   Chapter 12, Problem 107CP

Chapter
Section
Textbook Problem

# You are studying the kinetics of the reaction H2(g) + F2(g) ⟶ 2HF(g) and you wish to determine a mechanism for the reaction. You run the reaction twice by keeping one reactant at a much higher pressure than the other reactant (this lower-pressure reactant begins at 1.000 atm). Unfortunately, you neglect to record which reactant was at the higher pressure, and you forget which it was later. Your data for the first experiment are: Pressure of HF (atm) Time(min) 0 0 0.300 30.0 0.600 65.8 0.900 110.4 1.200 169.1 1.500 255.9 When you ran the second experiment (in which the higher pressure reactant was run at a much higher pressure), you determine the values of the apparent rate constants to be the same. It also turns out that you find data taken from another person in the lab. This individual found that the reaction proceeds 40.0 times faster at 55°C than at 35°C. You also know, from the energy-level diagram, that there are three steps to the mechanism, and the first step has the highest activation energy. You look up the bond energies of the species involved and they are (in kJ/mol): H8H (432), F8F (154), and H8F (565).a. Sketch an energy-level diagram (qualitative) that is consistent with the one described previously. Hint: See Exercise 106.b. Develop a reasonable mechanism for the reaction.c. Which reactant was limiting in the experiments?

(a)

Interpretation Introduction

Interpretation: An energy-level diagram (qualitative) that is consistent with the described experiment is to be sketched. A reasonable mechanism for the reaction is to be developed. The limiting reactant is to be stated.

Concept introduction: The energy profile diagram is a plot of reaction coordinate and the energy of reactants and products.

The energy profile diagram clearly tells the information regarding energy of reactants and products.

To determine: The sketch of an energy level diagram that is consistent with the given experiment.

Explanation

Explanation

Given

The given reaction is stated as,

H2(g)+F2(g)2HF(g)

The values of temperature and rate constant from the data are,

T1=35°CT2=55°Ck2k1=40

To draw an energy level diagram the activation energy is to be known.

With the help of the activation energy the reactants and the products are decided.

With the help of the given data the activation energy is calculated by the formula,

Rate2Rate1=k2k1ln(k2k1)=EaR(1T11T2)

Where,

• k1,k2 are the reaction rate constants.
• T1,T2 are the temperatures.
• Ea is the energy of activation.
• R is a gas constant.

Substitute the values of k1,k2,T1,T2 and R to calculate the activation energy.

ln(k2k1)=EaR(1T11T2)ln(40)=Ea8.314J/Kmol(1308K1328K)3.688=Ea8.314J/Kmol(0

(b)

Interpretation Introduction

Interpretation: An energy-level diagram (qualitative) that is consistent with the described experiment is to be sketched. A reasonable mechanism for the reaction is to be developed. The limiting reactant is to be stated.

Concept introduction: The energy profile diagram is a plot of reaction coordinate and the energy of reactants and products.

The energy profile diagram clearly tells the information regarding energy of reactants and products.

To determine: The reasonable mechanism for the given reaction.

(c)

Interpretation Introduction

Interpretation: An energy-level diagram (qualitative) that is consistent with the described experiment is to be sketched. A reasonable mechanism for the reaction is to be developed. The limiting reactant is to be stated.

Concept introduction: The energy profile diagram is a plot of reaction coordinate and the energy of reactants and products.

The energy profile diagram clearly tells the information regarding energy of reactants and products.

To determine: The limiting reactant in the given experiment.

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