Energy: Concept and Units

There are not, however, an unlimited number of different kinds of energy available to do this work, nor are they inexhaustible. There is nuclear energy, quantitatively given by E = mc², which we can at least partially release in nuclear reactors and nuclear weapons. There is kinetic energy, the energy possessed by moving bodies, quantitatively given by E = mv²/2 where m is the mass of the body and v is the velocity with which it is moving; this is the energy which destroys a moving automobile when it hits a stationary object. There is potential energy, the energy of position of a body, quantitatively given by E = mgh where m is the mass of the body, g is the force of gravity, and h is the height of the body above the ground. This is the energy a falling apple has when it drops from a tree. Other important forms of energy are electrical energy, light energy, and heat energy. And finally there is chemical energy, the energy stored in the chemical bonds between the atoms in molecules. Chemical energy is, of course, the reason for taking up the study of energy in chemistry.

Each form of energy can be converted into any other, although sometimes this is very inefficiently done or impractical. In principle, all forms of energy are interconvertible. We express this generalization as the First Law of Thermodynamics (the law of conservation of energy): "Energy can neither be created nor destroyed, only converted from one form to another." Note that this does not say that energy will always be converted only to the form we want! No energy is ever lost or destroyed, but often some of it appears in a form we do not want and cannot use. The heat of a light bulb is an unwanted byproduct of the inefficient conversion of electrical energy to light energy. No incandescent bulb or fluorescent tube we can devise produces light without heat, but fluorescent tubes produce less heat than do incandescent bulbs and thus, for the same electrical energy, produce more light.

Since in principle every form of energy can be converted into every other, we need only one unit in which we can measure energy. In practice, different measuring units grew up with different types of energy because it was not realized that all forms of energy are fundamentally the same. Thus for lifting weights one used a foot-pound (energy required to lift one pound of mass the height of one foot) as the unit of potential energy, the calorie (energy required to raise the temperature of one gram of water exactly one degree Celsius) as the unit of heat energy, and the kilowatt-hour (energy of 1000 watts, or volt-amperes, provided continuously for one hour) as the unit of electrical energy. Conversion factors abounded so that each unit of energy could be converted into every other.

With the advent of the International System of Units (SI) we use only one unit for energy. That unit, the joule (symbol: J), is named after the English brewer and scientist James Prescott Joule. It is a defined unit; one joule (J) is defined as being exactly equal to one kilogram meter² / second². This is a unit of mechanical energy, since the units would correspond to a moving (mv², or kilogram-(meter/second)²) object or a falling object (mgh, or kilogram-meter-meter/second²), but because all forms of energy are interconvertible this one unit suffices for them all. The joule is the unit to which chemists are converting, but some older chemistry books still use the calorie. One thermochemical calorie is exactly equal to 4.184 J. (Some of the earlier work used several different calories having slightly different values. Moreover, the calorie is sometimes confused with the Calorie, 1000 calories or 1 kcal, used by nutritionists and dieting weight-watchers.)

Chemists virtually never consider nuclear energy as within the province of chemistry because the energy of nuclear reactions is so many orders of magnitude greater than the energy of ordinary chemical reactions. The occurrence of a nuclear reaction disrupts, as a matter of course, all the chemical bonds in the vicinity of the atom undergoing nuclear reaction. Nuclear reactions always have energies which are far too large, and heat content is sometimes an energy which is too small, to be significant in chemical calculations.

Like matter, energy is conserved in a chemical reaction. That is, the amount of energy given off or absorbed in a chemical reaction is a constant, just as the masses of reactants used and products formed are constant. By constant we here mean constant with respect to any arbitrarily selected amount of any arbitrarily selected reactant or product. If, for example, hydrogen is burned in air, then the amount of air, or more correctly atmospheric oxygen, that can react with one kilogram of hydrogen is fixed, and the amount of energy given off is fixed also. If the hydrogen is doubled to two kilograms, twice as much atmospheric oxygen is required and twice as much energy is obtained. This is an obvious point, but it is worth keeping in mind that one bushel of coal gives half as much heat as two bushels of coal as one goes through the more theoretical discussions of thermodynamics.

The understanding of heat at an elementary level requires no understanding of the actual structure of matter. Modern
thermodynamics likewise requires no knowledge of the real nature of matter -- at least at an elementary level. It is, however,
necessary to introduce some specifically thermodynamic ideas and concepts here before we can talk intelligently about chemical
thermodynamics. These terms apply when changes involving chemical reactions do not occur as well as to those changes in
which they do; thermodynamics is as much a part of physics as it is of chemistry.

In thermodynamics, it is necessary to deal with only one part of the universe at a time, for the simple reason that it is impossible
to know what is going on throughout the entire universe. The choice of the particular chunk of the universe to deal with,
however, is an arbitrary one and can be whatever we like from a single gas molecule to an entire planet or solar system. The
size is usually taken as a convenient one, such as a beaker of solution or a balloon of gas. This chunk of the universe is then
referred to as the system -- the system being studied. The rest of the universe is referred to as the surroundings. It is
convenient to think of the system as cut off from the surroundings by some sort of a wall. The system includes everything inside
the wall, while the surroundings include everything outside the wall. The wall is not impenetrable to matter and energy, but is
designed to permit us to control and keep track of all movements of matter and energy in or out -- much as the medieval city or
castle controlled access through its gates.

A system can be described, and for any useful calculations must be quantitatively described, by specifying quantitatively each of
the properties of each of the components of the system. Such a description is called the state of a system, and must include the
overall properties of the system such as its pressure, volume, and temperature as well as the composition of the system. This is
reasonable only if the system is a fairly simple one. The state of the surroundings can never be completely specified; fortunately,
it is not necessary to do so.

A state function is any function whose value depends only upon the state of a system and not upon its previous history. If two
systems are in the same state, their state functions must be identical. If the state of a system is changed, as by heating so that
energy flows in, the values of its state functions change, and if the system is restored, as by cooling so that energy flows out, to
its original state, the values of its state functions are restored also. We have already used, in earlier sections, one of the more
common state functions, enthalpy (symbol: H). In this and the following sections we will describe enthalpy more quantitatively
and introduce other state functions.

First Law of Thermodynamics

One of the characteristics of any system is the total amount of energy it contains. This characteristic is called the total internal
energy (symbol: E). The total internal energy is a state function, and must necessarily be so if we accept the fact that energy
cannot be created or destroyed. The energy of a system can, of course, be changed by moving energy in from the surroundings
or by moving energy out to the surroundings. We do this using devices such as furnaces and refrigerators daily. But energy is
only transferred and not changed in quantity by such processes. The type of energy can be changed either inside or ouside a
system -- but energy is transformed in type only, and its quantity is not changed, whatever transformation procedure is
employed. Even in nuclear reactions energy is conserved, because mass and energy are considered equivalent.

Total internal energy E is not a particularly useful state function, since we have no method of measuring E for any system and
no simple one of measuring changes in it, DU. Heat flow, as from a boiler to a condenser, and work flow, as in the work output
of a steam engine, are both measurable and highly significant quantities. Heat flow (symbol: q) is the change in heat, and work
flow (symbol: w) is the change in work. Heat and work are not the only forms of energy which exist, of course, and this is
indicated by the triple-dot (...) symbol in the equation form of the first law of thermodynamics:

q + w + ... - E = 0

The first law of thermodynamics says that all of the energy changes in a system must add up to zero. In other words, no net
change, or no creation or destruction of energy, is possible. Any change in heat which is not exactly equal and opposite to a
change in work must appear as a change in the total internal energy. Chemists usually find it easier to assume, as we will do
from now on, that all of the other forms of energy such as light energy and electrical energy do not change at all. Then their
changes are zero, and under these conditions we write the first law of thermodynamics as q + w - E = 0, or E = q + w.

Heat can flow into, and out of, a system to its surroundings. Work can be done by the system on the surroundings, and vice
versa. The internal energy of a system can increase or decrease by any of these processes. Thus energy as heat, work, total
internal energy, or any other form must be an algebraic quantity -- a quantity which has a positive sign (for increase) or a
negative sign (for decrease). Increases or decreases in heat and work are more easily visualized as heat or work flows between
system and surroundings and are looked at from the point of view of the system:

If q is negative, heat flows OUT of the system (to the surroundings).
If q is positive, heat flows INTO the system (from the surroundings).
If w is negative, work is done BY the system (on the surroundings).
If w is positive, work is done ON the system (by the surroundings).

Enthalpy: A Backward Look

Physical work is the product of a force multiplied by the distance over which that force is exerted. One foot-pound of work is
the force required to lift one pound of matter a distance of one foot. If, as in a steam engine, or internal combustion engine, this
work is done by a gas expanding under or above a piston, that force F is the pressure of the gas p multiplied by the area of the
piston A. Now volume V is the product of an area A times a distance d, and so from the successive equations w = F x d,
F = P x A, and V = A x d it follows that the work of gas expansion is PV.  At a constant pressure,

w = -PV

The negative sign is necessary because work is negative when it is done by a system, while the change V is taken as
the final volume less the starting volume. In gas expansion the volume increases when work is done by the gas, so work w is
negative, while in gas compression work is done on the gas and so work w is positive.

The total internal energy, as mentioned above, is not a useful state function because its value cannot be measured. However, the
total internal energy can be used, together with pressure-volume work, to define other more useful state functions.

E = q + w

E = q - PV

  q = E + PV

At constant pressure, we can define a new state function, enthalpy ("to warm" in Greek),

 H = E + PV

The condition of constant pressure is a realistic one because we live under the more or less constant pressure of the
atmosphere. The law of conservation of energy applies under conditions of constant pressure as well as generally.
The heat flow at constant pressure q_p the heat flow which will actually be observed under conditions of constant pressure --
as in an open fire or a burning candle. The equation above shows that this heat flow is the measurable change in the
state function enthalpy.

Enthalpy is a state function because it is defined only in terms of a state function, E, and two properties characteristic of states,
pressure P and volume V. Therefore H (the change in enthalpy) is the same as the heat flow at constant pressure q_p, and has
the same sign. When H is positive, heat is given to the system by the surroundings. The process is then called endothermic
because heat flows into the system from the surroundings. When H is negative, heat is given off by the system to the
surroundings and the process is called exothermic.

Calorimetry

One method of determining the energy exchange between the reaction system and its environment is to conduct a calorimetric analysis. A calorimeter is a thermally insulated container where a reaction system can be performed and the energy exchange between the system and its surroundings can be measured. The calorimeter and its contents are considered the surroundings.
The reaction system is a chemical or physical process that occurs within the confines of the calorimeter.

 q_system = -q_calorimeter

The q_calorimeter can be determined if one knows the heat capacity, C, of the calorimeter. This heat capacity can be experimentally determined and is expressed in kilojoules / ^oC. In order to determine the q_calorimeter you multiply the heat capacity of the calorimeter by the difference between the final and initial temperature.

 q = -CT = H

 For example if the heat capacity of a calorimeter was determined to be 25.4 kJ/^oC, determine the q if the initial temperature during a calorimetric analysis was 30 ^oC and the final temperature was 50 ^oC.

H = -CT = 25.4 kJ/^oC ( 50 - 30 ^oC) = 508 kJ

Sometimes the heat capacity is determined for the calorimeter and its contents which might be water. Frequently, a coffee cup calorimeter made of styrofoam is used. Styrofoam has a zero heat capacity so water is usually added to such a calorimeter and the q_cal = q_water.

Example1:

The combustion of 10 g of methane, CH₄, in a calorimeter changed the temperature inside the calorimeter from 25.4 to 29.4 ^oC. The Heat capacity of the calorimeter was determined in a separate experiment and found to be 26.2 kJ/^oC.
Determine the H per gram of methane and the heat of combustion per mole methane.

The process:

  1.  Determine the q_cal which is equal to -q_system

  q_cal = CT = 26.2 kJ/^oC (29.4 - 25.4 ^oC) = 104.8 kJ

 2. H = -q_cal

H = -104.8 kJ

 3.  Determine the H per gram:

H = H / mass of methane = -104.8 kJ / 10 g = -10.48 kJ/g

 4.  Determine the H per mole = -10.48 kJ/g  x 16.043 g CH₄ / 1 mole CH₄ = -167.7 kJ/mole

Example 2:

Twenty grams of a salt was dissolved in 100.0 mL of water inside a calorimeter increasing the temperature of the water from 25.0 to 28.5 ^oC.  Calculate H_solution per gram.

First assume that the heat capacity of the calorimeter is the same as the heat capacity of the water in it.  C of the calorimeter is then the specific heat of water (4.184 J / g-^oC) times the mass of water, in grams,

H = -(100.0 mL water x 1 g water / 1 mL water x 4.184 J / 1 g water-^oC) x (28.5 - 25.0 ^oC) = -1464.4 J

H = -1464.4 / 20.0 g = -73.2 J / g

Hess's Law

For example: When phosphoric acid (a triprotic acid) is neutralized with a base, the hydrogens are neutralized in 3 steps.

H₃P0₄ + NaOH  NaH₂PO₄ + H₂O, this is step one, and will give x amount of heat.

NaH₂P0₄ + NaOH  Na₂HPO₄ + H₂O, this is step two, and will give y amount of heat.

Na₂HPO₄ + NaOH Na₃PO₄ + H₂O, this is step three, and will give z amount of heat.

The sum of these three reactions is

H₃PO₄ + 3 NaOH  Na₃PO₄ + 3 H₂O

So the total heat is the sum of the individual heats (x + y + z)

Try these:

3 C(graphite) + 4 H₂(g) => C₃H₈(g)       (-102)

From:

C₃H₈(g) + 5 O₂{g} => 3 CO₂(g) + 4 H₂O(l)       -2220

C(graphite) + O₂(g) => CO₂(g)      -394

H₂(g)  + 1/2 O₂(g) => H₂O(l)       -285
 
 

FeO(s)  +  CO(g) => Fe(s)  +  CO₂(g)       (1)

From:

Fe₂O₃(s) + 3 CO(g) => 2 Fe(s) +  3 CO₂(g)       -23

3 Fe₂O₃(s)  +  CO(g) => 2 Fe₃O₄(s) +  CO₂(g)       -39

Fe₃O₄(s)  +  CO(g) => 3 FeO(s) +  CO₂(g)       -18
 
 

N₂O₄(g) => 2 NO₂(g)       (58.2)

From:

N₂(g)  +  2 O₂(g) => 2 NO₂(g)       67.8

N₂(g)  +  2 O₂(g) => N₂O₄(g)       9.6
 
 

cis-C₄H₈(g) => trans-C₄H₈(g)       (-4)

From:

cis-C₄H₈(g)  +  6 O₂(g) => 4 CO₂(g) + 4 H₂O(g)       -2710.9

trans-C₄H₈(g)  +  6 O₂(g) => 4 CO₂(g) + 4 H₂O(g)       -2706.9
 
 

C(s) +  2 H₂(g) => CH₄(g)       (-74.6)

From:

C(s) +  O₂(g) => CO₂(g)       -393.5

H₂(g)  +  1/2 O₂(g) => H₂O(l)       -285.8

CH₄(g) + 2 O₂(g) => CO₂(g) +  2 H₂O(l)       -890.5
 
 

C₂H₆(g) + 7/2 O₂(g) => 2 CO₂(g) +  3 H₂O(l)       (-1559.7)

From:

C(s) +  O₂(g) => CO₂(g)       -393.5

H₂(g)  +  1/2 O₂(g) => H₂O(l)       -285.8

2 C(s) +  3 H₂(g) => C₂H₆(g)       -84.7
 
 

PCl₃(g)  +  Cl₂(g)=>PCl₅(g)       (-111)

From:

4 PCl₃(g) => P₄(s)  +  6 Cl₂(g)       1084

P₄(s)  +  10 Cl₂(g) => 4 PCl₅(g)       -1528
 
 

2 C(graphite)  +  2 H₂(g)  +  O₂(g) => CH₃COOH(l)       (-489)

From:

2 CO₂(g) +  2 H₂O(l) => CH₃COOH(l)  +  2 O₂(g)       871

C(graphite) +  O₂(g) => CO₂(g)       -394

2 H₂(g) +  O₂(g) => 2 H₂O(l)       -572
 
 

6 Fe(s)  +  4 O₂(g) => 2 Fe₃O₄(s)       (-2234.3)

From:

2 Fe₃O₄(s)  +  1/2 O₂(g) => 3 Fe₂O₃(s)       -232.2

6 Fe(s) +  9/2 O₂(g) => 3 Fe₂O₃(s)       -2466.5
 
 

C₂H₄O(l)  +  5/2 O₂(g) => 2 CO₂(g)  +  2 H₂O(g)       (-1167.5)

From:

2 C₂H₆O(l) +  O₂(g) => 2 C₂H₄O(l) + 2 H₂O(l)       -407

C₂H₆O(l)  +  3 O₂(g) => 2 CO₂(g)  +  3 H₂O(l)       -1371
 
 

C₂H₆(g) +  7/2 O₂(g) => 2 CO₂(g)  +  3 H₂O(g)       (-1132)

From:

C₂H₆(g) => C₂H₂(g) + 2 H₂(g)       378

C₂H₂(g) +  5/2 O₂(g) => 2 CO₂(g)  +  H₂O(g)       -940

H₂(g) + 1/2 O₂(g) => H₂O(g)       -285
 
 

CH₄O(l) => CH₂O(g) +  H₂(g)       (-130)

From:

N₂H₄(l)  +  CH₄O(l) => CH₂O(g)  +  N₂(g)  +  3 H₂(g)       -74

2 NH₃(g) => N₂H₄(l)  +  H₂(g)       36

N₂(g)  +  3 H₂(g) => 2 NH₃(g)       -92
 
 

1/2 N₂(g) +  2 H₂0(l) => NO₂(g)  +  2 H₂(g)       (170)

From:

N₂(g)  +  3 H₂(g) => 2 NH₃(g)       -92

NO₂(g)  +  7/2 H₂(g) => 2 H₂O(l)  +  NH₃(g)       -216
 
 

H₂O(l) => H₂(g)  +  1/2 O₂(g)       (-35)

From:

N₂(g)  +  3 H₂(g) => 2 NH₃(g)      -92

2 NH₃(g)  +  4 H₂O(l) => 2 NO₂(g)  +  7 H₂(g)       -114

2 NO₂(g) => N₂(g) +  2 O₂(g)       66
 
 

H₂S(g) +  1/2 O₂(g) => S(s)  +   H₂O(l)       (155)

From:

H₂S(g)  +  3/2 O₂(g) => H₂SO₃(l)       -204

H₂SO₃(l) => H₂O(l)  + SO₂(g)       62

SO₂(g) => S(s)  +  O₂(g)       297
 
 

CH₂Cl₂(l) +  H₂(g)  +  3/2 O₂(g) => COCl₂(g)  +  2 H₂O(l)       (-161)

From:

CH₂Cl₂(l)  +  O₂(g) => COCl₂(g)  +  H₂O(l)       -19

1/2 H₂(g)  +  1/2 Cl₂(g) => HCl(g)       -92

2 HCl(g)  +  1/2 O₂(g) => H₂O(g)  +  Cl₂(g)       42
 
 

H₂O(l) => H₂O(g)       (77)

From:

H₂S(g)  +  2 O₂(g) => H₂SO₄(l)       -549.5

H₂SO₄(l) => SO₃(g)  +  H₂O(g)       143.5

H₂S(g)  +  2 O₂(g) => SO₃(g)  +  H₂O(l)       -483
 
 

H₂CO(aq)  +  O₂(g) => H₂O(l)  +  CO₂(g)       (-50)

From:

H₂CO₃(aq) => H₂O(l)  +  CO₂(g)       62

H₂CO(aq) +  O₂(g) => H₂CO₃(aq)       -112
 
 

Zn(OH)₂(s)  +  H₂CO₃(aq) => 2 H₂O(l)  +  ZnCO₃(s)       (116.8)

From:

ZnO(s)  +  CO₂(g) => ZnCO₃(s)       -17.2

H₂CO₃(aq) => H₂O(l)  +  CO₂(g)       62

Zn(OH)₂(s) => ZnO(s)  +  H₂O(l)       72

Heats of Formation

A convenient reaction to use in Hess's law applications is the formation of one mole of a compound from its element in their standard state.  These enthalpy values (H_f ) are tabulated and can be applied to any reaction where all H_f's are known.  For a reaction:

  aA  +  bB  cC  +  dD

H = (c mole x H_f C + d mole x H_f D) - (a mole x H_f A + b mole x H_f B)