Chapter 8. Chemical and Physical Change
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Chapter 8. Chemical and Physical Change: Energy, Rate, and
Equilibrium
Energy
Thermodynamics
Two laws of thermodynamics, the science involved with energy flow in physical and chemical
change, are of particular importance to us. The first law, the law of conservation of energy, and the
second law, entropy or disorder, can provide us with basic information regarding the spontaneity of
chemical or physical processes as well as the amount of energy absorbed or released by the reaction.
Exothermic reactions release energy; endothermic reactions require energy input. The practical side of
the thermodynamics is presented through discussion of enthalpy, entropy, and free energy.
Universe, System and Surrounding
The basic abstraction of thermodynamics is the division of the world into systems delimited by real
or ideal boundaries. The systems not directly under consideration are lumped into the surrounding.
Usually systems can be assigned a well-defined state solid/liquid or a gas which can be summarized by a
small number of parameters. The flow of between the system and surrounding is measured.
First law of thermodynamics
Energy may exist in a variety of forms and may be transformed from one type of energy to another.
However, these energy transformations are constrained by a fundamental principle, the Conservation of
Energy principle: Energy can neither be created nor destroyed. Heat is the main form of energy
involved with chemical reactions.
Enthalpy change (∆H): Heat given our in a chemical reaction. Enthalpy is measured in kJ or calories.
Exothermic. As the dissolution reaction proceeds, the solution gets hotter because heat is produced.
Enthalpy change, ∆H˚ is negative, meaning that energy is released by the reaction.
Endothermic. As the dissolution reaction proceeds, the solution gets colder because heat is absorbed.
Enthalpy change, ∆H˚ is positive, meaning that energy is absorbed during the reaction.
Second law of thermodynamics
Disorder (measured as entropy) of the Universe (defined as system + surrounding) increases during a
spontaneous process.
Entropy (S): Measure of disorder is measured in J/K.
Entropy increases during these processes:
i) Solid ---> liquid (melting)
ii) Liquid ---> gas (boiling)
iii) Solid ----> gas (sublimation)
iv) Increase in temperature (increase in kinetic energy)
v) Decomposition reactions
vi) Anything that breaks up in to smaller particles
v) Mixing: Diffusion, solution process
Example: Conversion of a single solid object, the log, into carbon monoxide, carbon dioxide, and
water (all gases) and ashes (disordered solid) increases the disorder of the substance.
Entropy decreases. A gas (more disordered) is converted to a liquid or solid (less disordered). Upon
freezing the randomness of the water molecules has decreased.
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Third law of thermodynamics
All substances have zero S at 0 K.
A chemical reaction could be exothermic or endothermic
Experimental Determination of Energy Change in Reactions
A calorimeter measures heat changes (in calories or joules) that occur in chemical reactions. The
specific heat of substances is the number of calories of heat needed to raise the temperature of one gram
of the substance by one degree Celsius.
The amount of energy per gram of food is its fuel value, commonly reported in units of nutritional
Calories (1 nutritional Calorie = 1 kcal). A bomb calorimeter is useful for measurement of the fuel value
of foods.
Measuring Heat: Calorimetry
A calorimeter is a device that is used to measure the quantity of heat flow in a chemical reaction.
Two common types of calorimeters are the coffee cup calorimeter and the bomb calorimeter.
Coffee Cup Calorimeter
A coffee cup calorimeter is essentially a polystyrene (Styrofoam) cup with a lid. Really, any
well-insulated container will work. The cup is partially filled with a known volume of water and a
thermometer is inserted through the lid of the cup so that the thermometer bulb is below the water
surface. The water absorbs the heat of any chemical reaction taking place in the calorimeter.
Bomb Calorimeter
A coffee cup calorimeter is great for measuring heat flow in a solution, but it can't be used for
reactions which involve gases, since they would escape from the cup. Also, a coffee cup calorimeter
can't be used for high temperature reactions, since high heat would melt the cup. A bomb calorimeter is
used to measure heat flows for gases and high temperature reactions like combustion reactions.
Heat flow is calculated in Calorimeters:
Q = m (mass) x ∆T(temperature change) x SH (specific heat)
where Q is heat flow, m is mass in grams, and ∆T is the change in temperature. The specific heat is the
amount of heat required to raise the temperature of 1 gram of a substance 1 degree Celsius. The specific
heat of (pure) water is 4.18 J/(g·°C).
Calorie: Amount of heat required to raise the temperature of 1 gram of a substance 1 degree Celsius.
Nutritional (dietary) calorie = 1 k cal = 1000 cal
103 cal
1 nutritional Cal
2
How many Joules of heat energy is in 7.0 x 10 cal?
4.18 J
2
3
7.0 x 10 cal x 1 cal = 2.9 x 10 J
Specific Heat
The specific heat of a substance is the number of calories of heat needed to raise the temperature of one
gram of substance by one degree Celsius.
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Chapter 8. Chemical and Physical Change
Substance
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kJ/ g·°C cal/ g·°C
Copper
0.386
0.0923
Brass
0.380
0.092
Gold
0.126
0.0301
Lead
0.128
0.0305
Silver
0.233
0.0558
2.4
0.58
4.184
1.00
Alcohol(ethyl)
Water
Heat Calculations
For example, consider a chemical reaction which occurs in 200 grams of water with an initial
temperature of 25.0°C. The reaction is allowed to proceed in the coffee cup calorimeter. As a result of
the reaction, the temperature of the water changes to 31.0°C. The heat flow is calculated:
Q water = m water x ∆T water x SH water
Q water = 200 g x (31.0°C - 25.0°C) x 4.18 J/(g·°C)
Q water = +5.0 x 103 J
In other words, the products of the reaction evolved 5000 J of heat, which was lost to the water.
The enthalpy change, ∆H, for the reaction is equal in magnitude but opposite in sign to the heat flow for
the water:
∆Hreaction = -( Q water)= - 5.0 x 103 J
What would be the temperature change if 200g of another liquid with a specific heat of
0.800 cal/(g°C is in the calorimeter and absorb 6.5 x 102 cal of heat?
Q=m
liquid
x ∆T
liquid
Solving for ∆T ,
l
Substituting,
x SH
liquid
Q
∆T = m l x SHl
l
6.5 x 10 2 cal
∆T = (1.00 x 102 g)(0.800 cal/g ⋅ °C) = 8.1˚C
l
What is the mass of water that absorb 3.00 nutritional calories to yield a temperature
change of 5.00˚C?
Q = m x ∆T x SH
w
w
w
Q
Solving for m , m = ∆Tw x SH w
w
w
Substituting,
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

103 cal

3.00 nutritional Cal x 
 1 nutritional Cal 
2
(5.00˚C)(1.00 cal/g ⋅ °C)
m =
= 6.0 x 10 g
w
The fuel value
The fuel value of a substance is the amount of energy, in units of nutritional Calories, derived from one
gram of that substance.
The Chemical Reaction and Energy
Chemical reactions are also known as chemical changes. This refers to the changes in the
structure of molecules. Such reactions can result in molecules attaching to each other to form larger
molecules, molecules breaking apart to form two or more smaller molecules, or rearrangements of atoms
within molecules. Chemical reactions usually involve the making or breaking of chemical bonds.
Enthalpy
By calculating the amounts of energy required to break all the bonds on the left ("before") and
right ("after") sides of the equation, we can calculate the energy difference between the reactants and the
products. This is referred to as ∆H, where ∆ (Delta) means difference, and H stands for enthalpy, a
measure of energy which is equal to the heat transferred at constant pressure. ∆H is usually given in
units of kJ (thousands of joules) or in kcal (kilocalories). ∆H˚ is the enthalpy measure at standard
thermodynamic temprearture and pressure: 25˚C (298 K) and 1 atm (760 torr).
If ∆H is negative for the reaction, then energy has been released. This type of reaction is referred
to as exothermic (literally, outside heat, or throwing off heat). An exothermic reaction is more
favourable and thus more likely to occur. Our example reaction is exothermic, which we already know
from everyday experience, since burning gas in air gives off heat.
Exothermic Reactions
A reaction may have a negative ∆H. This means that, to proceed, the reaction does not require
energy from outside. This type of reaction is called exothermic (literally, outide heat, or releasing heat).
Endothermic Reactions
A reaction may have a positive ∆H. This means that, to proceed, the reaction requires an input of
energy from outside. This type of reaction is called endothermic (literally, inside heat, or absorbing
heat).
Spontaneous and Nonspontaneous Reactions
The spontaneity of a reaction is favored if it is exothermic, but endothermic reactions are
possible too. Why? The other factor that affects the direction of spontaneous change may dominate.
Disorder - Disorder transitions, regardless of their energetics appear to be favored in the world around
us. They point the arrow of time. Humpty Dumpty couldn't be put back together because of the disorder
his fall created. A measure of the disorder of a system is called its Entropy, S. Therefore endothermic
reactions could be spontaneous if the disorder or Entropy, S could out weigh the endothermic effect.
Reactions that split molecules up increase the disorder in the universe and have a positive change in
entropy and have a positive ∆H (endothermic but still spontaneous reaction).
How can one tell whether a reaction is spontaneous, if both entropy and enthalpy affect
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spontaneity?
Free Energy
We can combine entropy and enthalpy together to make a new quantity, the Free Energy which, under
conditions of constant temperature and pressure, will determine the direction of spontaneous change
How is free energy (∆G) related to enthalpy and entropy?
Rates of Reactions
Kinetics
Chemical kinetics is the study of the rate of a chemical reaction. Recognizing that chemical reactions
result from effective collisions between potentially reacting particles, we show that factors such as the
structure of the reactant, its concentration, reaction temperature, and the presence or absence of a
catalyst influence reaction rates. The role of the activation energy in chemical processes determines
reaction rates, for we view the formation of the activated complex as an energy barrier to be overcome.
Mathematical Representation of Reaction Rate
The reaction rate of a chemical reaction is the speed of production of products from reactants. The rate
value is always positive. Reaction rates are expressed by the formula: A Æ B
In this equation, [A] is the molar concentration of the reactant (there may be several) A, n is the
order of the reaction, and k is the rate constant. Order establishes the mathematical relation of
concentration to rate. For instance, in a second-order reaction, if the concentration doubles, the rate
quadruples.
When there is more than one reactant involved in a reaction, the rate is simply the product of all of the
reactants and their orders:
A+B+CÆD+E
Rate is often expressed in the units mol/Ls.
Write the general form of the rate equation for the following reactions:
a) CH4(g) + 2 O2 Æ CO2 (g) + 2 H2O(g)
b) 2NO2(g) Æ 2NO(g) + O2 (g)
Answer:
n
n'
a. rate = k[CH ] [O ]
4
n
2
b. rate = k [NO ]
2
If the rate equation for the follwing reactions is given what are the orders with respect to each
reactant?
C2H5OH(l) + 3O2(g) Æ 2CO2 (g) + 3H2O(g)
Rate equation = k[C2H5OH] [O ]
2
2
Answer:
Order with respect to C2H5OH = 1 (first order)
Od
ith
t t C2H5OH
2(
d
d )
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Activation energy
Net energy is the difference in energy between products and reactants. Activation energy is the threshold
energy that must be overcome in order to cause a chemical reaction.
Activation Energy and the Activated Complex
This is the energy that must be reached by 2 colliding molecules before a reaction can take place.
Factors that Affect Reaction Rate:
Temperature: Conducting a reaction at a higher temperature puts more energy into the system and
increases the reaction rate. The influence of temperature is described by the Arrhenius equation. As a
rule of the thumb, the reaction rate doubles for every 10 degrees Celsius increase in temperature.
Why is growth of bacteria slowed down in a refrigerator?
The rate of chemical reactions critical to the growth process decreases at the lower temperature
of the refrigerator.
Order: Clearly the order of the reaction has a major effect on its rate. The order of a reaction is found
experimentally, and, for most basic reactions, is an integer value.
A catalyst: The presence of a catalyst increases the reaction rate in both the forward and reverse
reactions by lowering the activation energy of the reaction.
•
Catalysts increase the rate of reaction.
Catalyzed rxn
proceeding through
an intermediate
Ea
Ea
catalyzed
∆G Reactant
•
•
•
Catalysts are not consumed by the reaction.
A small quantity of catalyst should be able to
affect the rate of reaction for a large amount of
reactant.
Catalysts do not change the equilibrium constant
for the reaction.
∆G
Products
Reaction Coordinate
Particle size or the state of sub-division of
reactants: The larger the surface area compared
to the volume, the faster a reaction can take place, as more simultaneous reactions can occur.
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A December 1977 explosion in Westwood, LA, blew away the top 100 feet of head house atop this grain
elevator facility. The blast killed 36 people and injured nine, making it the worst such disaster in U.S.
history.
For a dust explosion to occur, several factors must come together, according to Dust Explosions in
Process Industries by Rolf K. Eckhoff. First, there must be fuel, or grain dust. The critical parameter for
grain particle size is 0.1 mm or smaller. As the size of the particle decreases, the risk of a deflagration or
explosion increases.
The nature of the reactants: If a reaction involves the breaking and reforming of bonds (complex)
compared to just the forming of bonds (simple) then it generally takes longer. The reactants position in
the reactivity series also affects reaction rate.
Equilibrium
Not all reactions proceed to completion. Many establish a dynamic equilibrium between products
and reactants, where the rates of the forward and reverse reactions are equal. LeChatelier's Principle
states that if a stress is placed on a system in equilibrium, the system will respond by altering the
equilibrium in such a way as to minimize the stress.
Equilibrium Chemical Reactions
On the other hand, there are many chemical reactions that stop far short of completion. An example is
the dimerization of nitrogen dioxide:
NO2(g) + NO2(g)
N2O4(g)
The reactant, NO2, is a dark brown gas, and the product, N2O4, is a colorless gas. When NO2 is
placed in an evacuated, sealed glass vessel at 25°C, the initial dark brown color decreases in intensity as
it is converted to colorless N2O4. However, even over a long period of time, the contents of the reaction
vessel do not become colorless. Instead, the intensity of the brown color eventually becomes constant,
which means that the concentration of NO2 is no longer changing. Making the container colder makes
equilibrium to shift to left and warming shift the equilibrium to right.
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Other examples:
3H2(g) + N2(g)
2NH3(g)
Any chemical reaction could be considered as a forward and backward reactions occurring at the same
time(
) as described previously. If the rates of backward and forward reactions chemical reactions
are comparable both reactants and products can coexist leading to a condition called chemical
equilibrium reaction.
Dynamic Equilibrium
The equilibrium process is dynamic; products and reactants continuously interconvert at the same rate.
Physical Equilibrium
z Phases and phase transitions
liquid -> gas : Vaporization
gas -> liquid : Condensation
solid -> liquid : Fusion (Melting)
liquid -> solid : Freezing
solid -> gas : Sublimation
gas -> solid : Deposition
Example: H2O(l)
H2O(g)
z
Solubility
Supersaturated solution
Chemical Equilibrium
When a chemical reaction takes place in a container which prevents the entry or escape of any of the
substances involved in the reaction, the quantities of these components change as some are consumed
and others are formed. Eventually this change will come to an end, after which the composition will
remain unchanged as long as the system remains undisturbed. The system is then said to be in its
equilibrium state, or more simply, "at equilibrium".
The Chemical Equilibrium Constant
Equilibrium constant comes from a law that applies to chemical equilibrium called Law of Mass
action.
The Generalized Equilibrium-Constant Expression for a Chemical Reaction
Law of Mass Action:
Law of mass action describes an equilibrium process by quantifying the equilibrium
concentration of reactants and products. It uses the ratio of backward and forward reactions and express
it terms of an equilibrium constant (K). For example consider a hypothetical equation:
jA+kB
lC+mD
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[C]l[D]m
[A]… are equilibrium concentration of A, B, C, D etc.
K = ----------------j, k, l, m are stoichiometric coefficients
j
k
[A] [B]
K = equilibrium constant
Equilibrium Expression:
Equilibrium expression is the Law of mass action equation with the equilibrium concentration of
reactants and products and the equilibrium constant (K).
Example: Equilibrium expression for the formation of NH3 gas:
N2(g) + 3H2(g)
2NH3(g)
[NH3]2
K = ------------ = 6.02 x 10-2 L2/mol2 at 127oC
[N2][H2]3
Equilibrium Constant (K): The constant in the equilibrium expression is called equilibrium constant
(K).
2 H2(g) + O2(g)
2H2O(g)
[H2O]2
K = ------------[H2] 2[O2]
MgCO3(s)
MgO(s) + CO2(g)
K = [CO2]
Equilibrium position
An increase in the rate of the forward reaction favors products. This increases the numerator of the rate
constant expression, hence, the magnitude of the equilibrium constant. The equilibrium favors reactants.
A very low value for the equilibrium constant indicates that the ratio of products to reactants is very low.
Therefore reactant concentration is larger than product concentration.
Write the equilibrium constant for he following reaction:
2HI(g)
2H2(g) + I2(g)
K eq =
[H2 ][I2 ]
[HI]2
A reaction chamber contains following mixture at equilibrium:
2H2(g) + S2(g)
2 H2S(g)
[H2] = 0.22 M
[S2] = 1.0 x 10-6 M
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[H2S] = 0.80 M
Calculate the equilibrium constant.
Answer:
[H2S]2
K eq =
[H2 ]2 [S2 ]
K eq =
[0.80]2
2
7
-6
[0.22] [1.0 x 10 ]
= 1.3 x 10
Rate and Reversibility of Reactions
Once a system has reached equilibrium, any factor which causes a change in the rate of either the
forward or reverse reaction will disturb or shift the equilibrium. The system will readjust itself so that a
new equilibrium is reached and the rates will again become equal. Reestablishing the equilibrium is
summarized by Le Châtelier.
Le Châtelier's Principle
When a stress is applied to a system at Equilibrium, the system readjusts so as to relieve or offset the
stress. Stress is any imposed factor which upsets the balance in rates between the forward and reverse
reactions. Stress factors may be changes in concentrations [], total pressure with gases only, volume
changes (which cause the pressure changes), and temperature.
For the hypothetical equilibrium reaction
A(g) + B(g)
C(g) + D (g)
Predict weather the amount of A in a 5.0-L container would, or remain the same for each of the
following changes.
a. Removal of some B.
b. Removal of some C.
c. Addiction of excess D.
d. Removal of a catalyst.
Answer:
a. A would increase; C and D would react to produce more B, to compensate for its removal,
and more A as well. the equilibrium shifts to the left.
b. A would decrease; A and B would react to produce more C, to compensate for its removal.
The equilibrium shifts to the right.
c. A would increase; excess D would react with C to produce more A and B. The equilibrium
shifts to the left.
d. A would remain the same; removal of the catalyst would delay the attainment of equilibrium,
but not affect the equilibrium position.
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