# Energy and Enthalpy

Chemical reactions can be used as sources of energy or as a means of storing energy. If the energy occurs principally as heat then the reaction is called a thermochemical reaction. If the energy occurs principally as light energy then the reaction is called a photochemical reaction. If the energy occurs principally as electricity then the reaction is called an electrochemical reaction. During the course of the two semesters of General Chemistry we will examine all types, but for now we are primarily concerned with thermochemical reactions.

Thermodynamics deals with the relationships between heat energy and other forms fo energy known as work. So let's define a few terms.

Energy is defined as the capacity to do work and transfer heat and consists of kinetic energy and potential energy. Kinetic energy is given by KE = 0.5*m*v2 and has a definite zero value: when the velocity of the particle is zero. Potential energy has no general equation form but exists by virtue of position of elements of the system. The Principle of Conservation of Energy is : "Total energy must not change, it just changes form."

Think about a person standing on a diving board where she has no kinetic energy and potential energy because of her position above the surface of the water. As she dives the potential energy is converted into kinetic energy and upon impact the kinetic energy does work to push apart the water molecules.

Let's calculate the kinetic energy of a baseball (1/4 lb = 114 g) traveling at 100 mi/hr (44.7 m/s).

KE = 0.5*m*v2 = 0.5 (114g) (44.7m/s)2 (1kg/1000g) = 114 kgm2/s2 = 114 joule (note that a joule is kgm2/s2).

The SI unit for energy is the joule(j) and 1 cal = 4.184 j.

Work is mechanical work which is performed when a force acts through a distance:

W = f*d with units of joule = newton*meter

The work associated with expansion or compression of gases which is equivalent to a weight being lifted in the surroundings is the only type of work that we will consider now.

Heat is energy that is transferred as a result of a temperature difference between two or more systems. Heat always flows from Thigh to Tlow. The heat flow will continue until all systems have the same temperature. Remember that temperature is a measure of the molecular motion of the system. Heat flowing from a hotter body to a colder body will cause an increase of molecular motion in the colder system and hence a temperature rise. All energy can be converted to heat.

The calorie is the amount of heat needed to raise the temperature of water (1.00 g pure) 1.0 0C from 14.5 0C to 15.5 0C. One kilocalorie is 1000 calories. The food calorie is Calorie and is really the kcal. So if you see on a box that 1 serving = 200 calories this is really 200 kcal.

Specific heat (SH) is the heat lost or gained divided by (the grams of material times the change in temperature caused by the heat flow):

SH = (heat lost or gained)/((grams of material)*T))

Note that T = degrees T change = Tf - Ti where the sub f stands for the final temperature and the sub i stands for the initial temperature. Now note that

T = (tf C + 273.15) - (ti C + 273.15) and the conversion factors for converting from Celcius to Kelvin cancel. So T has the same value whether in Celcius or in Kelvin. Try it with the initial temperature being 300 0C and the final temperature being 400 0C. You get the numerical value of 100 whether you use Celcius or convert to Kelvin.

the specific heat (SH) has been determined experimentally for many substances and some of them are listed in your text. We can use our equation for SH to solve for either heat lost or gained:

heat lost or gained = (SH) * (grams of material) * T

or for T:

T = (heat lost or gained)/((SH)*(grams of material))

If the SH is very large then much heat must be lost or gained to change the temperature very much. The SH of water is very large (4.184 j/gK) which is the reason that the water temperature of a swimming pool is slow to get warm as summer comes and slow to cool as summer leaves.

We will use the symbol q to be either heat lost (q less than zero) or heat gained (q greater than zero).

Look at an example of the huge energy change required for a large sample of water to change temperature. Consider a volume of the ocean 10 feet deep, 1 mile wide, and 1 mile long. (this is 7.9 x 1012liters of water -- you might want to check that). How many joules of energy would have to be lost for the water temperature to change 1 degree Celcius? The density of water is about 1 g/ml so the total grams of water is

7.9 x 1012liters * 1000ml/l * 1.0g/ml = 7.9 x 1015g

The heat lost is then

q = 4.184 j/gK * (7.9 x 1015g) * (-1K) = -3.3 x 1013 kj -- a huge amount of energy.

Consider a cup of coffee initially at 60.0 degrees C. How many j of energy must the cup of coffee lose for its temperature to drop to body temperature (37.0 degrees C)? A cup holds 250.0 ml of coffee (consider density to be that of water) so we have

q = 4.181 j/gK * (250.0g)(37.0 - 60.0)K = -24.1 kj

Now let's say that we can capture that heat lost and use it to warm a piece of aluminum weighing the same amount as the coffee (250.0g). What will be the final temperature of the aluminum if it is initially at normal body temperature? (SH of aluminum = 0.902 j/gK)

T = q/(SH*mass) = 24.1 x 103j/((0.902 j/gK) * (250g)) = 107 K

Tfinal = T + Tinitial = 144 degrees Celcius.

Because of the difference in the specific heats of the two substances, we were able to use the heat lost by the coffee in going from 60 degrees C to 37 degrees C to raise the same quantity of aluminum from 37 degrees C to 144 degrees C. A lot of difference!

The molar heat capacity is often used in chemistry and it is defined as

SH * molar mass

So for water the molar heat capacity is

4.184 j/gK * 18.0 g/mol = 75.3 j/molK

Looks look at a specific system to make some more definitions. CO2(g) cooled to -78 degrees C is a solid and commonly called dry ice. The physical reaction can be written as:

CO2(gas, 25 degrees C) <====> CO2 (solid, -78 degrees C) + heat

When heat is lost the reaction is said to be exothermic. If heat had been gained the reaction would be said to be endothermic. We define the system to be the carbon dioxide contained in some container. The surroundings are everything external to the system and the boundary is what separates the system from the surroundings. If we are studying what is occuring in a cell then we would call the cell our system, the cell membrane the boundary and the body the surroundings. The boundary can be either real or imaginary depending upon what is being studied. If we are studying the earth then the earth is our system, the universe is the surroundings, and the boundary is an imaginary sphere of whatever radius we want it to have for our particular study.

Let's assume that we put dry ice inside a baloon (which will not break) and let the dry ice change state to the gaseous state (heat will flow into the system -- endothermic). Now the container is expandable so as the gas is formed the system expands the balloon and hence does work against the surroundings. The Principle of Conservation of Energy says that the heat flowing into the system goes into some other form and we can consider the process in three steps:

1. Energy is required to separate the solid into separate particles.
2. The gas is warmed to RT (room temperature)
3. The system expands

Steps one and two are caused by E = Ef - Ei and step three is work = W. So since all forms of energy are conserved, we must have

q = E - W

where q is the energy put in as heat, deltaE is the energy to break the solid lattice and raise the temperature, and W is the work done by the system on the surroundings (taken as negative by convention). We can solve for deltaE and have

E = q + W

which is a statement of the first law of thermodynamics. For this particular process

W = -P*V because the process was carried out at constant P (atmospheric pressure).

If we had carried this out in a rigid container then there could be no expansion and the pressure inside the system would increase.

Many reactions are carried out at constant pressure and so we have a new term:

qp = E - W = H = Hf - Hi .........(1)

where this new symbol is

called the enthalpy.

qp = + then the reaction is endothermic and if qp = - then the reaction is exothermic.

The definition of enthalpy is really:

H = E + PV

where E is the internal energy of the system (sum of kinetic and potential energies), P is the pressure and V is the volume. This definition results in the same equation 1 above :

H = E + PV + VP

but if the reaction is at constant P then P = 0 so

H = E + PV

but PV is -W so we have

H = E - W which is the same as equation 1.

 Now take a practice quiz to help you understand if you understand the basic concepts. You must use your real name when it asks for a name. The test will only submit when you have answers all of the questions correctly. If you are not taking this course for credit please do not answer all the questions correctly for I don't want to be flooded with email answers to the tests.

Web Author: Dr. Leon L. Combs