Malic Acid Data

The tables of data for the pure aqueous acid are given below.

(1a) Water Activities from Electrodynamic Balance Measurements

    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

Notes and References

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).

(1b) Osmotic Coefficients from Bulk Solution Measurements

   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       -

Notes and References

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.