time = 27minsTherefore,ln[SO2Cl2]t=-kt+ ln[SO2Cl2]0ln (0.31×103mol/L)     = (2.8×103min1)(t)+ ln(1

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