EEEC 507 Spring 2016

SOLUTION -- HW 1: REVIEW of BASIC KINETIC CONCEPTS

1. Why are chemical reactions important to energy, environmental and process engineering?

Name as many reasons as you can think of.Chemical reactions are heavily involved in all

these fields mentioned above, interacting with almost all the chemical substances in the

systems. Actually it is the core and also the fundamental of universe. Reasons can be

various.

2. What is a chemical reaction?

3. What do we mean by reaction stoichiometry? What does stoichiometry represent? What is

the convention used for stoichiometric coefficients of products, reactants, inerts?

4. What is a mole? What is the relationship between a kmole and a mole? What is the

relationship between a lb-mole and a mole?

The mole is a unit of measurement for amount of substance. It is defined as the amount of

any chemical substance that contains as many elementary entities. This number is

expressed by the Avogadro constant, which has a value of 6.022×1023. In other words, the

mole is the name given to an amount of a substance equal in mass (in grams) to the

combined mass (in amu) of the atoms of the constituent molecules of the substance

multiplied by Avogadro's number.

1 kmole = 1000 mole, 1 lb-mole = 453.4 mole

Consider a single reaction systemand answer questions 5-7.

5. Progress of a single reaction of known stoichiometry can be represented by a molar extent

of reaction. What is the relationship between the moles of reactants, products and inerts

present in the system at some state of the system when extent of reaction is nonzero and

the initial moles of each component in the system their stoichiometric coefficients and the

reaction extent?

The amount of inerts does not include in the expression.

6. Relate the molar extent of reaction to the fractional conversion of the limiting reactant, its

initial moles and its stoichiometric coefficient. What is the limiting reactant?

If A is the limiting reactant then nA=0, xA=1, XA= nA0/-νA

7. What is the relationship between mole fraction of products and reactants and reaction

extent?

0

0

j j

j

tot j

n v Xy

n v X

8. Extend the relationship developed in answering question 5. to multiple reactions consisting

of R independent reactions between S species?

9. In a set of R’ stoichiometric reactions between S species how would you determine

the set R of independent reactions?

10. What is the rate of reaction? What does the rate of reaction depend on? What form

can the rate dependence on concentration of reactants and products take?

The dependence of the rate on concentrations is presented by a power law

function. Take an irreversible reaction a A + b B → p P , an n-th order rate form is

A Br kC C .

11. What temperature dependence does the rate of reaction exhibit? What is the

meaning of the activation energy for the reaction? Can it be always defined?

1 2

/( )

1

(T) (C)

0 Arrhenius form

(T) 1/ 2 Collision theory

1 Transition state theory

m E RT

R f f

m

f AT e m

m

The activation energy describes the minimum energy which must be

available to a chemical system with potential reactants to result in a chemical

reaction. Activation energy may also be defined as the minimum energy required to

start a chemical reaction. It cannot be always defined (Question 15 is an example).

12. What is the Arrhenius form of the rate constant? What is the meaning of the

activation energy in the Arrhenius form./(RT)

0

ER k e

The activation energy is the threshold energy that the reactant(s) must

acquire before reaching the transition state. A reaction with a large activation

energy requires much more energy to reach the transition state. Likewise, a reaction

with a small activation energy doesn't require as much energy to reach the transition

state.

13.Which reaction rate constant increases more rapidly with temperature, the one with lower or higher activation energy?

The higher one. Because lnk=lnk0-E/(RT), so d lnk/d T = E/(RT2) is larger when E is higher.

14. How can an n-th order reaction rate be represented? If (mol/L) units are used for

concentration and time is measured in seconds what are the units for the rate

constant?n

Ar kC

Units for the rate constant are 1( / ) /nL mol s

15. Can the temperature and composition dependence term be separated in reaction rates that follow the Langmuir-Hinshelwood (Hougen-Watson) form? Can an activation energy be defined for the rate from of that type?

No for both.

16. What is molar internal energy? What is it a function of?

Internal energy is defined as the energy associated with the random, disordered motion of molecules. Molar internal energy is the internal energy expressed relative to units of amount of substance(mol), which unit is J/mol.

The internal energy of a given state of a system cannot be directly

measured. It is determined through some convenient chain of thermodynamic

operations and thermodynamic processes by which the given state can be prepared,

starting with a reference state which is customarily assigned a reference value for

its internal energy. Such a chain, or path, can be theoretically described by certain

extensive state variables of the system, namely, its entropy, S, its volume, V, and its

mole numbers, {Nj}. The internal energy, U(S, V, {Nj}), is a function of those. So molar internal energy is a function of entropy and volume.

17. How is molar enthalpy defined? What about partial molar enthalpy? What

information is needed to calculate it at a given temperature and composition?

Enthalpy(H) is defined as a state function that depends only on the prevailing

equilibrium state identified by the variables internal energy(U), pressure(p), and

volume(V). H = U + pV. Molar enthalpy Hm = H/n, where n is the number of

moles.

A partial molar property is a thermodynamic quantity which indicates how

an extensive property of a solution or mixture varies with changes in

the molar composition of the mixture at constant temperature and pressure.

Essentially it is the partial derivative of the molar enthalpy with respect to the

amount (number of moles) of the component of interest.

To calculate the partial molar property of a binary solution, one begins

with the pure component denoted as and, keeping the temperature and pressure

constant during the entire process, add small quantities of component ;

measuring after each addition. After sampling the compositions of interest one

can fit a curve to the experimental data. This function will be .

Differentiating with respect to will give . is then obtained from the

relation:

18. What is the standard heat of reaction?

The standard enthalpy of reaction (denoted ΔHr⊖) is the enthalpychange that

occurs in a system when one mole of matter is transformed by a chemical reactions

under standart conditions, defined as at a temperature of 298.15K and a pressure of

1 atm.

19. What is molar Gibbs free energy in terms of molar enthalpy and entropy?

m m mG H TS

20. What is the thermodynamic condition for equilibrium in a reactive system?

The Gibbs free energy is at a minimum:

21. How is the thermodynamic equilibrium constant defined?

22. How is the standard Gibbs free energy for reaction calculated and how does it relate

to the equilibrium constant?

23. What is Van’t Hoff’s equation for variation of equilibrium constant with

temperature?Th

This is called van Hoff’s equation.

24. How can one calculate the heat of reaction as a function of temperature?

dΔH/dT = ΔCp. Integration of this equation from standard condition can calculate the heat of reaction when Cp(T) is known.Or calculate numerically:ΔH⊖=∑ΔvpΔH⊖f(products)−∑ΔvrΔH⊖f(reactants)\withvp= stoichiometric coefficient of the product from the balanced reactionvr= stoichiometric coefficient of the reactants from the balanced reactionΔHºf= standard enthalpy of formation for the reactants or the products

25. Does the equilibrium constant have units?

No.

26. How does one relate activity to mole fraction? Activity to concentration?

27. Show using customary notation how to calculate the equilibrium conversion of

SO2 reacting with air at 25˚C and at 600˚C when P= 1 atm for a feed that

contains: i) stoichiometric ratio of reactants only, ii) stoichiometric ratio of

reactants when using air as oxygen source, iii)very large excess of air . For which

of these three cases would the equilibrium conversion be the highest? Explain why!

i)

or T=25℃=298K

Solve equation (C)

When at 298 K, high K298 value results in Xe almost close to 1. So

2 , 1SO eqx

ii) 2 2,0 ,0/ 0.79 / 0.21 3.76N On n

3 3.76 6.76totn X X

Similarly as in part i),

2

3

(6.76 )

(1 )y

X XK

X

2

2

, @298

, @873

1

0.7080

SO eq K

SO eq K

x

x

iii) When with large access of air, 2Oy becomes constant equals to 0.21. So

2

20.21(1 )y

XK

X

2

2

, @298

, @873

1

0.8349

SO eq K

SO eq K

x

x

In conclusion, the equilibrium conversion is highest for case iii. It is easy to understand because all the SO2 can be reacted due to the large amount of O2.

28. What would happen to the equilibrium conversion in problem 27 above if you: i)

lowered the temperature from 6000 to 200˚C; ii) if you raised the pressure of

operation from 1 to 100 atm.

i) Exothermic reaction, thus lower temperature gives rise to higher equilibrium

conversion.

ii) With larger number of moles of gas on the reactant side, an increase in pressure

will result in a higher equilibrium conversion.

29. What is the kinetic definition of equilibrium? What constraint does that impose on

the reaction forms for the reverse and forward reactions?

Chemical kinetics is concerned with the rate of a chemical reaction. So in

a reversible reaction, chemical equilibrium is reached when the rates of the forward

and reverse reactions are equal (the principle of detailed balance) and the

concentrations of the reactants and products no longer change.

30. If Arrhenius form is used to represent the rate constant kc ((mol/L)1-n s-1) when

concentration is used for the driving force and the rate constant for the same gas

phase reaction is evaluated as kp (mol/L) atm-n s-1) when parital pressure ios used

for the driving force, what is the relationship between kco and kpo and EP and Ec?

Assume ideal gas law holds as the equation of state.

2

2

0

0 0

0

(ln )

( ) (ln )

combine previous two equations and ( )

c

n

p

c cn n

c A p A n

c p c p

p pA A

E

RTc c n

c pE

RTp p

d k E

r k C k P dT RTk k RT E E nRT

d k EP C RT

dT RT

k k ek k RT e

k k e