Читать книгу Geochemistry - William M. White - Страница 68

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	SO J/K-mol	kJ/mol	cc/mol*	a	CP b	c
H2Og	H2O (gas)	−241.81	188.74	−228.57	24789.00	30.54	0.01029	0
H2Ol	H2O (liquid)	−285.84	69.92	−237.18	18.10	29.75	0.03448	0
CO2	CO2	−393.51	213.64	−394.39	24465.10	44.22	0.00879	861904
Calcite	CaCO3	−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	CaCO3	−1207.21	90.21	−1129.16	34.15	84.22	0.04284	1397456
α-Qz	SiO2	−910.65	41.34	−856.24	22.69	46.94	0.03431	1129680
β-Qz	SiO2	−910.25	41.82	−856.24		60.29	0.00812	0
Cristobalite	SiO2	−853.10	43.40	−853.10	25.74	58.49	0.01397	1594104
Coesite	SiO2	−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	Fe3O4	−1118.17	145.73	−1014.93	44.52	91.55	0.20167	0
Spinel	MgAl2O4	−2288.01	80.63	−2163.15	39.71	153.86	0.02684	4062246
Hematite	Fe2O3	−827.26	87.61	−745.40	30.27	98.28	0.07782	1485320
Corundum	Al2O3	−1661.65	50.96	−1568.26	25.58	11.80	0.03506	3506192
Kyanite	Al2SiO5	−2581.10	83.68	−2426.91	44.09	173.18	0.02853	5389871
Andalusite	Al2SiO5	−2576.78	92.88	−2429.18	51.53	172.84	0.02633	5184855
Sillimanite	Al2SiO5	−2573.57	96.78	−2427.10	49.90	167.46	0.03092	4884443
Almandine	Fe3Al2Si3O12	−5265.50	339.93	−4941.73	115.28	408.15	0.14075	7836623
Grossular	Ca3Al2Si3O12	−6624.93	254.68	−6263.31	125.30	435.21	0.07117	11429851
Albite	NaAlSi3O8	−3921.02	210.04	−3708.31	100.07	258.15	0.05816	6280184
K-feldspar	KAlSi3O8	−3971.04	213.93	−3971.4	108.87	320.57	0.01804	12528988
Anorthite	CaAl2Si2O8	−4215.60	205.43	−3991.86	100.79	264.89	0.06190	7112800
Jadeite	NaAlSi2O6	−3011.94	133.47	−2842.80	60.44	201.67	0.04770	4966408
Diopside	CaMgSi2O6	−3202.34	143.09	−3029.22	66.09	221.21	0.03280	6585616
Enstatite	MgSiO3	−1546.77	67.86	−1459.92	31.28	102.72	0.01983	2627552
Wollatonite	CaSiO3	−1632.0	82.03	−1656.45	39.93	139.58	0.00236	1401200
Forsterite	Mg2SiO4	−2175.68	95.19	−2056.70	43.79	149.83	0.02736	3564768
Clinozoisite	Ca2Al3Si3O12(OH)	−68798.42	295.56	−6482.02	136.2	787.52	0.10550	11357468
Tremolite	Ca2MgSi8O22(OH)2	−12319.70	548.90	−11590.71	272.92	188.22	0.05729	4482200
Chlorite	MgAl(AlSi3)O10(OH)8	−8857.38	465.26	−8207.77	207.11	696.64	0.17614	15677448
Pargasite	NaCa2Mg4Al3Si8O22(OH)2	−12623.40	669.44	−11950.58	273.5	861.07	0.17431	21007864
Phlogopite	KMg3AlSi3O10(OH)2	−6226.07	287.86	−5841.65	149.66	420.95	0.01204	8995600
Muscovite	KAl3Si3O10(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_f is 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^–2 J/K-mol.

where S₀ is the entropy at 0 K (the configurational, or third law entropy) and ΔSφ is the entropy change associated with any phase change. Compilations for S₂₉₈ are available for many minerals. Table 2.2 lists some heat capacity constants for the power series formula as well as other thermodynamic data for a few geologically important minerals. Example 2.6 illustrates how entropy and enthalpy changes are calculated.