William M. White - Geochemistry

We cannot measure the absolute enthalpy of substances, but we can determine the enthalpy changes resulting from transformations of a system, and they are of great interest in thermodynamics. For this purpose, a system of relative enthalpies of substances has been established. Since enthalpy is a function of both temperature and pressure, the first problem is to establish standard conditions of temperature and pressure to which these enthalpies apply. These conditions, by convention, are 298.15 K and 0.1 MPa (25°C and 1 bar). Under these conditions the elements are assigned enthalpies of 0. Standard state enthalpy of formation , or heat of formation, from the elements, ΔH° , can then be determined for compounds by measuring the heat evolved in the reactions that form them from the elements (e.g., Example 2.2). For example, the heat of formation of water is determined from the energy released at constant pressure in the reaction: H 2+ ½O 2→ H 2O, which yields a ΔH° of −285.83 kJ/mol, where water is in the liquid state. The minus sign indicates heat is liberated in the reaction , that is, the reaction is exothermic (a reaction that consumes heat is said to be endothermic ).

Having established such a system, the enthalpy associated with a chemical reaction is easily calculated using Hess's law, which is:

(2.115)

where ν iis the stoichiometric coefficient for the i thspecies. In other words, the enthalpy of reaction is just the total enthalpy of the products less the total enthalpy of the reactants. The use of Hess's law is illustrated in Example 2.5below.

The heat of vaporization of a substance is the energy required to convert that substance from liquid to gas, i.e., to boil it. If the reaction H 2+ ½O 2→ H 2O is run to produce water vapor, the ΔH° turns out to be −241.81 kJ/mol. The difference between the enthalpy of formation of water and vapor, 44.02 kJ/mol, is the heat consumed in going from liquid water to water vapor. This is exactly the amount of energy that would be required to boil 1 mole of water. Analogously, the heat of melting (or fusion) is the enthalpy change in the melting of a substance. Because reaction rates are often very slow, and some compounds are not stable at 298 K and 1 MPa, it is not possible to measure the enthalpy for every compound. However, the enthalpies of formation for these compounds can generally be calculated indirectly.

What is the energy consumed or evolved in the hydration of corundum (Al 2O 3) to form gibbsite (Al(OH) 3)? The reaction is:

Answer: We use Hess's law . To use Hess's law, we need the standard state enthalpies for water, corundum, and gibbsite. These are: Al 2O 3: −1675.70 kJ/mol, H 2O: −285.83 and Al(OH) 3: −1293.13. The enthalpy of reaction is .

This is the enthalpy of reaction at 1 bar and 298 K. Suppose you were interested in this reaction under metamorphic conditions such as 300°C and 50 MPa. How would you calculate the enthalpy of reaction then?

Since

(2.62)

and

(2.57)

then at constant pressure

(2.116)

Thus, at constant pressure, the entropy change in a reversible reaction is simply the ratio of enthalpy change to temperature.

Entropies are additive properties and entropies of reaction can be calculated in the same manner as for enthalpies, so Hess's law applies:

(2.117)

The total entropy of a substance can be calculated as:

(2.118)

Table 2.2 Standard state thermodynamic data for some important minerals.

Phase/ Compound	Formula	kJ/mol	S OJ/K-mol	kJ/mol	cc/mol*	a	C Pb	c
H 2O g	H 2O (gas)	−241.81	188.74	−228.57	24789.00	30.54	0.01029	0
H 2O l	H 2O (liquid)	−285.84	69.92	−237.18	18.10	29.75	0.03448	0
CO 2	CO 2	−393.51	213.64	−394.39	24465.10	44.22	0.00879	861904
Calcite	CaCO 3	−1207.30	92.68	−1130.10	36.93	104.52	0.02192	2594080
Graphite	C	0	5.740		5.298
Diamond	C	1.86	2.37		3.417
Aragonite	CaCO 3	−1207.21	90.21	−1129.16	34.15	84.22	0.04284	1397456
α-Qz	SiO 2	−910.65	41.34	−856.24	22.69	46.94	0.03431	1129680
β-Qz	SiO 2	−910.25	41.82	−856.24		60.29	0.00812	0
Cristobalite	SiO 2	−853.10	43.40	−853.10	25.74	58.49	0.01397	1594104
Coesite	SiO 2	−851.62	40.38	−851.62	20.64	46.02	0.00351	1129680
Periclase	MgO	−601.66	26.94	−569.38	11.25	42.59	0.00728	619232
Magnetite	Fe 3O 4	−1118.17	145.73	−1014.93	44.52	91.55	0.20167	0
Spinel	MgAl 2O 4	−2288.01	80.63	−2163.15	39.71	153.86	0.02684	4062246
Hematite	Fe 2O 3	−827.26	87.61	−745.40	30.27	98.28	0.07782	1485320
Corundum	Al 2O 3	−1661.65	50.96	−1568.26	25.58	11.80	0.03506	3506192
Kyanite	Al 2SiO 5	−2581.10	83.68	−2426.91	44.09	173.18	0.02853	5389871
Andalusite	Al 2SiO 5	−2576.78	92.88	−2429.18	51.53	172.84	0.02633	5184855
Sillimanite	Al 2SiO 5	−2573.57	96.78	−2427.10	49.90	167.46	0.03092	4884443
Almandine	Fe 3Al 2Si 3O 12	−5265.50	339.93	−4941.73	115.28	408.15	0.14075	7836623
Grossular	Ca 3Al 2Si 3O 12	−6624.93	254.68	−6263.31	125.30	435.21	0.07117	11429851
Albite	NaAlSi 3O 8	−3921.02	210.04	−3708.31	100.07	258.15	0.05816	6280184
K-feldspar	KAlSi 3O 8	−3971.04	213.93	−3971.4	108.87	320.57	0.01804	12528988
Anorthite	CaAl 2Si 2O 8	−4215.60	205.43	−3991.86	100.79	264.89	0.06190	7112800
Jadeite	NaAlSi 2O 6	−3011.94	133.47	−2842.80	60.44	201.67	0.04770	4966408
Diopside	CaMgSi 2O 6	−3202.34	143.09	−3029.22	66.09	221.21	0.03280	6585616
Enstatite	MgSiO 3	−1546.77	67.86	−1459.92	31.28	102.72	0.01983	2627552
Wollatonite	CaSiO 3	−1632.0	82.03	−1656.45	39.93	139.58	0.00236	1401200
Forsterite	Mg 2SiO 4	−2175.68	95.19	−2056.70	43.79	149.83	0.02736	3564768
Clinozoisite	Ca 2Al 3Si 3O 12(OH)	−68798.42	295.56	−6482.02	136.2	787.52	0.10550	11357468
Tremolite	Ca 2MgSi 8O 22(OH) 2	−12319.70	548.90	−11590.71	272.92	188.22	0.05729	4482200
Chlorite	MgAl(AlSi 3)O 10(OH) 8	−8857.38	465.26	−8207.77	207.11	696.64	0.17614	15677448
Pargasite	NaCa 2Mg 4Al 3Si 8O 22(OH) 2	−12623.40	669.44	−11950.58	273.5	861.07	0.17431	21007864
Phlogopite	KMg 3AlSi 3O 10(OH) 2	−6226.07	287.86	−5841.65	149.66	420.95	0.01204	8995600
Muscovite	KAl 3Si 3O 10(OH) 2	−5972.28	287.86	−5591.08	140.71	408.19	0.110374	10644096
Gibbsite	Al(OH) 3	−1293.13	70.08	−1155.49	31.96	36.19	0.19079	0
Boehmite	AlO(OH)	−983.57	48.45	−908.97	19.54	60.40	0.01757	0
Brucite	Mg(OH) 2	−926.30	63.14	−835.32	24.63	101.03	0.01678	2556424

Data for the standard state of 298.15 K and 0.1 MPa. ΔH fis the molar heat (enthalpy) of formation from the elements; S° is the standard state entropy; V is the molar volume; a, b and c are constants for the heat capacity ( C p) computed as: C p= a + bT − cT –2J/K-mol.