Chapter 14.3, Problem 14.3CYU

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# The initial rate (‒ Δ[NO]/ Δt] of the reaction of nitrogen monoxide and oxygenNO(g) + ½2O2(g) → NO2(g)was measured for various initial concentrations of NO and O2 at 25 °C. Determine the rate equation from these data. What is the value of the rate constant, k, and what are its units?

Interpretation Introduction

Interpretation: The reaction rate and the value of rate constant 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 given as,

â€‚Â ReactionÂ Rateâ€‰Â =Â kÂ [NO]m[O2]n,whereÂ m,Â andÂ nÂ areÂ ordersÂ ofÂ theÂ reactants.Givenâ€‰reaction:Â NO(g)+Â 1/2Â O2(g)Â®NO2(g)â€‰Orderâ€‰ofâ€‰theâ€‰reaction:_*Comparingâ€‰firstâ€‰twoâ€‰experimentsâ€‰1â€‰andâ€‰2,rateâ€‰1=â€‰kÂ [NO]1m[O2]1n,Â rate1Â =Â 0.028Â mol/L.hrateâ€‰2Â =Â kÂ [NO]2m[O2]2n,Â rateÂ 2Â =Â 0.057Â mol/L.hrate2rateâ€‰1=kÂ [NO]2m[O2]2nkÂ [NO]1m[O2]1n0.057â€‰mol/L.h0.028â€‰mol/L.h=(0.020)m(0.020)n(0.020)m(0.010)nâ€‰â€‰Â 2.0Â =Â (2)nnÂ =Â 1Comparingâ€‰lastâ€‰twoâ€‰experimentsâ€‰2â€‰andâ€‰4,rateâ€‰2Â =â€‰kÂ [NO]2m[O2]2n,rateÂ 2Â =Â 0.057Â mol/L.hrateâ€‰4Â =Â kÂ [NO]4m[O2]4n,rateÂ 4Â =Â 0.227Â mol/L.hrateÂ 4rateâ€‰2Â =kÂ [NO]4m[O2]4nkÂ [NO]2m[O2]2n0

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