# Last edited on 2018-01-15 19:27:06 by jstolfi

Analysis and separation of a N-P grass fertilizer

Data

  Solubility of ammonium dihydrogenphosphate in water
  Source: NIST/IUPAC solubilty tables

  Raw data: solub_NH4_H2PO4_raw.txt
  
  Fitted formula (fairly good from 10 C to 160 C)

    function theoretical_solub(tc, t0,s0,t1,s1,z,r,mr,e) {
      # Theoretical solubility (g NH4H2PO4 per per 100 ml H2O).
      # The data seems to fit quite well an exponential of {tc}
      # with a slight correction.
      # The model breaks down at negative {tc} and above 120 C.
      # (There is an eutectic point at -4.3 C perhaps).
      # Two reference points on the solubility curve:
      t0 =  20; s0 =  36.8;
      t1 = 130; s1 = 311.5;
      mr = 0.13;  # Magnitude of correction term.
      z = (tc - t0)/(t1 - t0);  # Relative temperature in {t0_t1}.
      r = z*(1-z)*(1-z);        # Cubic correction term
      e = (z + mr*r);           # Corrected exponential parameter.
      s = s0*exp(e*log(s1/s0)); # Theoretical solubility.
      return s;
    }

  Conversion and comparison with model:
  
    solub_NH4_H2PO4_convert.gawk \
        solub_NH4_H2PO4_raw.txt \
        | txtable-reformat \
        > solub_NH4_H2PO4_cooked.txt 
    solub_NH4_H2PO4_plot.sh 

  Adopted values (from exponential fit in the above, 
  with hand corrections):
  
    g_w["NH4H2PO4",  -4.3] =   20.3; # Hand corrected.
    g_w["NH4H2PO4",   0.0] =   23.8; # Hand corrected.
    g_w["NH4H2PO4",   5.0] =   26.2;
    g_w["NH4H2PO4",  10.0] =   29.4;
    g_w["NH4H2PO4",  15.0] =   32.9;
    g_w["NH4H2PO4",  20.0] =   36.8;
    g_w["NH4H2PO4",  25.0] =   41.0;
    g_w["NH4H2PO4",  30.0] =   45.6;
    g_w["NH4H2PO4",  35.0] =   50.7;
    g_w["NH4H2PO4",  40.0] =   56.1;
    g_w["NH4H2PO4",  45.0] =   62.1;
    g_w["NH4H2PO4",  50.0] =   68.6;
    g_w["NH4H2PO4",  55.0] =   75.7;
    g_w["NH4H2PO4",  60.0] =   83.4;
    g_w["NH4H2PO4",  65.0] =   91.7;
    g_w["NH4H2PO4",  70.0] =  100.9;
    g_w["NH4H2PO4",  75.0] =  110.8;
    g_w["NH4H2PO4",  80.0] =  121.7;
    g_w["NH4H2PO4",  85.0] =  133.6;
    g_w["NH4H2PO4",  90.0] =  146.7;
    g_w["NH4H2PO4",  95.0] =  160.9;
    g_w["NH4H2PO4", 100.0] =  176.6;
    g_w["NH4H2PO4", 105.0] =  193.8;
    g_w["NH4H2PO4", 110.0] =  212.8;
    g_w["NH4H2PO4", 120.0] =  257.1;
    g_w["NH4H2PO4", 130.0] =  311.5;
    g_w["NH4H2PO4", 140.0] =  379.2;
    g_w["NH4H2PO4", 150.0] =  464.3;
    g_w["NH4H2PO4", 160.0] =  572.6;