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conversion from molarity to molality

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ss13217:
I am trying to calculate the negative pH of a 2 mol/L H2SO4 solution using the Pitzer model. I understand that Pitzer uses molality (mol/kg) for pH calculations and can convert molarity (mol/L) to molality using the solution's density.  am confused as to how 2 mol/L H2SO4  becomes 2.476 mol/kg?  based on my calculation, molality should be 2.131 mol/kg. Here is my calculation

density = 1134.58 g/L
mass of solute = 2 mol/L * 98.08 g/mol * 1 L = 196.16 g
mass of water in 1 L solution = 1134.58 - 196.16 =  938.42 g
 
molality = moles of solute/mass of water (kg)  = 2 mol / 0.93842 kg = 2.131 mol/kg



--- Quote ---Reading input data for simulation 19.
-------------------------------------

   SOLUTION 18
   pH 7.0 charge
   temp 25
   units     mole/L
   S(6)     2
   END
-------------------------------------------
Beginning of initial solution calculations.
-------------------------------------------

Initial solution 18.   

-----------------------------Solution composition------------------------------

   Elements           Molality       Moles

   S(6)              2.476e+00   2.476e+00

----------------------------Description of solution----------------------------

                                       pH  =  -0.873      Charge balance
                                       pe  =   4.000   
      Specific Conductance (?S/cm,  25?C)  = 745920
                          Density (g/cm?)  =   1.13458
                               Volume (L)  =   1.09539
                        Activity of water  =   0.885
                 Ionic strength (mol/kgw)  =   3.690e+00
                       Mass of water (kg)  =   1.000e+00
                 Total alkalinity (eq/kg)  =  -4.951e+00
                         Temperature (?C)  =  25.00
                  Electrical balance (eq)  =  -4.578e-10
 Percent error, 100*(Cat-|An|)/(Cat+|An|)  =  -0.00
                               Iterations  =  26
                         Gamma iterations  =   6
                      Osmotic coefficient  =   1.21925
                         Density of water  =   0.99704
                                  Total H  = 1.159637e+02
                                  Total O  = 6.540878e+01

----------------------------Distribution of species----------------------------

                                                    MacInnes  MacInnes
                                MacInnes       Log       Log       Log    mole V
   Species          Molality    Activity  Molality  Activity     Gamma    cm?/mol

   H+              3.083e+00   7.461e+00     0.489     0.873     0.384      0.00
   OH-             8.709e-15   1.201e-15   -14.060   -14.921    -0.861      1.70
   H2O             5.551e+01   8.851e-01     1.744    -0.053     0.000     18.07
S(6)          2.476e+00
   HSO4-           1.869e+00   1.417e+00     0.272     0.151    -0.120     41.74
   SO4-2           6.070e-01   1.994e-03    -0.217    -2.700    -2.484     23.76

--- End quote ---

dlparkhurst:
mol/L is converted to mol/kg solution by dividing by the density. You have not defined a density for the solution, so the default is 1 kg/L, which is a poor estimate.

You can specify the density, in which case you will get a result much closer to your expectation.


--- Code: ---SOLUTION 1
-units mol/L
-density 1.13458
pH 2 charge
S(6) 2
USER_PRINT
10 PRINT TOTMOL("S(6)") / SOLN_VOL
END

--- End code ---

However, when you try to recover the concentration in mol/L, the calculated concentration is 1.96 mol/L. It is more consistent to use the density that PHREEQC calculates by using "calc" in the density definition. PHREEQC will adjust the density used to convert the units so that it is the same as the density that is calculated by PHREEQC. If you then calculate mol/L for sulfate, it will be 2.0.


--- Code: ---SOLUTION 1
-units mol/L
-density 1.13458 calc
pH 2 charge
S(6) 2
USER_PRINT
10 PRINT TOTMOL("S(6)") / SOLN_VOL
END

--- End code ---

The density may differ from your calculated or estimated density, but the calculation is internally consistent. You can choose how you want to deal with it.

dlparkhurst:
As for your other post,

The molality does not depend on the volume of your solution. You can use MIX to adjust the volume by 1/1.09539 to create a solution with 1 L (assuming you have considered the response to your previous post). The concentrations and pH will not change.

The Pitzer-Guggenheim approach does not claim to calculate the activity of an individual ion, which is unmeasurable. It attempts to calculate things like the mean activity coefficient for an H2SO4 solution, which is measurable. The calculation of pH relies on various conventions. I think NIST uses a model for HCl solutions to define a pH scale. In PHREEQC, the MacInnes assumption is used to define a pH scale. The MacInnes assumption is that the activity of K+ is equal to the activity of Cl- in KCl solutions. With that assumption, pH is calculated. There is no guarantee that this calculated pH will agree with a glass electrode measurement with its associated conventions for a pH scale.

The pH calculated by the Pitzer approach with the MacInnes assumption equal to pH = -log(m(H+)*g(H+)), where m(H+) is molality and g(H+) is the activity coefficient.

ss13217:
Thank you so much, David! I get it now. I was confused earlier because I noticed the solution description already included the density. I tried calculating it myself but couldn?t match the result from PHREEQC.

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