Chemical Thermodynamics

Thermodynamics is the study of energy transfer and energy changes that accompany physical and chemical processes. It does not tell us how fast a spontaneous reaction will occur or the mechanism of a reaction.

The First Law of Thermodynamics states that the energy of the universe is constant. It is related to the Law of Conservation of Energy which states that energy can be converted from one form to another but cannot be created or destroyed. DE = q + w

The universe is divided into two parts: the system and the surroundings. The system is the part of the universe being studied; the surroundings includes everything else.

An exothermic reaction is one in which energy flows out of the system, as in:
CH_4(g) + 2O_2(g) ® CO_2(g) + 2H₂O_(l) + 890 kJ

An endothermic reaction is one in which energy flows from the surroundings into the system, as in:
N_2(g) + O_2(g) + 180 kJ ® 2NO_(g)

Enthalpy:

At the start of any reaction each of the reactants has a certain heat content. Enthalpy is the amount of heat energy that a substance has at a given temperature and pressure. Enthalpy is symbolized by the letter "H". The enthalpy of a substance cannot be measured directly. However, changes in enthalpy can be measured.

Changes in enthalpy occur whenever heat is released or absorbed in chemical reactions. A change in enthalpy is symbolized by DH.  It is also referred to as the heat of reaction.

Standard conditions for measuring DH are 25° C (298 K) and 1 atm (1M for solutions).

v An endothermic reaction has a positive DH.  
 N_2(g) + O_2(g) + 180 kJ ® 2NO_(g)   DH=+180 kJ


v  An exothermic reaction has a negative DH.
  CH_4(g) + 2O_2(g) ® CO_2(g) + 2H₂O_(l) + 890 kJ  DH= -890 kJ

If a reaction is reversed, the sign of DH is also reversed. The magnitude of DH is directly proportional to the quantities of the reactants and products.

The Standard Heat of Formation, DH°_f , is the change in enthalpy that is associated with the formation of one mole of a compound from its elements in their standard states. DH°_f for elements in their standard states = 0.

½N_2(g) + O_2(g) ® NO_2(g)  DH°_f=34 kJ/mol

C_(s) + 2H_2(g) + ½O_2(g) ® CH₃OH_(l)  DH°_f=-239 kJ/mol

Stability:
A compound with a large negative heat of formation gives off a large amount of energy during its formation. It will require the same input of energy to decompose the compound into its elements. A compound such as this is usually very stable.

DH°_f values can be used to calculate DH values.

Example:
CH_4(g) + 2O_2(g) ® CO_2(g) + 2H₂O_(l)

DH = S H°_{f (products)}- S H°_{f (reactants)}  

v Be sure to multiply the number of moles (from the balanced equation) by the H°_f 
for each substance.
DH =[1 mol(-393.5 kJ/mol) + 2 mol(-286 kJ/mol)] - 
[ 1 mol (-74.85 kJ/mol + 2 mol (0 kJ/mol)]
DH = -890 kJ

Calorimetry can be used to calculate the heat of combustion from the amount of 
energy transferred.
Reminder: heat energy (q)= (mass) (DT) (specific heat)

Example: Calculate the DH (in kJ/mol) for the combustion of C₁₀H₁₆O from the following information: 2.0 g of C₁₀H₁₆O was burned. The heat from the reaction caused the temperature of 500 g of water to increase by 37°C. 

q = (500 g)(37°C)(4.184 J/g°C) = 77400 J = 77.4 kJ
(2 g C₁₀H₁₆O)(1 mol/152 g)  = 0.013 mol
                        
77.4 kJ/0.013 mol = 5954 kJ/mol
Since the heat was given off during combustion, the DH = -5954 kJ/mol.

Entropy:
The measure of the disorder of a system is its entropy, S, which is expressed in J/K mol. Things tend to move spontaneously in the direction of maximum chaos or disorder. A spontaneous process occurs without outside intervention.

Spontaneous processes are often exothermic, but not always. For example, ice melts at room temperature (an endothermic process).

The Second Law of Thermodynamics states that whenever a spontaneous event takes place in our universe, the total entropy of the universe increases. 

1. For a given substance, the entropy of a gas is greater than the entropy of a liquid or a solid. Gases>Liquids>Solids (This is referred to as positional entropy.)
   Entropy increases in reactions in which solid reactants give liquid or gaseous products.
   

2. Entropy increases when a substance is divided into parts. It increases in reactions in which the total number of product molecules is greater than the total number of reactant molecules.
   

3. Entropy increases with a temperature increase because the motions of molecules become more chaotic.
   

4. Entropy increases with increasing molecular complexity.
   

5. Entropy increases when the volume increases.

A change in entropy is represented by DS. An increase in entropy (DS is +) favors a spontaneous change. In nature, changes tend to take place that create a greater state of disorder. DS _universe = DS _system + DS _surroundings

Relationship between DS and DH:
DS _surroundings = - DH/T

DS _universe = - DH/T + DS _system

Example:

DS _system =2(189)- [2(130.7) + 205] = -88.4 J/K

DH = 2(-241.8) - [2(0) + 0] = -483.6 kJ

DS _surroundings = - DH/T = -(-483.6 kJ/298 K) = 1.623 kJ/K = 1623 J/K
 
So, DS _universe = -88.4 J/K + 1623 J/K = 1534.6 J/K = 1530 J/K.

Since DS _universe = a positive value, the reaction tends to be spontaneous.

A chemical change tends to proceed spontaneously in the direction of a decrease in enthalpy and an increase in entropy.