Enthalpy

Outline

• Heat Energy in Reactions
  • Heat and Systems
  • Enthalpy and Chemical Reactions
• Practice with Concepts
• Discussion Questions
• Optional Website Reading

Heat Energy in Reactions

While other forms of energy such as light and sound production occur in chemical reactions, it is most useful to track the production of heat energy or absorption by monitoring changes in temperature. This information can tell us how the energy stored in chemical bonds is changing as bonds are broken in reactant molecules and reformed in product molecules, and which way a particular reaction will run in obedience to the laws of thermodynamics.

Heat and Systems

In the most basic terms, heat is the transfer of thermal energy between to bodies. Note the implications:

• heat transfer always involves a temperature change
• the bodies which change temperatures are at different temperatures
• no heat flows between bodies at the same temperature

Since there is a flow, we must define the boundaries of the system containing the heat at the beginning of any heat flow scenario. Let's first look at what we mean by system.

	A system is a group of objects that lie within some defined boundary. The boundary can be real (a wall, a thermos jar) or it can be imagined (the edges of a hydrogen-II cloud in space). In an open system, both energy and matter can cross this boundary. In a closed system, matter cannot cross the boundary, but energy still can. In an isolated system, nothing crosses the boundary. What happens in an isolated system does not -- it cannot -- affect the surrounding universe.
	In a closed system, matter cannot cross the boundary, but energy still can.
	In an isolated system, nothing crosses the boundary. What happens in an isolated system does not -- it cannot -- affect the surrounding universe.

The First Law of Thermodynamics stipulates that the total energy of a closed or isolated system cannot change. Another way to say this is that energy is not created or destroyed. We think the universe is a closed system, so the total energy of the universe does not change with time.

The Second Law of Thermodynamics stipulates that the total disorder of a closed system, measured by the amount of useless heat energy (energy which cannot do work) is increasing. This does not contradict the first law. There are two kinds of energy here: one in several forms which we can use to do work, and one random, disordered form of energy which does no work.

In mathematical terms, the change of energy inside the system (ΔE) equals the energy flow across the boundary of the system (heat flow = q) plus any work done on the system by the environment or by the environment on the system (work = w).

ΔE = q + w

q is positive if heat flows into the system and negative if heat flows out of the system. w is positive if the environment does work on the system and negative if the system does work on the environment. We can measure work done if there is a change in volume as negative work = pressure * change in volume. The work is negative because expanding volume does work on the environment, which we've defined as negative. In simple formula terms, w = P*ΔV, so we can also write

ΔE = q + PΔV

Any chemical reaction in which the energy stored in the products is not equal to the energy in the reactants involves the flow of heat across the boundary between the materials in the reaction (products and reactants) and the environment around them. If the final energy of the products is less than the original energy in the reactants, heat has flowed out of the system into the environment, and the reaction is exothermic. If the energy at the end of the reaction is greater than that stored in the reactants before the reaction started, energy must have been applied to the system by the environment and the reaction is endothermic. Since nature tends to favor changes of state and matter which lower the energy level (like water flowing downhill), exothermic reactions are usually favored to continue.

This makes a certain amount of sense, even if a reaction requires some initial input of energy. The energy produced by the first few molecules which react is available to fuel the energy of activation or startup energy required by the next few molecules to react. Once started, an exothermic reaction will continue until the limiting reactants are used up or until the system reaches an equilibrium state.

Because the energy stored in chemical bonds is determined by type of bond and molecule involved, a specific reaction always releases or absorbs the same amount of heat. This change is called the enthalpy of reaction, and it is the difference between the enthalpy or heat energy stored in the products and the energy stored in the reactants.

Every compound molecule has a heat of formation, which is defined as the amount of the energy change that occurs when the compound is formed from its elements. Note that this heat can be positive or negative. Heats of formation are determined experimentally for compounds at a particular temperature and pressure and are listed in tables (like the Appendices in your text).

By definition, elements in a pure state have a zero heat of formation. So solid silver's enthalpy of formation is 0. But silver chloride, AgCl, has a heat of formation of -127.04 kiloJoules/mole. This means that the reaction Ag + Cl → AgCl releases 127.04 Joules for every mole of AgCl formed.

Enthalpy and Chemical Reactions

We need an unambiguous way to write reaction equations that show the change in energy for the reaction. The notation for an exothermic reaction is

AB + CD → AD + BC + energy

Since the final energy state of the products is less than the initial state of the reactants, the energy state has decreased, and ΔH is negative.

The notation for an endothermic reaction is

AB + CD + energy → AD + BC

Since the final energy state of the products is greater than the initial state of the reactants, the energy state has increased, and ΔH is positive.

Practice with the Concepts

Calculating enthalpy for state changes

If 27.0 grams of ice at 0 degrees celsius is added to 123 grams of water at 100 degrees Celsius, figure out the final temperature. (The specific heat of water is 4.184 J/K-g).

Two actions by heat occurs: the ice melts and the temperature of the melted water is raised to the final temperature (which we don't know yet). This heat comes from the 123grams of water at 100 degrees, which cools down to the same final temperature.

FIRST STEP

What is the heat required to melt the ice? q = heat of fusion of ice * moles of ice. If the heat of fusion of ice is 6.009 kJ/mole of ice, how many joules are required to melt the 27 grams of ice? (We'll call this q_1.)

SECOND STEP

How much heat is required to raise the temperature of water to the final temperature T_f from T_i = 0?. (We'll call this q₂.)

THIRD STEP

How much heat is lost by the hot water in going from its initial temperature of 100 degrees to T_f? (We'll call this q₃.)

FOURTH STEP

So what is the final temperature T_f? Well, we know that the heat gained by the ice water (q₁ + q₂) must equal the heat lost by the hot water (q₃). So we can equate the two and solve for the single unknown T_f.

Discussion Questions

• How can you determine whether a reaction is spontaneous? What do we mean by this?
• What is the relationship of energy and power?

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