Properties of Aqueous (NH₄)₂SO₄

The experimental data are listed in the tables below. Notes at the end of each table define the listed quantities, and identify the sources of the measurements.

1.  Osmotic Coefficients of Aqueous (NH4)2SO4 from Isopiestic Measurements

   m(NH4)2SO4      osm      t    ref.  weight   series    
    0.1294       0.7542     25    a     1.0       -
    0.7454       0.6558     25    a     1.0       -
    2.068        0.6253     25    a     1.0       -
    4.051        0.6634     25    a     1.0       -
    4.772        0.6817     25    a     1.0       -
    0.2171       0.7250     25    a     1.0       -
    0.9376       0.6446     25    a     1.0       -
    2.305        0.6265     25    a     1.0       -
    4.289        0.6696     25    a     1.0       -
    5.301        0.6947     25    a     1.0       -
    0.2809       0.7103     25    a     1.0       -
    1.076        0.6379     25    a     1.0       -
    2.739        0.6315     25    a     1.0       -
    4.451        0.6728     25    a     1.0       -
    5.486        0.6993     25    a     1.0       -
    0.4536       0.6827     25    a     1.0       -
    1.380        0.6311     25    a     1.0       -
    3.174        0.6407     25    a     1.0       -
    4.552        0.6753     25    a     1.0       -
    5.596        0.7022     25    a     1.0       -
    0.5682       0.6701     25    a     1.0       -
    1.755        0.6250     25    a     1.0       -
    3.592        0.6529     25    a     1.0       -
    4.691        0.6793     25    a     1.0       -
    5.830        0.7077     25    a     1.0       -
    0.583        0.6683     25    b     1.0       -
    0.883        0.6451     25    b     1.0       -
    0.997        0.6417     25    b     1.0       -
    1.182        0.6372     25    b     1.0       -
    1.307        0.6296     25    b     1.0       -
    1.415        0.6275     25    b     1.0       -
    1.553        0.6261     25    b     1.0       -
    1.722        0.6169     25    b     0.0       -
    1.820        0.6225     25    b     1.0       -
    1.915        0.6249     25    b     1.0       -
    1.942        0.6236     25    b     1.0       -
    2.098        0.6265     25    b     1.0       -
    3.019        0.6355     25    b     1.0       -
    4.053        0.6593     25    b     1.0       -
    5.124        0.6882     25    b     1.0       -
    5.714        0.7017     25    b     1.0       -
    1.0538       0.6426     25    c     1.0       1
    0.8616       0.6499     25    c     1.0       1
    0.8874       0.6491     25    c     1.0       1
    0.7207       0.6591     25    c     1.0       1
    0.6882       0.6614     25    c     1.0       1
    0.6449       0.6622     25    c     1.0       1
    0.6197       0.6658     25    c     1.0       1
    0.5812       0.6705     25    c     1.0       1
    0.5541       0.6728     25    c     1.0       1
    0.5179       0.6750     25    c     1.0       1
    0.4841       0.6790     25    c     1.0       1
    0.3997       0.6847     25    c     0.0       1
    0.4423       0.6862     25    c     1.0       2
    0.3600       0.6968     25    c     1.0       2
    0.2973       0.7086     25    c     1.0       2
    0.2070       0.7241     25    c     0.0       2
    0.9607       0.6456     25    c     1.0       3
    1.0262       0.6426     25    c     1.0       3
    1.1906       0.6366     25    c     1.0       3
    1.3060       0.6334     25    c     1.0       3
    1.5894       0.6292     25    c     1.0       3
    3.9076       0.6611     25    c     1.0       3
    1.5890       0.6277     25    c     1.0       4
    1.8037       0.6261     25    c     1.0       4
    1.8314       0.6260     25    c     1.0       4
    1.9359       0.6259     25    c     1.0       4
    2.2750       0.6277     25    c     1.0       4
    2.9050       0.6367     25    c     1.0       4
    3.1566       0.6418     25    c     1.0       4
    3.3390       0.6458     25    c     1.0       4
    4.0425       0.6630     25    c     1.0       4
    3.8930       0.6591     25    c     1.0       4
    4.0904       0.6641     25    c     1.0       4
    5.1463       0.6917     25    c     1.0       4
    5.6834       0.7046     25    c     1.0       4
    5.8586       0.7096     25    c     1.0       4
    3.8586       0.6580     25    c     1.0       4
    1.0354       0.6431     25    c     1.0       5
    1.0350       0.6478     50    c     0.0       4
    1.1686       0.6404     50    c     1.0       4
    1.1350       0.6399     50    c     1.0       4
    0.9005       0.6489     50    c     1.0       4
    0.8232       0.6530     50    c     1.0       4
    0.7039       0.6550     50    c     0.0       4
    0.5907       0.6689     50    c     1.0       4
    0.5308       0.6743     50    c     1.0       4
    0.4551       0.6820     50    c     1.0       4
    0.3885       0.6897     50    c     1.0       4
    0.3395       0.6966     50    c     1.0       4
    0.2925       0.7020     50    c     1.0       4
    0.1441       0.7276     50    c     0.0       4
    0.1319       0.7400     50    c     0.0       4
    0.1373       0.7379     50    c     0.0       4
    3.8870       0.6505     50    c     1.0       5
    3.6411       0.6454     50    c     1.0       5
    4.6835       0.6655     50    c     1.0       5
    3.7385       0.6473     50    c     1.0       5
    5.2017       0.6747     50    c     1.0       5
    5.6098       0.6816     50    c     1.0       5
    6.0414       0.6884     50    c     1.0       5
    4.6785       0.6609     50    c     1.0       5
    3.5260       0.6393     50    c     1.0       5
    3.1680       0.6333     50    c     1.0       5
    2.7780       0.6285     50    c     1.0       5
    2.4825       0.6251     50    c     1.0       5
    2.1541       0.6234     50    c     1.0       5
    1.7670       0.6244     50    c     1.0       5
    1.4848       0.6277     50    c     1.0       5
    1.2824       0.6220     50    c     0.0       5

Notes and References

• Prefix m denotes molality; osm - stoichiometric molal osmotic coefficient; t - experimental temperature (^oC); ref. - source of data; weight - the weight given to the data point in the fit of the model.
• Sources: a - B. F. Wishaw and R. H. Stokes (1954) Trans. Faraday Soc. 50, 952-954; b - V. K. Filippov, M. V. Charykova, and Yu. M. Trofimov (1986) J. Appl. Chem. USSR 58: 1807-1811; c - S. L. Clegg, S. Milioto, and D. A. Palmer (1996) J. Chem. Eng. Data 41, 455-467.
• The osmotic coefficient osm is related to the water activity of the solutions (aW) by:

  ln(aW) = (MW/1000) × 3 × m(NH4)2SO4 × osm

  where MW is the molar mass of water in grams. Calculation of the osmotic coefficients from the pairs of isopiestic molalities was carried out using osmotic coefficients of the NaCl reference solutions from Archer (D. G. Archer (1992) J. Phys. Chem. Ref. Data 21, 793-829).

2a.  Water Activities, Osmotic Coefficients, and Molalities from Electrodynamic Balance Measurements

  m(NH4)2SO4    osm      aW      wt%     m      t     ref.  weight   
   5.9003     0.79965   0.800  43.571  5.843    25     a     1.0     
   3.5586     0.88405   0.884  31.810  3.530    25     a     1.0     
   4.0317     0.86709   0.867  34.569  3.998    25     a     1.0     
   4.6783     0.84099   0.841  37.995  4.637    25     a     1.0     
   4.8828     0.83402   0.834  39.005  4.839    25     a     1.0     
   5.4907     0.81092   0.811  41.819  5.439    25     a     1.0     
   6.4085     0.77697   0.777  45.600  6.344    25     a     1.0     
   8.2570     0.71513   0.715  51.891  8.163    25     a     1.0     
   9.4058     0.67593   0.676  55.110  9.291    25     a     1.0     
   11.082     0.63707   0.637  59.097  10.934   25     a     1.0     
   12.258     0.60915   0.609  61.491  12.084   25     a     1.0     
   14.146     0.56994   0.570  64.791  13.926   25     a     1.0     
   16.570     0.52600   0.526  68.272  16.284   25     a     1.0     
   18.036     0.50208   0.502  70.057  17.706   25     a     1.0     
   19.727     0.48105   0.481  71.878  19.343   25     a     1.0     
   21.340     0.45920   0.459  73.416  20.900   25     a     1.0     
   22.912     0.43824   0.438  74.760  22.415   25     a     1.0     
   24.550     0.41789   0.418  76.019  23.989   25     a     1.0     
   27.559     0.39419   0.394  78.026  26.872   25     a     1.0     
   4.9082     0.83609   0.836  39.127  4.864    25     a     1.0     
   5.5312     0.81087   0.811  41.993  5.479    25     a     1.0     
   5.8252     0.80092   0.801  43.258  5.769    25     a     1.0     
   6.0088     0.79204   0.792  44.018  5.950    25     a     1.0     
   6.8968     0.76084   0.761  47.418  6.825    25     a     1.0     
   7.9467     0.72384   0.724  50.940  7.858    25     a     1.0     
   9.3935     0.67797   0.678  55.078  9.279    25     a     1.0     
   11.055     0.63291   0.633  59.037  10.907   25     a     1.0     
   13.269     0.58415   0.584  63.332  13.071   25     a     1.0     
   15.037     0.54900   0.549  66.158  14.794   25     a     1.0     
   17.017     0.51520   0.515  68.839  16.718   25     a     1.0     
   18.821     0.49185   0.492  70.931  18.466   25     a     1.0     
   20.533     0.46607   0.466  72.670  20.122   25     a     1.0     
   23.341     0.42898   0.429  75.103  22.828   25     a     1.0     
   28.007     0.38326   0.383  78.296  27.300   25     a     1.0     
   2.8676     0.90806   0.908  27.331  2.846    25     a     1.0     
   3.0413     0.90205   0.902  28.512  3.018    25     a     1.0     
   3.3171     0.89304   0.893  30.309  3.291    25     a     1.0     
   3.6465     0.88102   0.881  32.340  3.617    25     a     1.0     
   4.1612     0.86295   0.863  35.286  4.126    25     a     1.0     
   4.5528     0.84696   0.847  37.359  4.513    25     a     1.0     
   4.8666     0.83495   0.835  38.926  4.823    25     a     1.0     
   5.2465     0.82102   0.821  40.720  5.198    25     a     1.0     
   5.6701     0.80589   0.806  42.600  5.616    25     a     1.0     
   5.9388     0.79596   0.796  43.731  5.881    25     a     1.0     
   6.2949     0.78202   0.782  45.162  6.232    25     a     1.0     
   6.6785     0.76990   0.770  46.624  6.610    25     a     1.0     
   6.9425     0.76089   0.761  47.582  6.870    25     a     1.0     
   7.4810     0.73996   0.740  49.438  7.400    25     a     1.0     
   7.9620     0.72493   0.725  50.987  7.873    25     a     1.0     
   8.1624     0.71787   0.718  51.605  8.070    25     a     1.0     
   8.8719     0.69694   0.697  53.670  8.767    25     a     1.0     
   9.7361     0.67408   0.674  55.957  9.615    25     a     1.0     
   10.213     0.65910   0.659  57.125  10.083   25     a     1.0     
   11.425     0.62986   0.630  59.824  11.269   25     a     1.0     
   12.376     0.60708   0.607  61.715  12.199   25     a     1.0     
   12.850     0.59284   0.593  62.591  12.662   25     a     1.0     
   14.318     0.56308   0.563  65.064  14.094   25     a     1.0     
   15.870     0.53894   0.539  67.340  15.604   25     a     1.0     
   16.658     0.52377   0.524  68.385  16.369   25     a     1.0     
   17.919     0.50286   0.503  69.923  17.593   25     a     1.0     
   19.140     0.48506   0.485  71.272  18.775   25     a     1.0     
   20.702     0.46574   0.466  72.829  20.285   25     a     1.0     
   21.970     0.45102   0.451  73.972  21.508   25     a     1.0     
   23.091     0.43124   0.431  74.904  22.587   25     a     1.0     
   25.655     0.41089   0.411  76.798  25.049   25     a     1.0     
   28.154     0.38822   0.388  78.383  27.441   25     a     1.0     
   28.776     0.37977   0.380  78.744  28.035   25     a     1.0     
   29.595     0.37082   0.371  79.200  28.816   25     a     1.0     

Notes and References

• Prefix m denotes molality; osm - stoichiometric molal osmotic coefficient; t - experimental temperature (^oC); aW - experimental water activity; wt% - weight percent of (NH4)2SO4 in the suspended particles (as determined by Tang and Munkelwitz, 1994); m - (NH4)2SO4 molality determined by Tang and Munkelwitz (1994), ref. - source of data; weight - the weight given to the data point in the fit of the model.
• Source: a - I. N. Tang and H. R. Munkelwitz (1994) J. Geophys. Res. 99, 18801-18808.
• Values of the m(NH4)2SO4, and the osmotic coefficient osm, are values obtained from the listed wt% and aW by re-standardising the data to improve agreement with data obtained from isopiestic experiments. The procedure is described in section 3 of Clegg et al. (S. L. Clegg, S. S. Ho, C. K. Chan and P. Brimblecombe (1995) J. Chem. Eng. Data 40, 1079-1090). Columns 3-5 in this table were obtained in a personal communication from I. N. Tang in 1997 (the data were not tabulated in the publication above).

2b.  Water Activities and Molalities from Electrodynamic Balance Measurements

  n    aW       Vdc    m(NH4)2SO4  t   ref.  weight        n     aW       Vdc   m(NH4)2SO4  t    ref.  weight
  1   0.8010   17.594     5.68     5    a      -           6    0.7088    7.854     8.40    25    a     1.0 
  1   0.7617   15.908     6.82     5    a      -           6    0.7971    9.720     5.59    25    a     0.0 
  1   0.6588   13.651     9.34     5    a      -           6    0.6827    7.696     8.77    25    a     1.0 
  1   0.6125   12.688    11.09     5    a      -           6    0.5703    6.449    13.49    25    a     1.0 
  1   0.5645   11.862    13.21     5    a      -           6    0.5264    6.104    15.84    25    a     0.0 
  1   0.4646   10.633    18.46     5    a      -           6    0.4562    5.647    20.63    25    a     0.5 
  1   0.4180   10.172    21.70     5    a      -           6    0.8271   10.315     5.06    25    a     1.0 
  3   0.8475   20.169     4.52     5    a      -           6    0.3955    5.369    25.26    25    a     1.0 
  3   0.8005   17.509     5.73     5    a      -           7    0.5166    5.946    17.28    25    a     0.0 
  3   0.7447   15.552     7.12     5    a      -           7    0.8069    9.679     5.64    25    a     1.0 
  3   0.6485   13.284     9.94     5    a      -           7    0.7044    7.930     8.24    25    a     1.0 
  3   0.5433   11.669    13.83     5    a      -           7    0.6534    7.317     9.83    25    a     1.0 
  3   0.4464   10.462    19.54     5    a      -           7    0.5472    6.369    14.01    25    a     1.0 
  3   0.7502   15.529     7.15     5    a      -           7    0.5061    6.009    16.70    25    a     1.0 
  3   0.3980    9.900    24.19     5    a      -           7    0.4470    5.593    21.45    25    a     0.5 
  4   0.8296   18.965     5.00     5    a      -           2    0.8247   15.716     5.21    35    a      -  
  4   0.7447   15.718     6.98     5    a      -           2    0.7616   13.727     6.62    35    a      -  
  4   0.6678   13.596     9.43     5    a      -           2    0.6742   11.705     9.15    35    a      -  
  4   0.5937   12.374    11.81     5    a      -           2    0.5757   10.074    13.22    35    a      -  
  4   0.5391   11.354    14.97     5    a      -           2    0.5236    9.422    16.08    35    a      -  
  6   0.5510   11.740    13.59     5    a      -           2    0.4668    8.781    20.41    35    a      -  
  6   0.8236   18.579     5.17     5    a      -           2    0.4206    8.461    23.59    35    a      -  
  6   0.7720   16.728     6.21     5    a      -           5    0.8103   15.155     5.54    35    a      -  
  6   0.7392   15.407     7.26     5    a      -           5    0.7503   13.306     7.03    35    a      -  
  6   0.6530   13.391     9.76     5    a      -           5    0.7123   12.314     8.21    35    a      -  
  6   0.5978   12.377    11.80     5    a      -           5    0.6683   11.574     9.38    35    a      -  
  6   0.5270   11.387    14.84     5    a      -           5    0.6303   11.004    10.54    35    a      -  
  6   0.4924   10.890    17.04     5    a      -           5    0.5977   10.476    11.91    35    a      -  
  6   0.4495   10.415    19.86     5    a      -           5    0.5306    9.528    15.53    35    a      -  
  6   0.3977    9.892    24.28     5    a      -           5    0.4788    9.070    18.20    35    a      -  
  5   0.4473   12.882    19.55    10    a      -           7    0.8383   16.489     4.81    35    a      -  
  5   0.4707   13.251    17.73    10    a      -           7    0.7393   12.976     7.38    35    a      -  
  5   0.5100   13.730    15.82    10    a      -           7    0.6435   11.182    10.15    35    a      -  
  5   0.5485   14.362    13.85    10    a      -           7    0.5228    9.385    16.27    35    a      -  
  5   0.5977   15.227    11.83    10    a      -           7    0.4746    8.864    19.73    35    a      -  
  5   0.6694   17.014     9.10    10    a      -           7    0.4982    9.132    17.79    35    a      -  
  5   0.6982   17.646     8.41    10    a      -           8    0.8144   38.020     5.47    40    a      -  
  5   0.7589   19.976     6.58    10    a      -           8    0.7032   30.013     8.59    40    a      -  
  5   0.8299   23.340     5.00    10    a      -           8    0.6500   27.566    10.40    40    a      -  
  5   0.8299   23.209     5.05    10    a      -           8    0.6037   26.132    11.87    40    a      -  
  2   0.3883    7.336    24.14    15    a      -           8    0.5508   24.775    13.69    40    a      -  
  2   0.4448    7.738    19.64    15    a      -           8    0.4990   22.799    17.65    40    a      -  
  2   0.5449    8.625    13.91    15    a      -           8    0.4488   21.634    21.27    40    a      -  
  2   0.6467    9.914     9.77    15    a      -           3    0.8092    9.650     5.65    25    b      -  
  2   0.7012   10.706     8.26    15    a      -           3    0.7811    9.131     6.24    25    b      -  
  2   0.7398   11.673     6.94    15    a      -           3    0.7572    8.685     6.85    25    b      -  
  2   0.8446   14.809     4.58    15    a      -           3    0.6874    7.707     8.73    25    b      -  
  1   0.4249    7.731    19.70    15    a      -           3    0.5970    6.761    11.86    25    b      -  
  1   0.4759    8.131    16.61    15    a      -           3    0.5086    6.009    16.59    25    b      -  
  1   0.5247    8.546    14.28    15    a      -           5    0.8046    9.607     5.73    25    b      -  
  1   0.5740    9.028    12.28    15    a      -           5    0.7701    8.851     6.65    25    b      -  
  1   0.5779    9.111    11.99    15    a      -           5    0.7079    8.009     8.10    25    b      -  
  1   0.6759   10.358     8.86    15    a      -           5    0.6251    7.019    10.88    25    b      -  
  1   0.7776   12.247     6.35    15    a      -           5    0.5302    6.279    14.65    25    b      -  
  1   0.8255   13.787     5.15    15    a      -           9    0.8030    9.510     5.81    25    c      -  
  1   0.6297    7.091    10.64    25    a     1.0          9    0.7900    9.310     6.04    25    c      -  
  1   0.7181    8.057     8.02    25    a     1.0          9    0.7630    8.680     6.87    25    c      -  
  1   0.7781    8.987     6.48    25    a     1.0          9    0.7380    8.080     7.92    25    c      -  
  1   0.5264    6.212    15.17    25    a     1.0          9    0.5190    6.090    15.96    25    c      -  
  1   0.4807    5.921    17.65    25    a     1.0          9    0.5780    6.590    12.72    25    c      -  
  1   0.4299    5.619    21.26    25    a     1.0          9    0.6370    7.160    10.32    25    c      -  
  1   0.8172   10.026     5.33    25    a     1.0          9    0.6830    7.680     8.81    25    c      -  
  2   0.8399   10.714     4.81    25    a     1.0          9    0.7080    7.880     8.34    25    c      -  
  2   0.7521    8.673     6.98    25    a     1.0          9    0.7400    8.460     7.22    25    c      -  
  2   0.6939    7.803     8.65    25    a     1.0                                                                
  2   0.6477    7.173    10.46    25    a     1.0                                                             
  2   0.5474    6.420    13.95    25    a     1.0                                                   
  2   0.4476    5.745    19.90    25    a     1.0                                                   
  2   0.3946    5.279    28.19    25    a     0.0                                                   
  4   0.8397   10.805     4.75    25    a     1.0                                                   
  4   0.7290    8.191     7.83    25    a     1.0                                                   
  4   0.6155    6.876    11.62    25    a     1.0                                                   
  4   0.5112    6.192    15.54    25    a     1.0                                                   

Notes and References

• Key: n - particle number; aW - water activity; Vdc - dc voltage (V) required to suspend the particle; m(NH4)2SO4 - calculated molality (mol kg^-1) after standardisation of the measurements against bulk solution data; t - temperature (^oC); ref. - source of data; weight - the weight given to the data points in the fit of the model at 25 ^oC (data at other temperatures were used to estimate enthalpies and heat capacities).
• Source: a - S. L. Clegg, S. S. Ho, C. K. Chan and P. Brimblecombe (1995) J. Chem. Eng. Data 40, 1079-1090; b - C. K. Chan, R. C. Flagan and J. H. Seinfeld (1992) Atmos. Environ. 26A, 1661-1673; c - B. Wyslouzil, unpublished results.

3.  Water Activities of Aqueous (NH4)2SO4 from Vapour Pressure Measurements

 m(NH4)2SO4    aW         t    ref.       m(NH4)2SO4    aW         t    ref. 
   1.0542     0.9719    31.97   a           2.5126     0.9466    31.97   a    
   1.0542     0.9752    37.47   a           2.5126     0.9255    37.47   a    
   1.0542     0.9625    41.11   a           2.5126     0.9148    41.11   a    
   1.0542     0.9697    46.03   a           2.5126     0.9182    43.35   a    
   1.0542     0.9596    49.26   a           2.5126     0.9222    46.03   a    
   1.0542     0.9686    51.98   a           2.5126     0.9182    49.26   a    
   1.0542     0.9642    54.88   a           2.5126     0.9216    51.98   a    
   1.0542     0.9656    57.60   a           2.5126     0.9182    54.88   a    
   1.0542     0.9678    60.85   a           2.5126     0.9117    57.60   a    
   1.0542     0.9647    63.14   a           2.5126     0.9189    60.85   a    
   1.0542     0.9672    66.91   a           2.5126     0.9189    63.14   a    
   1.0542     0.9644    70.20   a           2.5126     0.9163    66.91   a    
   1.0542     0.9661    72.71   a           2.5126     0.9186    70.20   a    
   1.0542     0.9666    74.32   a           2.5126     0.9181    72.71   a    
   1.0542     0.9676    76.28   a           2.5126     0.9189    74.32   a    
   1.0542     0.9695    79.22   a           2.5126     0.9214    76.28   a    
   1.0542     0.9665    81.20   a           2.5126     0.9213    79.22   a    
   1.0542     0.9600    83.07   a           2.5126     0.9212    81.20   a    
   1.0542     0.9669    85.44   a           2.5126     0.9199    83.07   a    
   1.0542     0.9679    87.75   a           2.5126     0.9232    85.44   a    
   1.0542     0.9696    90.86   a           2.5126     0.9240    87.75   a    
   1.0542     0.9662    93.04   a           2.5126     0.9246    90.86   a    
   1.0542     0.9667    94.82   a           2.5126     0.9230    93.04   a    
   1.0542     0.9649    97.07   a           2.5126     0.9222    94.82   a    
   1.0542     0.9681   100.09   a           2.5126     0.9210    97.07   a    
   2.4891     0.9522    31.97   a           2.5126     0.9244   100.09   a    
   2.4891     0.9255    37.47   a           3.0961     0.9017    31.97   a    
   2.4891     0.9199    41.11   a           3.0961     0.9027    37.47   a    
   2.4891     0.9197    43.35   a           3.0961     0.8961    41.11   a    
   2.4891     0.9235    46.03   a           3.0961     0.9076    43.35   a    
   2.4891     0.9170    49.26   a           3.0961     0.8997    46.03   a    
   2.4891     0.9206    51.98   a           3.0961     0.8957    49.26   a    
   2.4891     0.9182    54.88   a           3.0961     0.8990    51.98   a    
   2.4891     0.9154    57.60   a           3.0961     0.8944    54.88   a    
   2.4891     0.9182    60.85   a           3.0961     0.8900    57.60   a    
   2.4891     0.9166    63.14   a           3.0961     0.8957    60.85   a    
   2.4891     0.9168    66.91   a           3.0961     0.8986    63.14   a    
   2.4891     0.9165    70.20   a           3.0961     0.8977    66.91   a    
   2.4891     0.9200    72.71   a           3.0961     0.8965    70.20   a    
   2.4891     0.9196    74.32   a           3.0961     0.8991    72.71   a    
   2.4891     0.9211    76.28   a           3.0961     0.9004    74.32   a    
   2.4891     0.9196    79.22   a           3.0961     0.9004    76.28   a    
   2.4891     0.9196    81.20   a           3.0961     0.8998    79.22   a    
   2.4891     0.9204    83.07   a           3.0961     0.9035    81.20   a    
   2.4891     0.9225    85.44   a           3.0961     0.9010    83.07   a    
   2.4891     0.9233    87.75   a           3.0961     0.9023    85.44   a    
   2.4891     0.9229    90.86   a           3.0961     0.9043    87.75   a    
   2.4891     0.9213    93.04   a           3.0961     0.9043    90.86   a    
   2.4891     0.9221    94.82   a           3.0961     0.9016    93.04   a    
   2.4891     0.9219    97.07   a           3.0961     0.9024    94.82   a    
   2.4891     0.9246   100.09   a           3.0961     0.9023    97.07   a    
                                            3.0961     0.9071   100.09   a    

Notes and References

• Prefix m denotes molality; aW - water activity, calculated from direct measurements of vapour pressure; t - experimental temperature (^oC); ref. - source of data.
• Source: a - G. Tammann, tabulated in: J. Timmermans (1960) The Physico-chemical Constants of Binary Systems in Concentrated Solutions, Vol. 4, Interscience: New York. Note that the solution concentrations listed by Timmermans are grams of salt per 100 g water, and not weight percent. (Original reference: G. Tammann (1885) Wiedemann's Ann. 24, 523-569.)
• Vapour pressures were converted to water activities by dividing by the vapour pressures of pure water at the temperature of interest (listed by Timmermans, 1960). These data were not used in the fitted models of Clegg et al. (1995, 1996), but are consistent with them (see Figure 8a of Clegg et al., 1995).

4.  Water Activities and Osmotic Coefficients from Boiling Points

 m(NH4)2SO4    aW       osm        T      weight  ref.     
   0.02673   0.99900   0.6899    373.178    0.0    a
   0.04798   0.99788   0.8182    373.210    0.0    a
   0.0       1.0       1.0       373.15     0.0    a
   0.11939   0.99554   0.6929    373.277    1.0    a
   0.14674   0.99467   0.6743    373.302    0.0    a
   0.18745   0.99369   0.6244    373.330    0.0    a
   0.21961   0.99212   0.6662    373.375    1.0    a
   0.26151   0.99076   0.6567    373.414    1.0    a
   0.30795   0.98918   0.6539    373.460    1.0    a
   0.02673   0.99952   0.3316    373.164    0.0    a
   0.04798   0.99825   0.6737    373.200    0.0    a
   0.11939   0.99563   0.6790    373.275    1.0    a       
   0.14674   0.99468   0.6727    373.302    1.0    a       
   0.18745   0.99336   0.6574    373.340    1.0    a       
   0.21961   0.99214   0.6651    373.375    1.0    a       
   0.26151   0.99043   0.6803    373.424    1.0    a       
   0.30795   0.98885   0.6739    373.470    1.0    a       
   0.11939   0.99551   0.6969    373.278    1.0    a       
   0.14674   0.99477   0.6613    373.299    1.0    a       
   0.18745   0.99345   0.6485    373.337    1.0    a       
   0.21961   0.99223   0.6576    373.372    1.0    a       
   0.30795   0.98893   0.6685    373.467    1.0    a       
   0.07212   0.99718   0.7233    373.230    1.0    a       
   0.40168   0.98616   0.6421    373.547    1.0    a       
   2.49585   0.92834   0.5513    375.281    1.0    a       
   3.46410   0.90046   0.5601    376.163    1.0    a       
   4.79806   0.86163   0.5743    377.447    1.0    a       
   5.02440   0.85349   0.5834    377.725    1.0    a       
   5.25917   0.84184   0.6057    378.128    1.0    a       
   5.50287   0.83222   0.6175    378.466    1.0    a       
   5.77950   0.83061   0.5942    378.523    1.0    a       
   5.97052   0.82403   0.5998    378.757    1.0    a       
   6.76540   0.81808   0.5497    378.971    0.0    a       
   7.32971   0.80611   0.5441    379.407    0.0    a       
   0.33270   0.98821   0.6594    373.488    1.0    a       
   0.30523   0.98905   0.6675    373.464    1.0    a       
   0.25944   0.99079   0.6601    373.414    1.0    a       
   0.21518   0.99246   0.6512    373.366    1.0    a       
   0.18619   0.99353   0.6453    373.335    1.0    a       
   0.14651   0.99468   0.6737    373.302    1.0    a       
   0.11904   0.99567   0.6749    373.274    1.0    a       
   0.09004   0.99668   0.6829    373.245    1.0    a       
   0.02594   0.99895   0.7478    373.180    0.0    a       
   0.30523   0.98930   0.6520    373.457    1.0    a       
   0.23350   0.99142   0.6826    373.395    1.0    a       
   0.21976   0.99247   0.6366    373.365    1.0    a       
   0.18466   0.99316   0.6880    373.345    1.0    a       
   0.13583   0.99501   0.6811    373.292    0.0    a       
   0.10988   0.99619   0.6421    373.258    1.0    a       
   0.07631   0.99707   0.7119    373.233    1.0    a       
   0.02594   0.99911   0.6371    373.175    0.0    a       
   0.0       1.0       1.0       373.15     0.0    b                              
   0.59070   0.98262   0.5492    373.65     0.0    b       
   1.16499   0.96558   0.5563    374.15     0.0    b       
   1.72589   0.94890   0.5623    374.65     0.0    b       
   2.27850   0.93257   0.5669    375.15     0.0    b       
   2.81622   0.91655   0.5725    375.65     0.0    b       
   3.34479   0.90087   0.5775    376.15     0.0    b       
   3.86579   0.88550   0.5820    376.65     0.0    b       
   4.38970   0.87044   0.5849    377.15     0.0    b       
   4.89582   0.85568   0.5891    377.65     0.0    b       
   5.43326   0.84121   0.5889    378.15     0.0    b       
   5.95117   0.82704   0.5904    378.65     0.0    b       
   6.47288   0.81315   0.5913    379.15     0.0    b       
   6.98592   0.79953   0.5926    379.65     0.0    b       
   7.50177   0.78618   0.5933    380.15     0.0    b       
   8.01371   0.77309   0.5942    380.65     0.0    b       
   8.51710   0.76030   0.5953    381.15     0.0    b       
   8.72487   0.75520   0.5954    381.35     0.0    b       
   7.89428   0.76550   0.6263    381.24     1.0    c       
   7.72664   0.77296   0.6167    380.95     1.0    c       
   7.12171   0.78839   0.6177    380.36     1.0    c       
   6.65957   0.80203   0.6129    379.85     1.0    c       
   6.17654   0.81539   0.6114    379.36     1.0    c       
   5.72589   0.82902   0.6059    378.87     1.0    c       
   5.25249   0.84321   0.6008    378.37     1.0    c       
   4.78184   0.85740   0.5953    377.88     1.0    c       
   4.28064   0.87216   0.5912    377.38     1.0    c       
   3.76874   0.88692   0.5897    376.89     1.0    c       
   0.0       1.0       1.0       373.15     0.0    c                              
   7.91614   0.76897   0.6140    380.18     1.0    c       
   7.53464   0.77520   0.6253    379.94     1.0    c       
   6.18418   0.81333   0.6182    378.52     1.0    c       
   5.32517   0.83894   0.6102    377.61     1.0    c       
   4.36181   0.86848   0.5982    376.60     1.0    c       
   3.85588   0.88386   0.5924    376.09     1.0    c       
   3.37129   0.89926   0.5828    375.59     1.0    c       
   2.83617   0.91529   0.5775    375.08     1.0    c       
   2.28552   0.93166   0.5731    374.57     1.0    c       
   2.04329   0.93818   0.5779    374.37     1.0    c       
   1.81301   0.94475   0.5800    374.17     1.0    c       
   1.56344   0.95137   0.5900    373.97     1.0    c       
   1.32319   0.95839   0.5943    373.76     1.0    c       
   0.0       1.0       1.0       373.15     0.0    c                              
   7.75659   0.76900   0.6266    374.94     1.0    c       
   8.06935   0.77463   0.5855    374.73     0.0    c       
   6.78373   0.79685   0.6194    373.92     1.0    c       
   5.78382   0.82562   0.6130    372.91     1.0    c       
   4.79904   0.85560   0.6013    371.90     1.0    c       
   3.72663   0.88688   0.5960    370.89     1.0    c       
   2.65411   0.91953   0.5848    369.88     1.0    c       
   0.0       1.0       1.0       373.15     0.0    c                              
   7.71175   0.76663   0.6376    374.85     1.0    c       
   8.39078   0.76770   0.5829    374.81     0.0    c       
   7.25072   0.78065   0.6319    374.33     1.0    c       
   6.33291   0.80876   0.6202    373.32     1.0    c       
   0.0       1.0       1.0       373.15     0.0    c                               
   7.63817   0.76820   0.6388    371.56     1.0    c       
   8.81586   0.77067   0.5467    371.47     0.0    c       
   6.35302   0.80583   0.6287    370.22     1.0    c       
   5.35080   0.83564   0.6209    369.21     1.0    c       
   4.31293   0.86706   0.6119    368.19     1.0    c       
   0.0       1.0       1.0       373.15     0.0    c                               
   7.58030   0.76867   0.6422    371.69     1.0    c       
   7.63817   0.77581   0.6149    371.43     1.0    c       
   6.58289   0.79854   0.6323    370.62     1.0    c       
   5.60560   0.82799   0.6230    369.61     1.0    c       
   4.60046   0.85874   0.6125    368.60     1.0    c       
   3.45630   0.89409   0.5993    367.49     1.0    c       
   2.43752   0.92434   0.5972    366.58     1.0    c       
   0.0       1.0       1.0       373.15     0.0    c                              
   8.13300   0.73778   0.6919    382.05     0.0    d       

Notes and References

• Prefix m denotes molality; aW - water activity of the solution at the boiling temperature; osm - osmotic coefficient of the solution at the boiling temperature; T - experimental boiling point (K); weight - the weight given to the data point in the fit of the model; ref. - source of data.
• Sources: data for refererences (b) and (d) were taken from the compilation of Timmermans (1960); a - S. M. Johnston (1906) Trans. Roy. Soc. Edinburgh 45(1), 193-240; b - Gerlach (1886); c - J. Y. Buchanan (1899) Trans. Roy. Soc. Edinburgh 29, 529-573; d - Mulder (1866).
• The data used by Clegg et al. (1995) are plotted in Figure 7 of that paper.
• The data of Gerlach, which are presented as smoothed values in the compilation of Timmermans, were rejected, as were those of Mulder for which total pressures were not given. Water activities (aW) at the boiling point of the solution are calculated from the equation aW = pH2O/pH2O^o, where pH2O^o is the vapor pressure of pure water at the boiling temperature and pH2O, the equilibrium partial pressure of water, is equal to the total pressure of the system. The above relationship assumes that partial pressure is equivalent to fugacity. Test calculations using an equation of state to estimate fugacity coefficients showed that this was a satisfactory approximation. Values of pH2O^o were obtained using the equation of state of Hill (P. G. Hill (1990) J. Phys. Chem. Ref. Data 19, 1223-1274).
• Plots of boiling point elevation against molality for Johnston's data show systematic displacements consistent with different values of the boiling point of pure water (note that Johnston took into account the effect of variations of atmospheric pressure upon his results). All the measurements of Johnston (made close to sea level) were therefore adjusted to be consistent with a single boiling point of pure water of 373.15 K. This was done by adding a constant ΔT (K) to each data set, bringing the measurements into optimum agreement with each other and converging to a boiling point elevation of zero for pure water.
• The most extensive measurements are those of Buchanan for six pressures corresponding to boiling points of pure water ranging from 364.31 K (91.3 ^oC) to 373.43 K (100.28 ^oC).

5.  Osmotic Coefficients at the Freezing Temperature

  m(NH4)2SO4    osm         t      ref.  
    0.3030     0.6513     -1.1      a
    0.6057     0.6817     -2.3      a
    0.7567     0.6644     -2.8      a
    1.2106     0.6234     -4.2      a
    1.5140     0.6174     -5.2      a
    1.8158     0.6240     -6.3      a
    2.2708     0.6261     -7.9      a
    2.7244     0.6411     -9.7      a
    0.8409     0.5552     -2.6      b
    1.8920     0.5703     -6.0      b
    3.0315     0.6418    -10.8      b   
    5.0454     0.5720    -16.0      b   
    5.4132     0.5666    -17.0      b   
    2.1846     0.5847     -7.1      c   
    2.4241     0.5895     -7.94     c   
    3.0867     0.5922    -10.15     c   
    3.1138     0.6033    -10.43     c   
    3.5386     0.6111    -12.00     c   
    3.9810     0.6336    -13.99     c   
    4.4830     0.6434    -15.99     c   
    4.8102     0.6560    -17.49     c   
    5.0244     0.6587    -18.34     c   
    0.2539     0.7420     -1.05     d   
    0.5275     0.6772     -1.99     d   
    1.0548     0.6301     -3.70     d   
    1.5613     0.6080     -5.28     d   
    4.9931     0.6686    -18.50     d   
    0.2526     0.6392     -0.90     e   
    0.5045     0.6760     -1.90     e   
    0.7567     0.6407     -2.70     e   
    0.8409     0.7049     -3.30     e   
    1.0438     0.6024     -3.50     e   
    1.2618     0.6409     -4.50     e   
    1.5140     0.5936     -5.00     e   
    1.7649     0.5807     -5.70     e   
    1.8920     0.5893     -6.20     e   
    3.2435     0.6444    -11.60     e   
    3.7835     0.6672    -14.00     e   
    4.0305     0.6667    -14.90     e   
    4.2867     0.6733    -16.00     e   
    4.5408     0.6834    -17.20     e   
    4.6681     0.6880    -17.80     e   
    4.7900     0.6856    -18.20     e   
    4.9205     0.6913    -18.85     e   
    0.3816     0.7054     -1.50     f   
    0.7576     0.6636     -2.80     f   
    1.1309     0.6674     -4.20     f   
    1.5173     0.6398     -5.40     f   
    1.8920     0.6370     -6.70     f   
    2.5362     0.5606     -7.90     f   
    2.6453     0.6467     -9.50     f   
    3.0315     0.6418    -10.80     f   
    3.4002     0.6253    -11.80     f   
    3.7784     0.6585    -13.80     f   
    4.1654     0.6494    -15.00     f   
    4.5408     0.6674    -16.80     f   
    4.7779     0.7101    -18.80     f   
    0.0501     0.8589     -0.240    g   
    0.1005     0.8371     -0.469    g   
    0.2020     0.7264     -0.818    g   
    0.5136     0.6881     -1.969    g   
    1.0604     0.6245     -3.686    g   
    1.5268     0.6043     -5.133    g   
    0.76       0.6616     -2.80     h   
    1.52       0.6446     -5.45     h   
    2.28       0.6473     -8.20     h   
    3.04       0.6578    -11.10     h   
    3.79       0.6851    -14.40     h   
    4.17       0.7008    -16.20     h   
    4.56       0.7122    -18.00     h   
    4.92       0.7484    -20.40     h   

Notes and References

• Prefix m denotes molality; osm - osmotic coefficient of the solution at the freezing temperature; t - experimental temperature (^oC) at which the solution is saturated with respect to ice; ref. - source of data.
• Sources: references (a-f) were taken from the compilation of Timmermans (1960): a - Rudorf (1872); b - Guthrie (1876); c - Rodebush (1918); d - Ishikawa and Murooka (1929, 1933); e - Bergman and Sholokhovich (1942); f - Vasilenko (1948). Data from other sources are as follows: g - H. C. Jones and F. H. Getman (1903) Z. Phys. Chem. 46, 244-286; h - L. C. De Coppet (1904) J. Phys. Chem. 8, 531-538.
• Data of Scatchard and Prentiss (J. Amer. Chem. Soc. 54, 2696-2705, 1932) were rejected as erroneous by Clegg et al. (1995) and are not listed. None of the data in the table were included in the fit of the model of Clegg et al. (1995), but are shown to be consistent with the model in Figure 6 of that work. Freezing point depressions (equivalent to -t in the table) were used to calculate water activities of the solutions at the freezing temperature (hence osmotic coefficients) using eq. (19) of Clegg et al. (1995).

6.  Enthalpies of Solution of Aqueous (NH4)2SO4

   m(NH4)2SO4      φL      t    ref.   weight   
     0.02775     1852.0    25    a      0.1
     0.05551     1852.0    25    a      0.1
     0.11102     1748.0    25    a      1.0
     0.13877     1710.0    25    a      1.0
     0.27754     1417.0    25    a      1.0
     0.55509     1057.0    25    a      1.0
     1.11017      630.0    25    a      1.0
     1.85029      330.0    25    a      1.0
     5.55087     -250.0    25    a      1.0

Notes and References

• Prefix m denotes molality; φL - enthalpy of solution (J mol^-1) (see note below); t - experimental temperature (^oC); ref. - source of data; weight - the weight given to the data point in the fit of the model (normalised);
• Sources: a - Wagman, D. D., W. H. Evans, V. B. Parker, I. H. Schumm, S. M. Bailey, K. L. Churney, and R. L. Nuttall (1982) The NBS Tables of Chemical Thermodynamic Properties. J. Phys. Chem. Ref. Data 11 (Supplement No. 2): 392pp.
• The enthalpies of formation (from which enthalpies of solution were calculated) were originally estimated by Rossini et al. (1961), from the work of the following authors: Bouzat (1903), Roth and Zeumer (1931), and Thomsen (1882-1886). An earlier evaluation appears in the International Critical Tables of Numerical Data, Physics, Chemistry and Technology, for 0.134 - 5.55 mol kg^-1, based on the same data of Bouzat (1903) and Thomsen (1882-1886), and the work of Berthelot (1873).

7.  Apparent Molar Heat Capacities of (NH4)2SO4

 m(NH4)2SO4       φCp      t    ref.  weight  
   3.701         113.38    25    a     1.0
   2.22           72.59    25    a     1.0
   1.11           29.8     25    a     1.0
   0.5548         10.52    25    a     1.0
   0.2777        -24.96    25    a     1.0
   5.045          90.24    23    b     1.0
   2.469          79.78    23    b     1.0
   3.694          65.0     23    b     1.0
   0.1388        -30.51    25    c     1.0

Notes and References

• Prefix m denotes molality; φCp - apparent molar heat capacities of (NH4)2SO4 in aqueous solution (J mol^-1 K^-1); t - experimental temperature (^oC); ref. - source of data; weight - the weight given to the data point in the fit of the model (normalised).
• Source: a - J. D'Ans, H. Surawski, C. Synowietz (1977) In: Landolt-Bornstein Tables; Kl. Schafer (Ed.), Springer-Verlag, Berlin; b - W. Schneider, H. Muller, and C. Morke (1982) C. Chem. Tech. (Leipzig) 34, 31-32; c - G. Beggerow (1976) In: Landolt-Bornstein Tables; Kl. Schafer (Ed.), Springer-Verlag, Berlin, (New Series, Group IV, Vol. 2, p.85).
• The value for ref. (c) was calculated from tabulated heats of solution and a specific heat of (NH4)2SO4(cr) of 187.49 J mol K^-1. Apparent molar heat capacities were calculated from the specific heats listed in the Landolt-Bornstein Tables assuming units of cal(20 ^oC) g^-1 K^-1 (1 J = 0.23918 cal(20 ^oC)). Heat capacities of water were taken from from the CRC Handbook of Chemistry and Physics (64th Edn.).
• An apparent molar heat capacity of (NH4)2SO4 at infinite dilution equal to -133.1 J mol^-1 K^-1 was adopted by Clegg et al. (1995), from the NBS Tables of Chemical Thermodynamic Properties (1982).