Thermochemistry

Standard States and Calorimetry

An entire branch of chemical thermodynamics requires no more than the first law. The important feature of thermochemistry is that q_P tells about energy inherent in chemical interactions.

Enthalpy of reaction

For a reaction

the enthalpy of reaction is written

At P=1 bar, we have the Standard enthalpy of reaction

Exothermic and Endothermic Reactions

H(2) > H(1)	exothermic (exo="out of")	DrHo > 0
H(2) < H(1)	exothermic (endo="into")	DrHo < 0

Extent of reaction

Consider the reaction

The enthalpy of reaction is expressed per mole. Per mole of what?

We may write a general reaction as

where n_J are the stoichiometric coefficients

Note n_J < 0 for reactants, n_J >0 for products. (For the above reaction, n_A=-1,

n_B = -2, n_C = +2, and n_D = +3).

We may define the extent of reaction x such that the number of moles of J consumed or formed by the reaction.

x has units of moles. D_rHo refers specifically to =1 mole.

Thus, D_rHo is per mole of reaction as written. For the reactions.

D_rH^o(2) = ½D_rH^o(1)

Enthalpies of transition

Symbol	Process	Transition
DfusHo	fusion	solid ® liquid
DvapHo	vaporization	liquid ® vapor
DsubHo	sublimation	solid ® vapor
DtrsHo	phase transition	phasea ® phase b
DmixHo	mixing	pure A, B ® A,B solution
DsolHo	solution	A + solvent ® solution of A
DhydHo	hydration	A ® A(aq)
DionHo	ionization	A(g) ® A+(g) + e-(g)
DfHo	formation	ref. elements ® compound
DcHo	combustion	compound + O2(g) ® CO2(g) + H2O (l) (+N2(g) ?)
DatHo	atomization	compound(g) ® elements (atomic g)
Ho(A-B)	bond dissociation	A-B(g) ® A(g) + B(g)
DecHo	electron gain	A(g) + e-(g) ® A-(g)

Notes:

1. All of the above process deal with some form of bond breaking/making, including weak intermolecular and solvent/solute interactions as well as covalent and ionic chemical bonds and electron-nuclear bonds
2. All enthalpies of transition are expressed per mole.

Standard Thermodynamic Functions

Consider the indefinite integral

How do we find the constant of integration C?

Define a zero for the function H: Choose H=H^o=0 for a standard state, then integrate from that state.

Standard States

The standard state of liquid and solid substances is the pure substance at P=1 bar.

The standard state of a gaseous substance is the pure ideal gas at P=1 bar.

The standard state may be defined for any T. (typically tabulated for 298K).

Reference State

The reference state of a substance at a given T is its most stable form at standard pressure and the given T. Important reference state elements include graphite carbon and diatomic gases, e.g., C_(graphite), H₂(g), O₂(g), N₂(g).

Formation reaction

A formation reaction is reference state elements ® compound.

Example: formation of liquid benzene, C₆H₆ (l)

6C_(gr) + 3H₂(g)® C₆H₆(l)

D_rH^o for this process is H^o(C₆H₆(l)) - 6H^o (C(gr)) - 3H^o(H₂(g)). If we define the H of the reference state elements to be 0, then D_rH^o for the formation reaction is D_fH^o of the product.

Using path-independence of H

There are two practical consequences of the state function properties of H.

1. DH(A®B) = H_B H_A = (H_A H_B) = DH(B®A)
   
   
2. It is possible to choose a known path around the given path. H is the same for both paths. For example, we can calculate D_rH^o for any reaction by choosing a path through the reference state elements.

This picture shows that we can write

That is, we can use enthalpies of formation instead of absolute enthalpies in the calculation of a reaction enthalpy.

Bomb Calorimetry

Fixed volume apparatus: measures DU^o (q_V)

In order to measure the heat transferred from the temperature change of the calorimeter, the C_V (C_P) of the calorimeter must be known. This is assumed to be much larger than the C_V of the reactants and products.

2 approaches (K stands for calorimeter):

(1) measure C_V,K by burning a standard sample with known DU, measuring DT

(2) measure C_V,K by heating the bath with a known current for a known time (VIt=energy) and measuring DT

We want DU for reactants and products at the same T. We really measure the DT caused by the reaction in an insulated, constant V vessel. The difference between U of the experimental final state and the desired final state can be found from C_V of the calorimeter.

Differential Scanning Calorimetry

Essentially a thermostat that scans the temperature of the sample in slow, controlled way. Measures power dissipated in sample per unit time. (dq/dt). Since the temperature scan rate is known (dT/dt), the heat capacity dq_P/dT is measured.

Relating D_rU^o to D_rH^o

D_r H^o = D_r U^o+D_r (P^oV^o) = D_r U^o+P^oD_r V^o

Note that D_rV^o is calculated just like any other energy quantity of reaction:

Simplifications:

For most reactions near STP, it is reasonable to neglect the molar volumes of condensed-phase substances relative to those of gaseous substances.

Since the gaseous standard state is ideal behavior, for each gas, and

Thus,

D_rH^o = D_rU^o + Dn_gasRT

Example

aA(s) + bB(g) ® cC(g) + dD(g) + eE(l)

Neglecting volumes of A and E: D_rV^o = cV^o_m,C + dV^o_m,D - bV^o_m,B = (c+d-b)RT/P^o

(Dngas = c+d-b )