Malic Acid Data
The tables of data for the pure aqueous acid are given below.
aW mfs m np t uncert. ref. weight
0.8605 0.48560 7.040 1e 25.0 0.01 a 1.0
0.7519 0.58867 10.67 1e 25.0 0.01 a 1.0
0.6156 0.69001 16.60 1e 25.0 0.01 a 1.0
0.0678 0.93094 100.47 1e 25.0 0.01 a 1.0
0.1765 0.88733 58.72 1g 25.0 0.01 a 0.5
0.4458 0.77157 25.19 1g 25.0 0.01 a 1.0
0.7023 0.63138 12.77 1g 25.0 0.01 a 1.0
0.8449 0.50736 7.68 1g 25.0 0.01 a 1.0
0.9031 0.41020 5.19 1g 25.0 0.01 a 1.0
0.8922 0.42890 5.60 2e 25.0 0.01 a 1.0
0.8397 0.49385 7.28 2e 25.0 0.01 a 1.0
0.6556 0.66920 15.09 2e 25.0 0.01 a 1.0
0.3878 0.79992 29.81 2e 25.0 0.01 a 1.0
0.1311 0.93054 - 2e 25.0 0.01 a 0.0
0.8500 0.50332 7.557 3e 25.0 0.01 a 1.0
0.8046 0.54135 8.804 3e 25.0 0.01 a 1.0
0.5458 0.70695 18.00 3e 25.0 0.01 a 1.0
0.3162 0.80964 31.71 3e 25.0 0.01 a 1.0
0.0585 0.90873 - 3e 25.0 0.01 a 0.0
0.2812 0.82127 34.28 3g 25.0 0.01 a 1.0
0.4256 0.77282 25.37 3g 25.0 0.01 a 1.0
0.7111 0.64120 13.33 3g 25.0 0.01 a 1.0
0.8500 0.50332 7.557 4e 25.0 0.01 a 1.0
0.6394 0.67043 15.17 4e 25.0 0.01 a 1.0
0.4575 0.74473 21.75 4e 25.0 0.01 a 1.0
0.2500 0.84984 42.19 4e 25.0 0.01 a 1.0
0.0470 0.92828 96.55 4e 25.0 0.01 a 1.0
0.8500 0.50332 7.557 4g 25.0 0.01 a 1.0
0.0400 0.94243 122.02 4g 25.0 0.01 a 1.0
0.8246 0.52825 8.353 4g 25.0 0.01 a 1.0
- Symbols: aW - water activity; mfs - mass fraction of solute in the particle, as given by Peng et al. (2001)
and at http://ihome.ust.hk/~keckchan/hygroscopic.html; m - solute molality of the particles (only
those particles that appear to be fully aqueous);
np - particle number (suffix e indicates
an evaporation experiment in an atmosphere of decreasing relative humidity, and g particle
growth in an atmosphere of increasing relative humidity); t - experimental temperature (oC);
uncert. - probable uncertainty in the water activity;
ref. - source of data; weight - the weight assigned in the fit of the model to determine parameter values.
- Source: a - C. Peng, M. N. Chan and C. K. Chan (2001) Environ. Sci. Technol. 35, 4495-4501.
- The uncertainty associated with mfs (and so also the molality m) has three sources: the determination
of the dc balancing voltage, solute evaporation, and the standardisation of the particle composition to a single
reference state (either dilute solution or solid particle). Based on the scatter in the listed mfs, an overall
uncertainty of at least ±0.01 in mfs seems likely. The corresponding values for molality can be obtained using
the conversion equation m = (mfs/(1 - mfs)) × (1000/MW) where MW is the molar mass of the acid (134.09 g).
M nS/nW aW m osm t uncert. ref. weight
- - - 0.0981 0.9276 25.0 0.13(a) a 0.0
- - - 0.1991 0.9099 25.0 0.12(a) a 0.0
- - - 0.3047 0.9021 25.0 0.10(a) a 0.0
- - - 0.4011 0.9271 25.0 0.09(a) a 0.0
- - - 0.4912 0.9484 25.0 0.08(a) a 0.0
- - - 0.5931 0.9711 25.0 0.06(a) a 0.0
- - - 0.6992 0.9762 25.0 0.05(a) a 0.0
- - - 0.7997 0.9841 25.0 0.04(a) a 0.0
- - - 0.8932 0.9908 25.0 0.02(a) a 0.0
- - - 1.0055 0.9996 25.0 0.015(a) a 0.0
- - - 1.2719 1.0080 25.0 0.015(a) a 0.0
- - - 1.6337 1.0143 25.0 0.015(a) a 0.0
- - - 1.9703 1.0176 25.0 0.015(a) a 0.0
- - - 2.9259 1.0380 25.0 0.015(a) a 0.0
- - - 8.1988 1.1741 25.0 0.015(a) a 0.0
- - - 10.8559 1.2305 25.0 0.015(a) a 0.0
- - - 0.5278 1.0227 25.0 0.01(b) b 1.0
- - - 1.1230 1.0198 25.0 0.01(b) b 1.0
- - - 1.9890 1.0185 25.0 0.01(b) b 1.0
- - - 2.4410 1.0362 25.0 0.01(b) b 1.0
- - - 2.5520 1.0364 25.0 0.01(b) b 1.0
- - - 3.0080 1.0414 25.0 0.01(b) b 1.0
- - - 3.0540 1.0498 25.0 0.01(b) b 1.0
- - - 3.5850 1.0537 25.0 0.01(b) b 1.0
- - - 3.7730 1.0548 25.0 0.01(b) b 1.0
- - - 4.6530 1.0900 25.0 0.01(b) b 1.0
- - - 6.1180 1.1292 25.0 0.01(b) b 1.0
- - - 6.4200 1.1400 25.0 0.01(b) b 1.0
- - - 0.3917 0.8529 25.0 0.43(c) c 0.0
- - - 0.8231 0.8824 25.0 0.21(c) c 0.0
- - - 1.8481 1.0390 25.0 0.093(c) c 0.0
- - - 3.2068 1.1079 25.0 0.055(c) c 0.0
- - - 4.9346 1.1852 25.0 0.038(c) c 0.0
- - - 7.3687 1.2420 25.0 0.027(c) c 0.0
- - - 0.500 1.0140 25.0 0.033(d) d 1.0
- - - 1.000 1.0282 25.0 0.017(d) d 1.0
- - - 1.500 1.0202 25.0 0.011(d) d 1.0
- - - 2.000 1.0307 25.0 0.008(d) d 1.0
- - - 2.500 1.0390 25.0 0.007(d) d 1.0
- - - 3.000 1.0462 25.0 0.006(d) d 1.0
- - - 10.05 1.198 25.0 0.021(c) e 1.0
- - - 10.211 1.332 25.0 0.003(e) f 1.0
- - - 1.0064 0.7777 25.0 0.17(c) g -
- - - 1.4844 0.8319 25.0 0.11(c) g -
- - - 1.9956 0.8759 25.0 0.086(c) g -
- - - 2.4371 0.9298 25.0 0.071(c) g -
- - - 2.9132 0.9774 25.0 0.060(c) g -
- - - 3.6137 1.0159 25.0 0.049(c) g -
- - - 3.9038 1.0472 25.0 0.046(c) g -
- - - 5.3893 1.1541 25.0 0.035(c) g -
- - - 7.9063 1.1908 25.0 0.025(c) g -
- 0.35069 0.6192 - - 25.0 0.009(f) h -
- 0.35069 0.6125 - - 25.0 0.009(f) h -
- 0.35069 0.5758 - - 25.0 0.009(f) h -
- 0.35069 0.5768 - - 25.0 0.009(f) h -
- 0.12906 0.8621 - - 25.0 0.009(f) h -
- 0.18875 0.7861 - - 25.0 0.009(f) h -
- 0.07505 0.9189 - - 25.0 0.009(f) h -
- 0.02776 0.9699 - - 25.0 0.009(f) h -
- 0.01616 0.9804 - - 25.0 0.009(f) h -
- 0.008598 0.9922 - - 25.0 0.009(f) h -
- 0.01323 0.9820 - - 25.0 0.009(f) h -
- 0.04293 0.9427 - - 25.0 0.009(f) h -
- 0.009531 0.9851 - - 25.0 0.009(f) h -
0.1855 - 0.995 0.1889 - 25.0 0.003(g) i -
0.3701 - 0.993 0.3829 - 25.0 0.003(g) i -
0.7669 - 0.985 0.8224 - 25.0 0.003(g) i -
1.1891 - 0.976 1.321 - 25.0 0.003(g) i -
1.6001 - 0.967 1.848 - 25.0 0.003(g) i -
2.4772 - 0.943 3.127 - 25.0 0.003(g) i -
3.4641 - 0.907 4.886 - 25.0 0.003(g) i -
4.3295 - 0.865 6.811 - 25.0 0.003(g) i -
- Symbols: nS/nW - moles of solute per mole of water in the aqueous solution; aW - water activity;
m - molality; osm - molal osmotic coefficient;
t - experimental temperature (oC);
uncert. - probable uncertainty in the water activity or osmotic coefficient (see also note below);
ref. - source of data; weight - the weight assigned in the fit of the model to determine parameter values.
- Sources: a - M. J. Carlo (1971) Thermodynamic quantities of some biochemically important organic acids in aqueous solutions at
25 oC, Ph.D Thesis, Texas A&M University;
b - R. A. Robinson, P. K. Smith and E. R. B. Smith (1942) Trans. Faraday Soc. 38, 63-70;
c - M. C. Maffia and A. J. A. Meirelles (2001) J. Chem. Eng. Data 46, 582-587;
d - M. Davies and D. K. Thomas (1956) J. Phys. Chem. 60, 41-44;
e - C. Marcolli, B. P. Luo and Th. Peter (2004) J. Phys. Chem. A 108, 2216-2224;
f - A. Apelblat, M. Dov, J. Wisniak and J. Zabicky (1995) J. Chem. Thermo. 27, 35-41;
g - C. Peng, M. N. Chan and C. K. Chan (2001) Environ. Sci. Technol. 35, 4495-4501;
h - E. Wise, J. D. Surratt, D. B. Curtis, J. E. Shilling and M. A. Tolbert (2003) J. Geophys. 108, doi:10.1029/2003JD003775, 8 pages;
i - C. E. Velezmoro and A. J. A. Meirelles (1998) Drying Technology 16(9 & 10), 1789-1805.
- Uncertainties: (a) comparisons with other data for this acid, and for citric acid, suggest that
osmotic coefficients below about 1 mol kg-1 (determined by vapour pressure osmometry) are too low by an amount that varies
with molality. These differences are the values listed. Measurements at higher molalities (by the isopiestic method) show a scatter
of about ±0.015 in the osmotic coefficient. (b) In the listed osmotic coefficient osm; (c) in the listed osmotic coefficient osm,
based upon ±0.003 in the measured water activity aW; (d) in the listed osmotic coefficient osm, based upon ±0.007 mmHg in the measured pressure
difference; (e) this uncertainty in osm was estimated from results in Table 1 of
Apelblat et al. (1995); (f) in the measured water activity (average of the 0.5% to 1.35% in RH given by Wise et al., 2003); (g) the uncertainty of the water activity meter used is ±0.003, but the authors carried out measurements
in triplicate, and quote a maximum standard deviation of ±0.0015.
- The original data of Wise et al. (2003), which are not tabulated in their paper, were obtained directly from the
authors.
- Conversion of molarities to molalities: densities of dilute solutions have been measured over a range of
temperatures by R. Darros-Barbosa, M. O. Balaban and A. A. Tiexeira (Int. J. Food Properties 6, 195-214, 2003). Their fitted equation was used
to obtain the molalities of the three most dilute solutions listed above for source (i). A fit of the densities
at 25 oC of Weiss and Downs (1922) (listed in J. Timmermans (1960) The Physico-Chemical
Constants of Binary Systems in Concentrated Solutions, Vol. 4, Interscience Publishers)
yields d (g cm-3) = 0.99705 + 0.0038044 × wt + 1.5176E-5 × wt2 from 0 to 45 wt, where
wt is the weight percent of malic acid in solution. Apparent molar volumes (cm3 mol-1) of
the solute from these data, for M > 1 mol dm-3, are given by 83.06 + 0.217M. This relationship
was used to obtain molalities for source (i) for M > 1 mol dm-3.