   # The decomposition of SO 2 Cl 2 SO 2 Cl 2 (g) → SO 2 (g) + Cl 2 (g) is first-order in SO 2 Cl 2 , and the reaction has a half-life of 245 minutes at 600 K. If you begin with 3.6 × 10 −3 mol of SO 2 Cl 2 in a 1.0-L flask, how long will it take for the amount of SO 2 Cl 2 to decrease to 2.00 × 10 −4 mol? ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 14, Problem 27PS
Textbook Problem
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## The decomposition of SO2Cl2SO2Cl2(g) → SO2(g) + Cl2(g)is first-order in SO2Cl2, and the reaction has a half-life of 245 minutes at 600 K. If you begin with 3.6 × 10−3 mol of SO2Cl2 in a 1.0-L flask, how long will it take for the amount of SO2Cl2 to decrease to 2.00 × 10−4 mol?

Interpretation Introduction

Interpretation: The time taken for the amount of SO2Cl2 has to be given.

Concept Introduction:

The rate of reaction is the quantity of formation of product or the quantity of reactant used per unit time.  The rate of reaction doesn’t depend on the sum of amount of reaction mixture used.

The raise in molar concentration of product of a reaction per unit time or decrease in molarity of reactant per unit time is called rate of reaction and is expressed in units of mol/(L.s).

Integrated rate law for first order reaction:

Consider A as substance, that gives the product based on the equation,

aAproducts

Where a= stoichiometric co-efficient of reactant A.

Consider the reaction has first-order rate law,

Rate=-Δ[A]Δt=k[A]

The integrated rate law equation can be given as,

ln[A]t[A]o=-kt

The above expression is called integrated rate law for first order reaction.

### Explanation of Solution

The time take for the amount of SO2Cl2 is calculated as,

Reactionrate = k [SO2Cl2]1.Given:t1/2=245 mins;t1/2=0.693kk=0.693245 mins=0.00283min-1[SO2Cl2]0=3.6×10-3mol/L[SO2Cl2]t=2.0×10-4mol/LTherefore,First order rate law,ln[SO2Cl2]t=-k

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