Units and Definitions of Energy

Energy is simply defined as the capacity to do work or supply heat. Work is a dynamic change such as an object moving a distance against a force…w = F x d.

Modern scientific convention uses a unit of energy called a joule (J).

Kinetic energy is the energy of a mass in motion…E_K = 1/2(mv²) The energy of a 2 kilogram mass moving 1 meter/second is…E_K = 1/2(2 kg)(1 m/s)² = 1 kgm²/s² = 1 J

Potential energy is defined as stored energy.

The total internal energy of a system is equal to the sum of the kinetic energy and the potential energy. A system is defined as a defined portion of the universe that is being studied. A closed system is one that can exchange heat but not mass with its surroundings.

The change in energy (DE = E_final - E_initial) involves changes in energy in the form of heat (q) and work (w)… DE = q + w

By convention, energy changes are measured from the point of view of the system.

Energy that flows from the system to the surroundings has a negative sign because it is lost from the system. [E_final is less than E_initial]

DE = a negative number when the system loses energy to its surroundings (exothermic). Work done by the system will be negative (-w) and heat given off by the system will also be negative (-q).

 

Energy that flows from the surroundings to the system has a positive sign because it is gained by the system. [E_final is greater than E_initial]

 

DE = a positive number when the system gains energy from its surroundings (endothermic). Work done on the system will be positive (+w) and heat added to the system will also be positive (+q).

 

The internal energy of a chemical system depends on the identity of the compounds, mass of the compounds, temperature, pressure and physical states of the compounds. It does not depend on the history of the compounds…how they were made or their previous physical states. The present conditions are all that matters. Internal energy is considered a state function. A state function is a property whose value depends only on the present state of the system. Pressure, volume and temperature are also state functions, but heat and work are not considered state functions.

The most common type of work experienced in chemical reactions is an increase in the volume of the system. A chemical reaction also does work by moving electrons or atoms.

The law of conservation of energy (1^st Law of Thermodynamics) states that energy is neither created nor destroyed only transferred or transformed.

Transfer of Thermal Energy

Heat is transferred by either direct transfer from one object touching another or by radiation in the form of infrared radiation.

Heat capacity is defined as the "heat required to produce a given temperature change in some substance" and depends on both the type of substance and the mass of the substance.

Molar heat capacity is used when the amount of a substance is given in moles.

Specific heat capacity is the "heat needed to produce a given temperature change per gram of substance" and is expressed in the units J/gK.

heat change= q = specific heat x mass x temperature change

 

Energy and Changes of Physical State

When the physical state of a substance is changed, heat is either absorbed or liberated but the temperature remains constant. The reason that this happens can be illustrated with water. When water is in the form of ice, virtually all of the hydrogen atoms and oxygen atoms are involved in hydrogen-bonds. If energy is applied in the form of heat, many of these hydrogen bonds are disrupted and the water molecules are free to move about.

When this happens, water becomes a liquid. If more heat is applied all of the hydrogen-bonds are disrupted and the molecules of water take the form of a gas.

The energy of a hydrogen-bond in water is about 20 kJ/mol. Chemical bond energies are about 400 kJ/mol. Although the energy of the hydrogen-bond is small it has a significant effect on the amount of energy that is required to melt ice or boil water.

The heat required to melt ice without any increase in the temperature of the system is equal to 333 J/g. This is called the heat of fusion and it relates to the energy needed to break the hydrogen-bonds that are holding the water molecules together in the solid state.

The heat required to boil water without an increase in temperature is equal to 2,260 J/g. This is called the heat of vaporization and it relates to the energy needed to break the hydrogen-bonds holding the water molecules together in the liquid state.

These are also called the enthalpy of fusion, DH_fusion, and enthalpy of vaporization, DH_vaporization.

The actual amount of heat that has to be added to change a solid substance to a gas depends on the following four properties.

1. Specific Heat of the Substance

2. Total Mass of the Substance

3. Heat of Fusion of the Substance

4. Heat of Vaporization of the Substance.

The changes in physical states are summarized in the following table.
 

Enthalpy

The heat changes of reactions are given a special symbol DH_rxn. This symbol represents the heat of reaction or change in enthalpy.

As with internal energy, enthalpy is a state function so only the change in enthalpy is important, not the history of how the change was arrived at.

DH_rxn = H_products - H_reactants
 

·DH will have a positive value for an endothermic reaction. H_products > H_reactants The system is absorbing heat from the surroundings.

·DH will have a negative value for an exothermic reaction. H_products < H_reactants The system is giving off heat to the surroundings.

CO_{2 (g)} ® C _{(s…diamond)} + O_{2 (g)} DH_rxn = +395 kJ endothermic

CH_{4 (g)} + 2 O_2(g) ® CO_{2 (g)} + 2 H₂O _(liq) DH_rxn = -890 kJ exothermic

·The sign of the enthalpy change indicates whether a reaction is endothermic or exothermic.

·Enthalpy depends on the amount of matter involved in the reaction so that if 2 moles of methane are burned in the above reaction…DH_rxn = -1,780 kJ. Therefore, DH_rxn can be used as a conversion factor in calculations.

· DH_rxn is equal to but will have the opposite sign of DH for the reverse reaction.

DH_{forward rxn} = - DH_{reverse rxn}

 

Standard Enthalpies of Formation

The standard state of a compound is defined as the physical state of the compound, which is most stable at 1 atmosphere of pressure and 298 K.

When a reaction takes place at standard conditions, we say that it has a standard enthalpy of reaction symbolized by DH^o_rxn. The superscript ^o indicates standard conditions.

The standard enthalpy change of a reaction for the formation of one mole of a compound directly from its elements (also in their standard states) is called the standard enthalpy of formation symbolized by DH^o_f.

By definition, the standard enthalpy of formation of the most stable form of an element is zero (no reaction energy is needed if the element is already in the standard state).

DH^o_f of O₂ = 0, DH^o_f of H₂ = 0, DH^o_f of C_graphite = 0, DH^o_f of N₂ = 0, etc.

 

Enthalpies of Reactions from DH^o_f

The DH_rxn for any reaction can be calculated if the energies needed to make all of the reactants and products are known.

D H^o_rxn = S n_p DH^o_{f (products)} - S n_r DH^o_{f (reactants)}

 

The term n_p refers to the mole coefficients of the products and the term n_r refers to the mole coefficients of the reactants.

Therefore the DH^o_f of CO₂ (formed by the equation…C _(graphite) + O_{2 (g)} ® CO_{2 (g)}) is equal to…DH^o_{f of carbon dioxide} - DH^o_{f of carbon} - DH^o_{f of oxygen} = -393.5 kJ because the DH^o_{f of carbon} and the DH^o_{f of oxygen} both are equal to zero.

Constant Pressure Calorimetry

Calorimetry is an experimental method by which heats of reaction are measured.

In constant pressure calorimetry, the reaction is open to the atmosphere and isolated from its general surroundings (in a container that does not transfer heat) in constant pressure calorimetry.

A simple experiment could be run in a Styrofoam cup. The cup is covered with a cork stopper but not sealed and a thermometer and a stirring device are inserted through the cork. The heat gained by the solution, q_soln is calculated as before…

q_soln = C_sp x mass of solution x DT

 

The heat gained or lost by the solution must be produced by the chemical reaction that is being studied. Therefore the heat of the reaction q_rxn is equal in magnitude and opposite in sign from q_soln. An increase in temperature would thus mean that the reaction was exothermic.

 

Constant Volume Calorimetry

The reaction is conducted in a "bomb calorimeter" and is isolated from its general surroundings (in a container that does not transfer heat). The typical types of reactions, studied by this method, are combustion reactions.

To calculate the heat of combustion from the measured change in temperature in the calorimeter, it is necessary to know the heat capacity of the calorimeter C_calorimeter. The calorimeter can be calibrated for this value by burning a sample that gives off a known quantity of heat.

Bond Energies of Individual Bonds
 

Another very useful method that can be used to determine the enthalpy change of a reaction is to use individual bond energies of only the bonds that are altered during a reaction. The bond dissociation energy, D_x-y, is defined as the enthalpy change for breaking a bond, X–Y, in a molecule when the molecule is in the gas phase. The bond dissociation energy represents the energy transferred to the molecule from its surroundings and it thus has a positive value. The amount of energy supplied to break a chemical bond must be equal to the amount of energy necessary to form the bond.

In a chemical reaction, if the energy needed to break the original bonds is greater than the energy gained by the formation of the new bonds, then the reaction will be an endothermic reaction. If the energy needed to break the original bonds is less than the energy gained by the formation of the new bonds, then the reaction will be an exothermic reaction.

The enthalpy change for any reaction can be approximated by the following equation…

DH^o_rxn = S D_{bonds broken} - S D_{bonds formed}

 

 

 Copyright © August 2000 by Richard C. Banks...all rights reserved.