18. Enthalpy and Heat
The study of energy and its transformations is known as thermodynamics.
Energy is commonly defined as the capacity to do work or to transfer heat.
Work is energy used to cause an object with mass to move.
Heat is energy used to cause the temperature of an object to increase.
Kinetic energy is the energy of motion, represented by the equation:
Ek = 1/2 mv2
Atoms and molecules have mass and are in motion, therefore they have kinetic energy.
Potential energy is energy of position, based on the relative position of one object with another.
Gravitational potential energy is represented by the equation:
Ep = mgh
Gravity, near the surface of the Earth, accelerates all objects at a rate equal to the gravitational constant, g, 9.8 m/s2.
Much more important in chemistry is the potential energy known as electrostatic potential energy, Eel, arising from the interactions between charged particles.
The SI unit for energy is the joule: J = 1 kg-m2/s2
A 2 kg mass moving at 1 m/s possesses a kinetic energy of 1 J:
Ek = 1/2 mv2 = 1/2 (2 kg) (1 m/s)2 = 1 kg-m2/s2 = 1 J
Since a joule is a small amount of energy, the unit kilojoules, kJ, is often used when describing chemical reactions.
Traditionally, energy changes in chemical reactions have been expressed in calories, a non-SI unit.
A calorie was originally defined as the amount of heat energy required to raise the temperature of 1 g of water from 14.5 oC to 15.5 oC. It is now defined in terms of the joule:
When chemists analyze energy changes, they focus their attention on a system, usually the reactants and products of a chemical reaction.
1 cal = 4.184 J (exactly)
A related energy unit used in nutrition is the nutritional Calorie (note the capital letter).
1 Cal = 1000 cal = 1 kcal
The container for a reaction and everything beyond it are considered the surroundings.
A closed system is one that can exchange energy, but not matter, with its surroundings.
Lab Burners and BTUs
Energy is transferred in two ways:
Note: It is generally thought that the opposite of heat is "cold". This is not the case! Cold is the opposite of "hot". Hot and cold are relative amounts of heat.
- Work is the energy transferred when an object is moved by a force.
w = F X d
- Heat is the energy transferred from a hotter object to a colder one.
Heat is transferred between a system and its surroundings as a result of their difference in temperature.
The First Law of Thermodynamics - Energy is conserved.
The internal energy of a system is the sum of all the kinetic and potential energies of all its components.
ΔE = Efinal − Einitial
The equation above indicates the change in internal energy, ΔE, is the difference between the final energy, Efinal, and the initial energy, Einitial.
Thermodynamic quantities like ΔE have three parts: a number, a unit, and a sign.
- The number and unit give the magnitude of the charge.
- The sign gives the direction.
- A positive ΔE, when Efinal > Einitial, indicates the system gained energy from its surroundsings. (diagram B below)
- A negative ΔE, when Efinal < Einitial, indicates the system lost energy to its surroundsings. (diagram A below)
In a chemical reaction the initial state of the system refers to the reactants and the final state refers to the products.
2 H2(g) + O2(g) → 2 H2O(g)
In the reaction above, the system loses energy to the surroundings as heat. Because heat is lost from the system, the internal energy of the products (final state) is less than that of the reactants (initial state), and ΔE is negative.
Another way of saying this - as heat is added to or removed from a system, work is done on or by the system.
Using q to represent the heat added to or removed from the system, and w to represent work, the First Law of Thermodynamics can be represented by the equation:
ΔE = q + w
- + means system gains heat
- − means system loses heat
- + means work is done on system
- − means work is done by system
When a process (such as a chemical reaction) occurs in which the system absorbs heat, the process is called endothermic.
- + means net gain of energy by system
- − means net loss of energy by system
A process in which the system loses heat is called exothermic.
The work involved in the expansion or compression of gases is called pressure-volume work, or P-V work.
When the pressure is constant, the sign and magnitude of the P-V work is given by
w = − P ΔV
where P is pressure and ΔV is the change in volume of the system
(ΔV = Vfinal − Vinitial).
Enthalpy, H is the thermodynamic function that accounts for heat flow in processes occurring at constant pressure when no forms of work are performed other than P-V work.
H = E + PV
At constant pressure, a change in enthalpy equals the change in internal energy plus the product of the constant pressure times the change in volume.
ΔH = ΔE + P ΔV
Enthalpy of reaction, the enthalpy change for a chemical reaction is expressed by the equation:
- When ΔH is positive, the system has gained heat from the surroundings - endothermic.
- When ΔH is negative, the system has lost heat to the surroundings - exothermic.
ΔH = Hproducts − Hreactants
Here is an example of a thermochemical equation:
2 H2(g) + O2(g) → 2 H2O(g) ΔH = − 483.6 kJ
This equation indicates two moles of hydrogen gas burn to form two moles of water at a constant pressure, releasing 483.6 kJ of heat.
Enthalpy change during a chemical reaction can also be represented in an enthalpy diagram, showing the reactants at the top and the products at the bottom.
Guidelines for using thermochemical equations and enthalpy diagrams:
- The magnitude of ΔH is directly proportional to the amount of reactant consumed in the process.
- The enthalpy change for a reaction is equal in magnitude, but opposite in sign, to ΔH for the reverse reaction.
- The enthalpy change for a reaction depends on the state of the reactants and products.
ΔH can be determined experimentally by measuring the magnitude of the ΔT the heat flow produces.
The measure of heat flow is called calorimetry.
The device used to measure heat flow is a calorimeter.
All substances change temperature when they are heated, but the magnitude of the temperature change produced by a given quantity of heat varies from substance to substance.
The heat capacity, C of an object is the amount of heat required to raise its temperature by 1 K (1 oC). The greater the heat capacity, the greater the heat required to produce a given increase in temperature.
The heat capacity of one mole of a substance is called its molar heat capacity, Cmolar.
The heat capacity of one gram of a substance is called its specific heat capacity, s - or simply specific heat, represented by the equation:
For heat calculations, the equation can be rearranged to:
- s = specific heat capacity
- m = mass, in grams
- q = heat, in Joules
- ΔT = temperature change, either K or oC
q = s X m X ΔT
Heat of Fusion of Ice
Specific Heat of a Metal
Hess's Law states that if a reaction is carried out in a series of steps, ΔH for the overall reaction will equal the sum of the enthalpy changes for the individual steps.
The enthalpy diagram below demonstrates Hess's Law.
Enthalpy changes associated with the formation of a compound from its constituent elements is known as enthalpy of formation, (or heat of formation), ΔHf.
To compare enthalpies of different reactions, a set of conditions must be defined at which the enthalpies will be tabulated. These conditions are called the standard state:
The standard enthalpy change, ΔHo, of a reaction is defined as the enthalpy change when all reactants and products are in their standard states.
- a pure substance
- at 1 atmosphere of pressure (1 atm)
- at 298 K (25 oC)
The standard enthalpy of formation of a compound, ΔHof, is the change in enthalpy for the reaction that forms one mole of the compound from its elements, with all substances in their standard states. This information is found in charts like this.
By definition, the standard enthalpy of formation of the most stable form of any element is zero, because there is no formation reaction needed when the element is already in its standard state.
Any reaction can be broken down into formation reactions:
ΔHorxn = ∑ n ΔHof (products) − ∑ m ΔHof (reactants)
The equation above states: the standard enthalpy change of a reaction is the sum of the standard enthalpies of formation of the products minus the sum of the standard enthalpies of formation of the reactants.
Note: (n and m are the coefficients from the balanced chemical equation)
Energy Values In Foods
The energy released when one gram of a material is burned is called its fuel value.
The amount of energy our bodies require varies considerably depending on such factors as weight, age, and muscular activity.
- The average fuel value of carbohydrates is 17 kJ/g (4 kcal/g).
- The average fuel value of fats is 38 kJ.g (9 kcal/g).
- The average fuel value of proteins 17 kJ/g (4 kcal/g).
- About 100 kJ per kilogram of body weight per day is required to keep the body functioning at a minimal level.
- The average 70 kg (154 lb) person expends about 800 kJ/hr when doing light work
- Strenuous activity often requires 2000 kJ/hr or more
Oil and gasoline prices are at record highs. Ethanol from corn is being presented as a "renewable" fuel resource. Just how good a fuel is ethanol?
Here are some ballpark fuel-value numbers:
- wood − 18 kj/g
- coal − 32 kj/g
- ethanol (C2H5OH) − 33 kj/g or 76,500 BTU/gal
- gasoline (octane, C8H18) − 48 kj/g or 124,800 BTU/gal
- natural gas (CH4) − 49 kj/g
- hydrogen (H2) − 142 kj/g
Miles Per Gallon