Enthalpy (H) - The sum of the internal energy of the system plus the product of the pressure of the gas in the system and its volume:

After a series of rearrangements, and if pressure if kept constant, we can arrive at the following equation:

 
where H is the H_final minus H_initial and q is heat

Enthalpy of Reaction (H)

• The difference between the sum of the enthalpies of the products and the sum of the enthalpies of the reactants:

In the above reaction, n and m are the coefficients of the products and the reactants in the balanced equation.

Exothermic - Reaction in which a system RELEASES heat to its surroundings.   H  is negative (H < 0) Ea is the activation energy which is discussed in more detail in the kinetics unit.  (See Activation Energy notes)

Endothermic - Reaction in which a system ABSORBS heat from its surroundings. H  is positive (H > 0)

Let's distinguish various phase changes of water as either endothermic or exothermic.

1) The above reaction is EXOTHERMIC because heat is released when liquid water freezes to form ice.

2) The above reaction is ENDOTHERMIC because there must be an input of energy in order for water molecules in the liquid phase to have enough energy to escape into the gas phase.

3) The above reaction is ENDOTHERMIC because there must be an input of energy to break the bonds holding water molecules together as ice.

Standard-State Enthalpy of Reaction (H)

Three factors can affect the enthalpy of reaction:

1. The concentrations of the reactants and the products
2. The temperature of the system
3. The partial pressures of the gases involved (if any)

The effects of changes in these factors can be shown relative to the standard-state enthalpy of reaction (H) which is the change in the enthalpy during a chemical reaction that begins and ends under standard-state conditions.

Standard-state conditions

• The partial pressures of any gases involved in the reaction is 0.1 MPa.
• The concentrations of all aqueous solutions are 1 M.

Measurements are also generally taken at a temperature of 25C (298 K)

Hess's Law

1940 - Germain Henri Hess

Hess's Law states that the heat transferred, or change in enthalpy (H), in a reaction is the same regardless whether the reaction occurs in a single step or in several steps. The method of calculating the enthalpy of reaction developed by Hess is called Hess's Law of Heat Summation. If a series of reactions are added together, the net change in the heat of the reaction is the sum of the enthalpy changes for each step.

Rules for using Hess's Law If the reaction is multiplied (or divided) by some factor, H must also be multiplied (or divided) by that same factor. If the reaction is reversed (flipped), the sign of H must also be reversed.

Example Calculations

1) Nitrogen and oxygen gas combine to form nitrogen dioxide according to the following reaction:

Calculate the change in enthalpy for the above overall reaction, given:

This problem is very simple.  If we simply add up the two reactions keeping all the reactants on the left and all the products on the right, we end up with the overall equation that we are given.  Since we didn't make any changes to the individual reactions, we don't make any changes to H.  If we add up H as well, we find the change in enthalpy:

Let's try one that is a bit more complicated.

2) From the following enthalpy changes:

calculate the value of H for the reaction:

If we look at the final reaction, we see that we need 2 S atoms on the reactants side.  The only reaction with S atoms is the third reaction, and in order to get 2 S atoms, we need to multiply the whole reaction by a factor of 2.  The next reactant in the final reaction is 2 OF molecules.  The only reaction with an OF molecule is the first reaction, and in order to get 2 OF molecules, we need to multiply the whole reaction by a factor of 2.  On the products side of the final reaction, there is 1 SF₄ molecule, and the only possible source of the SF₄ molecule is the second reaction.  However, the SF₄ molecule is on the reactants side, which is not the side we need it on.  So we'll have to FLIP the second reaction to get the SF₄ molecule where we need it.

Now if we total up the reactions, we should end up with the given overall reaction:

Remember that everything we did to each reaction, we have to do to each respective H.  So we have to multiply the first and third H values by a factor of 2.  We also have to reverse the sign of the second H.  When we add these up we get:

Enthalpy of formation (H_f)

• The enthalpy associated with the reaction that forms a compound from its elements in their most thermodynamically stable states.  These are measured on a relative scale where zero is the enthalpy of formation of the elements in their most thermodynamically stable states.

The standard-state enthalpy of reaction is equal to the sum of the enthalpies of formation of the products minus the sum of the enthalpies of formation of the reactants:

Sample enthalpy of formation calculation

Calculate the heat given off when one mole of B₅H₉ reacts with excess oxygen according to the following reaction:

Compound		Hf (kJ/mol-K)
B5H9(g)		73.2
B2O3(g)		-1272.77
O2(g)		0
H2O(g)		-241.82

In the reaction above 2 moles of B₅H₉ react with 12 moles of O₂ to yield five moles of B₂O₃ and 9 moles of H₂O.  We find the H_f by subtracting the sum of the enthalpies of the reactant from the sum of the enthalpies of the products:

• NOTE: The heat of formation of O₂ is zero because this is the form of the oxygen in its most thermodynamically stable state.

Bond Energy

• The energy required to break a bond.  Bond energy is always a positive number because the breaking of a bond requires an input of energy (endothermic).  When a bond is formed, the amount of energy equal to the bond energy is released.

The bonds broken are the reactant bonds.  The bonds formed are the product bonds.

Sample Calculation

Find H for the following reaction given the following bond energies:

We have to figure out which bonds are broken and which bonds are formed.  

• 2 H-H bonds are broken.

• 1 O=O bond is broken

• 2 O-H bonds are formed per water molecule, and there are 2 water molecules formed, therefore 4 O-H bonds are formed

Now we can substitute the values given into the equation:

Bond-dissociation enthalpy - The energy needed to break an X-Y bond to give X and Y atoms in the gas phase, such as in the following reaction:

Next:  "Entropy"