Energy can be defined as the capacity to do work (move matter) or produce heat. A wound clock acquires "something" with which it can do work. This "something" that enables the clock to do work is energy. An object can exhibit energy in two fundamental ways, kinetic energy (Ek) and potential energy (EP).
Kinetic energy is the energy of motion an object associated
with mechanical work, and is described mathematically
by the equation; EK = ½ mv2,
where m is mass and v is velocity.
Potential energy is stored energy, it is energy related to position. An object has potential energy by virtue of its position in a field of force. A 1 kg object held 1 m above the surface of the earth has a potential energy of EP = mgh = (1 kg)(9.8 m/s2)(1 m) = 1 kg×m2/s2. Potential energy can be thought of as work already done.
The SI unit of energy is a derived unit called the joule
(J). The SI natural units of energy are kg×m2/s2.
(1 J = 1 kg×m2/s2
)
1 calorie (cal) = 4.184 J
Example
How many joules are in 8.32 cal?
[34.8 J]
The Law of Conservation of Energy states that in
a physical or chemical change energy may be exchanged between a system
and its surroundings but energy cannot be created or destroyed. Energy
may be converted from one form to another, but the total quantity of energy
remains constant. The energy of the universe remains unchanged and is therefore
constant.
Work is defined by the mathematical relationship: work = force x distance. The SI unit of force is the newton (N). 1N = 1 kg×m/s2. Energy and work have the same units. work = force x distance = 1 N x 1 m = 1 kg×m2/s2 = 1 J
Chemists define work as directed energy change resulting
from a process. Chemical processes (reactions) are almost always accompanied
with the absorption or release of one form of energy, heat (thermal energy).
The study of the energy (heat) change associated with chemical reactions
is known as thermochemistry.
Thermal energy, Heat, and Temperature
Thermal energy is the energy of motion (kinetic
energy) of the unit particles of a substance. The unit particles of any
substance not at zero K (absolute zero) have thermal energy. The unit particles
of a solid are in close contact and movement of such particles is limited
to rotational and vibrational. Particles in a liquid exhibit all three
types of molecular motion (translational, rotational, and vibrational)
even though they are in constant contact with each other. The particles
of a gas have the greatest freedom of the three states of matter and move
freely about in space. The higher the temperature, the faster the particles
move.
Temperature is a relative measure of how hot or how cold an object is. It is a measure of the average random motion (kinetic energy) of the unit particles of an object. It is the property of an object that determines the direction in which thermal energy will be transferred when it is in contact with another object at a different temperature. When two objects are in contact with one another, and at the same temperature, the average kinetic energy of the unit particles of the two objects is equal.
Heat (q) is the thermal energy that "flows" into
or out of a substance due to a temperature difference. Heat flows spontaneously
from the warmer object to the colder object.
Thermochemistry Terms
To study the heat associated with a particular reaction,
scientists have developed a convention which defines and designates that
part of the universe where the heat is being transferred. The universe
is understood to be divided into two separate but integral parts, the system
and the surroundings (Universe = System + Surroundings). The system
is the substance or mixture of substances under study in which a change
occurs or simply stated, it is the part of the universe under investigation.
The surroundings compose the other part of the universe. In other
words, the surroundings include both the apparatus which contains the substance
under study, and the space around the apparatus. Separating the system
from the surroundings is the boundary, which can be real (like the
walls of a beaker) or imaginary.
The internal energy (E) of a system is the sum
of the kinetic energy (Ek) and potential energy (EP)
of all the unit particles (atoms, molecules, ions) of the system. E
= Ek+ EP The following table will perhaps aid
in understanding the concept and origin of the energies of a system’s composition.
| The kinetic energy (thermal energy) is associated with random molecular motion. There are three types. | The potential energy (chemical energy) is associated with electrostatic attractions within and between molecules. There are two types. |
| 1. Tranlational | 1. Intramolecular forces (bonds) |
| 2. Rotational | 2. Intermolecular forces |
| 3. Vibrational |
The Greek letter D (delta) is used to indicate changes in state functions. Thus, DE = Efinal - Einitial is the change of internal energy between initial and final states.
A positive value for DE (DE > 0) means internal energy increases. Energy is added to the system.
A negative value for DE (DE < 0) means internal energy decreases. Energy leaves the system.
Stated mathematically in terms of internal energy, heat and work, the law of conservation of energy is referred to as the first law of thermodynamics and is expressed as: DEsystem = qsystem + wsystem
In this equation, qsystem is the quantity of energy transferred by heating the system and wsystem is quantity of energy transferred by doing work on the system.
These two thermodynamic quantities will have a magnitude
and a sign. The sign conventions are as follows:
If heat is transferred into the system
from the surroundings, then q is assigned a positive sign, +q.
If heat is transferred out of the
system to the surroundings, then q is assigned a negative sign, -q.
If work is done on the system by the
surroundings, then w is assigned a positive sign, +w.
If work is done by the system on the
surroundings, then w is assigned a negative sign, -w.
Example
A gas absorbs 35.0 J of heat and does 15.0 J of work.
What is DE?
DE = q + w = (+35.0 J) + (-15.0 J) = +20.0 J
Example
How much heat is required to raise the temperature of
a 850 gram block of aluminum from 22.8oC to 94.6oC?
The specific heat of Al is 0.902 J/g.oC.
q = (mass)(specific heat)(DT)
= (850 g)(0.902 J/g.oC)(94.6oC-22.8oC)
= + 55.0 kJ
Example
What is the specific heat of iron at 25oC
if 285 J of heat were transferred when a 33.69 gram sample of iron cooled
from
43.8o0C to 25oC?
q = (mass)(specific heat)(DT)
-285 J = (33.69 g)(specific heat)(25.0oC
- 43.80oC)
specific heat = 0.45 J/g.oC
Example
A 25.88 g sample of a metal was heated to 85.32 oC
and then dropped into 35.14 g of water at 22.48 oC. The temperature
of the water rose to 26.47 oC. What is the identity of the metal?
Al 0.902 J/g.oC; Cu 0.385 24.5 J/g.oC;
Fe 0.449 J/g.oC; Pb 0.128 J/g.oC;
Ag 0.235 J/g.oC
[Answer specific Heat = 0.385 J/g.oC
The metal is copper.]
Example
Calculate the final temperature when 25.00 g of water
at 20.0 oC is mixed with 75.00 g of water at 40.00 oC.
[TFinal = 35.0 oC]
A change of state or phase transition is a change of a
substance from one state to another.
Melting (fusion) is the change of
a solid to the liquid state. H2O(s) ---> H2O(l)
Freezing is the change of a liquid
to the solid state.
H2O(l) ---> H2O(s)
Vaporization is the change of a liquid
to the vapor.
H2O(l) ---> H2O(g)
Condensation is the change of a gas
to a liquid.
H2O(g) ---> H2O(l)
Sublimation is the change of a solid
directly to the vapor. H2O(s) ---> H2O(g)
Deposition is the change of a vapor
directly to the solid. H2O(g) ---> H2O(s)
In any phase transition, heat (q) will be transferred
as the substance undergoes the transition.
Vaporization is an endothermic process.
Endothermic processes occur when heat energy is transferred into a system.
H2O(l) ---> H2O(g) q = +40.7 kJ/mol
Condensation is an exothermic process. Exothermic processes occur when heat energy is transferred out of a system.
H2O(g)
---> H2O(l) q = -40.7 kJ/mol
Enthalpy (DH) is the heat transferred
in a physical or chemical process occurring at constant pressure.
The quantity of heat associated with a physical change (e.g., heat
of vaporization, qvap) can be calculated as the product of the
amount (mole) of the substance and the enthalpy of the phase change (e.g.,
enthalpy of vaporization, qvap).
qvap = (mole)(DHvap)
Example
How much heat is required to vaporize 25.0 g of carbon
disulfide at 25oC?
The heat of vaporization (DHvap)
for carbon disulfide is +27.4 kJ/mol.
qvap = (mole)(DHvap)
= (25.0 g)(1mol/76.15 g)(27.4 kJ/mol) = 9.00 kJ
Example
Liquid butane, C4H10, is stored
in cylinders to be used as a fuel. Suppose 31.4 g of butane gas is
removed from a cylinder. How much heat must be provided to vaporize
this much gas? The heat of vaporization of butane is 21.3 kJ/mol.
qvap = (mole)(DHvap)
= (31.4 g)(1 mol/ 58.14 g)(21.3 kJ/mol) = 11.5 kJ
Heats of Reaction and Enthalpy Change, DH
A thermochemical equation is a balanced chemical
reaction equation (including phase labels) with the enthalpy of reaction
value written directly after the equation. 2Na(s) + 2H2O(l)
---> 2NaOH(aq) + H2(g) DH = -367.5
kJ
A negative value for enthalpy change (-DH)
indicates an exothermic reaction, that is heat is produced by the reaction
system.
CH4(g) + 2 O2(g)
---> CO2(g) + 2 H2O(g) DH
= - 890 kJ
A positive value for enthalpy change (+DH)
indicates an endothermic reaction, that is heat is absorbed by the reaction
system.
CH3OH(l) ---> CO(g) + 2H2(g)
DH = +90.7 kJ
Stoichometric Calculations Involving Thermochemical
Equations
1. When a thermochemical
equation is multiplied by any factor, the value of DH
for the new equation is obtained by
multiplying the value of DH in the original
equation by that same factor.
2. When a
chemical equation if reversed, the value of DH
is reversed in sign.
Example
Using the following thermochemical equation, calculate
how much heat is associated with the decomposition of
4.00 moles of NH4Cl.
NH3(g) + HCl(g) ---> NH4Cl(s)
DH = - 176 kJ
(4.00 mol NH4Cl)(+176 kJ/1 mol NH4Cl) = +704 kJ
Example
How much heat is associated with the synthesis of 45.0
g of NH3 according to the following equation?
4 NO(g) + 6 H2O(l) ---> 4 NH3(g)
+ 5 O2(g) DHrxn
= +1170 kJ
(45.0 g NH3)(1 mol/17.04 g NH3) = 2.641 mol NH3
(2.641 mol NH3)(+1170kJ/4 mol NH3) = +772 kJ
Example
Calculate the mass of ethane, C2H6,
which must be burned to produce 100 kJ of heat.
2 C2H6(g) + 7 O2(g)
---> 4 CO2(g) + 6 H2O(l) DH
= - 3120 kJ
(-100 kJ)(2 mol C2H6 / -3120 kJ) = 0.0641 mol C2H6
(0.0641 mol C2H6)(30.08 g C2H6/1 mol C2H6) = 1.93 g C2H6