   Chapter 12, Problem 86AE

Chapter
Section
Textbook Problem

# Sulfuryl chloride (SO2Cl2) decomposes to sulfur dioxide (SO2) and chlorine (Cl2) by reaction in the gas phase. The following pressure data were obtained when a sample containing 5.00 × 10−2 mol sulfuryl chloride was heated to 600. K in a 5.00 × 10−1-L container. Time (hours): 0.00 1.00 2.00 4.00 8.00 16.00 P SO 2 Cl 2 ( atm ) : 4.93 4.26 3.52 2.53 1.30 0.34 Defining the rate as − Δ [ SO 2 Cl 2 ] Δ t ,a. determine the value of the rate constant for the decomposition of sulfuryl chloride at 600. K.b. what is the half-life of the reaction?c. what fraction of the sulfuryl chloride remains after 20.0 h?

(a)

Interpretation Introduction

Interpretation: The pressure data obtained when a sample containing 5.00×102mol sulfuryl chloride was heated to 600K in a 5.00×101L container is given. The answers are to be given for each option.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The differential rate law provides the rate of a reaction at specific reaction concentrations.

The half-life of the first order reaction is calculated using the formula,

t12=0.693k

To determine: The value of the rate constant (k) for the decomposition of sulfuryl chloride (SO2Cl2) at 600K

Explanation

Explanation

Given

Temperature is 600K .

Given table,

 Time (hours) 0 1 2 4 8 16 PSO2Cl2(atm) 4.93 4.26 3.52 2.53 1.3 0.34

The formula of ideal gas law is,

PV=nRTnV=PRTM=PRT

Where,

• P is the total pressure.
• V is the volume.
• n is the total moles.
• R is the universal gas constant (0.08206Latm/Kmol) .
• T is the absolute temperature.
• M is the concentration.

The concentration of SO2Cl2 is calculated for each given pressure using the above equation. The value of concentration and ln[SO2Cl2] is,

 Pressure Concentration of SO2Cl2 (M=PRT) ln[SO2Cl2] 4.93 0.100079 −2.3 4.26 0.0865 −2.45 3

(b)

Interpretation Introduction

Interpretation: The pressure data obtained when a sample containing 5.00×102mol sulfuryl chloride was heated to 600K in a 5.00×101L container is given. The answers are to be given for each option.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The differential rate law provides the rate of a reaction at specific reaction concentrations.

The half-life of the first order reaction is calculated using the formula,

t12=0.693k

To determine: The half life of the given reaction.

(c)

Interpretation Introduction

Interpretation: The pressure data obtained when a sample containing 5.00×102mol sulfuryl chloride was heated to 600K in a 5.00×101L container is given. The answers are to be given for each option.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The differential rate law provides the rate of a reaction at specific reaction concentrations.

The half-life of the first order reaction is calculated using the formula,

t12=0.693k

To determine: The fraction of sulfuryl chloride (SO2Cl2) left after 20hours .

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