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RATE OF REACTIONS
Speed is a change of something in a definite time interval.
The phrase 'rate of reaction' means how fast is the reaction or the speed of the reaction. It can be measured as the formation (appearance) rates of products or the consumption (disappearance) rates of reactants.
If we use the quantity of reactants or products in terms of concentration, the rate can be defined as the change in concentration of products or reactants in a determined period of time.

In the reaction,
N0₂(g) + CO(g) -->NO(g) + C0₂(g)
NO₂ and CO are consumed, NO and C0₂ are produced.
The graph of the process is as follows.

 

 

The minus (-) sign indicates the decrease in concentration of reactants, and the positive sign (+) indicates the increase in concentration of products during the given time interval.

Let us examine the decomposition reaction of dinitrogen pentoxide, N₂O₅, at 30°C. 2N₂O₅(g) --> 4N0₂(g) + 0₂(g)
The rate of the reaction in terms of reactants and products is as below.

 

Let us calculate the average rate of reaction in 30 - 90 minutes by using Graph 1. The average rate of reaction during the time interval from 30-90 minutes in terms of decreasing concentration of N₂O₅;

Ex: Find the rate relationship of reactants and products for the given reaction.
2S0₂(g) + 0₂(g) -->2S03(g)
Ex: In a 1 L container, H₂ and N₂ gases react with each other. After 20 seconds, 0.4 mol of NH₃ is produced. Express and find the reaction rate in terms of reactants and products.
Ex: If 9.10^-2 mol/L NH₃ is consumed in 3 minutes according to the reaction below;
4NH₃(g) + 50₂(g) --> 4NO(g) + 6H₂0(g)
What will be the rate of formation of NO(g) and H₂O(g) in mol/L .s?

ACTIVATION ENERGY
The minimum energy which reacting molecules must have to result in a reaction is called activation energy, and is represented by Ea.
The figure given below is a graph of potential energy versus reaction coordinate for the following exothermic reaction;
A₂ + B₂ --> 2AB

 

 

Reactions having high activation energy are slow, while reactions having low activation energy are fast at the same conditions.

 

 

 

 

POTENTIAL ENERGY DIAGRAMS
During a chemical reaction, the potential energies of reacting particles change as the reaction proceeds. These changes can be shown with the following potential energy diagrams.

The difference between the potential energies of products and reactants gives the heat of reaction.

The difference between activation energy of forward reaction  and activation energy of reverse reaction also gives the heat of a reaction.

Ex: If the potential energy diagram is given for the reaction, X + Y -->Z

a. What is the activation energy for the forward and reverse reactions?
b. What is the energy of the activated complex?
c. What is the heat of reaction (enthalpy)?
d. Is the reaction endothermic or exothermic?

 

 

 

Ex: If the activation energy of the reaction is,
CH₄(g) + 20₂(g) --> C0₂(g) + 2H₂0(g) is 64.4 kJ.
What would be the activation energy for the reverse reaction?

Ex: Draw the potential energy diagram for a reaction whose potential energy of products is 2 kJ, the activation energy for the reverse reaction is 45 kJ, and its ∆H (enthalpy) is -30 kJ.
Ex: The activation energy for the following reaction is 167 kJ,
H₂(g) + l₂(g) --> 2HI(g)
If the enthalpy of this reaction is 54 kJ, what would be the activation energy of the reverse reaction?

FACTORS AFFECTING THE RATE OF REACTION
Rate of a chemical reaction is affected by several factors. These factors are listed below.
a. Nature of the reactants
b. The concentration of reactants
c. The temperature of the system
d. The presence of a catalyst
e. Interacting area

a. Nature of the Reactants
If the number of bonds broken and formed during a reaction is very large, then the reaction is generally slow.
C₅H₁₂+  80₂ -->5C0₂ + 6H₂0  (slow)
Ag⁺ + Cu --> Cu²⁺ + Ag (fast)

The reactions between ions are very fast.
Ag⁺ + Br^-  --> AgBr (fast)
If a reaction contains many different molecules and ions, then the reaction is generally slow.
Cr₂0₇^2- + 6Fe²⁺ + 14H⁺ --> 2Cr³⁺ + 6Fe³⁺ + 7H₂0  (slow)

Ex: Compare the rates for the following reactions.
I. Pb²⁺ + 2I^- -->Pbl₂
II. 2CO + 0₂ -->2C0₂
III. 2C₄H₁₀ + 130₂ --> 8C0₂ + 10H₂0
IV. Cu²⁺ + Zn --> Zn²⁺ + Cu(s)                                     
Ex: Compare the rates of the above reactions.
I. Ba²⁺ + CO₃^2- --> BaC0₃
II. 2S0₂+ 0₂ --> 2S0₃
III. 2C₂H₆ + 70₂ --> 4C0₂ + 6H₂0

b. Concentration of Reactants
The rate of a reaction is directly proportional to the concentration of reactants; the higher the concentration of reactants, the faster the reaction occurs.

Ex: If the following reaction occurs in the single step below,
2S0₂ + 0₂ --> 2S0₃ provide the following;
a. Write the rate expression for the reaction.
b. If the concentration of S0₂ is doubled, how will the rate be affected?

Ex: Three different experimental results of the rates of the following reaction for different concentrations of A and B are given below.
 2A+ B --> D + 2E

Find;
a. The rate equation,
b. The reactants for the slow step,

c. The Temperature of the System
The rates of most reactions increase as the temperature of the system rises. It is often stated that an increase in temperature of 10 °C doubles the reaction rate.

An increase in temperature increases the number of molecules, exceeding the activation energy.
When-temperature is increased by 20 °C, the fraction of molecules with very high energies increases. Thus, the number of molecules exceeding activation energy increases and reaction occurs in a shorter time.
At T °C, the number of molecules exceeding Ea is a.
At (T + 20) °C, the number of molecules exceeding Ea is (a + b).
Hence, the fraction of effective collisions increases. This is the major factor causing a reaction rate to increase with temperature.
 

 

 

d. The Presence of a Catalyst

A catalyst is a substance that increases the rate of a reaction without being consumed in reactions. It changes the reaction path by decreasing the activation energy.
H₂0₂ can be decomposed into H₂0 and 0₂. When a small amount of Mn0₂ is added as a catalyst for this reaction, it increases the rate of production of 0₂.

The presence of a catalyst is denoted over the arrow in a chemical equation, since it does not affect the overall reaction.
 

Properties of Catalysts
1. They remain unchanged after the reaction.
2. The energy of activation for the reverse reaction, Ear, is lowered by a catalyst to the same extent as the energy of activation for the forward reaction, Eaf.
3. The enthalpy change, ∆H, for the catalyzed reaction is the same with the ∆H for the uncatalyzed reaction.
4.  It does not make an improbable reaction.

 

 

 

 

 

 

 

e. Interacting Area
A solid in a solution can only react when particles collide with the surface. The increase in the surface area of this solid raises the number of collisions between reacting particles.
The surface area of a solid can be increased by smashing into small pieces. Smaller particles supply a bigger surface area than the larger particles for the same mass of solid.
For the reaction ;
HCl +CaC0₃ --> CaCl₂ + C0₂ + H₂0
CaC0₃ may be used as small chips or as marble chips. When small chips are used, the reaction will be completed in a much shorter time.

QUESTIONS

I. Photosynthesis
II. Rusting of iron
III. Sparking of a match
IV. Digestion of food
V. Spoiling of fruit

NH₄N0₂ --> N₂ + 2H₂0
If the concentration of NH₄N0₂ is 0.5 M at the beginning of the reaction, the concentration decreased to 0.432 M after 3 hours, what would be the rate of decomposition of NH₄N0₂ in this time interval?

What is the rate relationship between H₂, Cl₂ and HCI?

If the initial concentration of A is 0.4 M and the rate of disappearance of A is 1,76.10^-5 M/s
a. What is the rate of appearance of C?
b. How much time should pass at the point the concentration of A is 0.39 M? (Assume no change in rate)

 
According to the potential energy versus reaction coordinate graph given for the reaction above,
a. What is the energy of the activated complex?
b. What is the value of activation energy for the forward and reverse reactions?
c. Find the enthalpy change of this reaction.

According to the given graph, find the following;
a. Activation energy for forward reaction
b. Activation energy for reverse reaction
c. Enthalpy of the reaction
d. Energy of activated complex

If the activation energy for the forward reaction is 134 kJ and the heat of formations of CO, N0₂, C0₂ and NO are -110.5 kJ/mol, +33 kJ/mol, -393.5 kJ/mol and +91 kJ/mol, respectively:
a. Find the enthalpy of reaction.
b. Plot a potential energy versus reaction coordinate diagram.
c. Find the activation energy for the reverse reaction.
d. Calculate the energy of the activated complex.

If the rate of disappearance of 0₂ is 0.3 mol/s, what will be the rate of appearance of C0₂?

If the concentrations of reactants are doubled, how many times does the rate increase?