Enthalpy
- The internal energy change is heat supplied to (+) or extracted from (-) the system at constant volume. The corresponding state function at constant pressure is the enthalpy.
- dU = dq or DU = qv (no additional work, DV = 0, w = 0)
- For processes that occur at constant pressure we must add work necessary to change the volume.
- dH = dU + d(PV), the enthalpy is such a function.
- For an ideal gas, dH = dU + d(nRT).
- We can expand the enthalpy: dH = dU + d(PV) = dU + PdV + VdP
- Note that since dU = -PdV + dq we have that dH = -PdV + dq + PdV + VdP or dH = VdP + dq at constant pressure VdP = 0 so DH = dqp.
- Variation of the enthalpy with temperature.
- heat capacity at constant pressure, Cp. (extensive, units JK-1)
- nCp = (dH/dT) p. dH = nCpdT (provided Cp is a constant)
- This can be compared to DU = nCv DT.
- Relationship between Cv and Cp _à Cp – Cv = R.
- Since Cv = 3/2nR, we can conclude Cp = 5/2nR for a monatomic ideal gas.
- If Cp is a function of temperature it can have the form
Cp = a + bT + c/T2.
Thermochemistry
The study of the heat produced or required by a chemical reaction.\
- Measurement: Calorimetry.
- Adiabatic bomb calorimeter measures
DU (constant volume).
Adiabatic flame calorimeter measures DH (constant pressure).
- The standard enthalpy change,
Dis the change in enthalpy for a process in which the initial and final substances are in their standard states.
- The standard state of a substance at a specified temperature is its pure form at 1 bar.
- Examples:
Standard enthalpy of vaporization at 373 K (physical change)
H2O (l) ® H2O (g) Dvap= + 40.66 kJ/mol
Standard enthalpy of reaction at 298 K (chemical change)
CH4 (g) + 2 O2 (g) ® CO2 (g) + 2 H2O (l) D r= - 890.0 kJ/mol
The standard reaction enthalpy,
Dris the enthalpy change when reactants
in their standard states change to form products in their standard states.
To calculate
Dr treat the process as a thermochemical equation.
D
r= Dr(products) - Dr(reactants)
D
r= 2D f(H2O,l) + 2D f(CO2,g) - D f(CH4g) - 2D f(O2,g)
Note that the above reaction is an example of combustion i.e. the complete oxidation of an organic compound to CO2 and H2O.
- Enthalpy of forward and reverse processes differ only by a sign.
- Hess’s Law: The standard enthalpy of an overall reaction is the sum of the standard enthalpies of the individual reactions into which a reaction may be divided.
- The standard enthalpy of formation of a substance is the standard reaction enthalpy for formation of the compound from its elements in their reference states.
- The reference state of an element is its most stable state at the specified temperature and 1 bar of pressure.
- The standard enthalpy of formation of elements is zero.
- Thus, if we consider the formation of water the enthalpy is given as shown below.
Example:
H2 (g) + ½ O2 (g) ® H2O (g) Df( H2O ,g) = - 241.8 kJ/mol
The enthalpies of formation of both H2 and O2 are zero since they are elements in their standard states.