   Chapter 12, Problem 32E

Chapter
Section
Textbook Problem

# The following data were obtained for the gas-phase decomposition of dinitrogen pentoxide, 2N 2 O 5 ( g ) → 4 NO 2 ( g ) + O 2 ( g ) [N2O5]0(mol/L) Initial Rate (mol/L · s) 0.0750 8.90 × 10−4 0.190 2.26 × 10−3 0.275 3.26 × 10−3 0.410 4.85 × 10−3 Defining the rate as −∆[N2O5]/ ∆t write the rate law and calculate the value of the rate constant

Interpretation Introduction

Interpretation: A gas phase decomposition reaction of dinitrogen pentoxide and its rate expression is given. The rate law and the value of the rate constant are to be calculated.

Concept introduction: The change in the concentration of the reactants or the products formed in a chemical reaction per unit time is known as the rate of the given chemical reaction. The relation between the reaction rate and the concentration of the reactants is stated by the rate law.

To determine: The rate law for the given reaction.

Explanation

Given

The stated reaction is,

2N2O5(g)4NO2(g)+O2(g)

The rate law for the given reaction is calculated by the expression,

Rate=k[N2O5]n

Where,

• [N2O5] is the concentrations of N2O5 .
• k is the rate constant.
• n is the order of the reaction.

The value of n is calculated by the comparison of the different initial rate values from the given table.

The value of n is calculated using the first and second result. Substitute the values of the concentration of [N2O5] in the last two experiments in the above expression.

Rate1=k[0.0750]n

Rate2=k[0.190]n

According to the given rate values in the table,

Rate4Rate3=2.26×103mol/Ls8.90×104mol/Ls

Therefore,

k[0.190]nk[0.0750]n=2.26×103mol/Ls8.90×104mol/Ls(2.53)n=2.53n=1

Substitute the values of n in the rate law expression.

Rate=k[N2O5]1

To determine: The value of the rate constant, k

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