How do you find the density of a solution if you know the identity of the solute and solvent, the amount that you combine of each, and their individual densities?

1 Answer
Truong-Son N.
May 24, 2017

You probably mean #"g/mL"#... Density is defined as:

#D = "mass solution"/"volume solution"#

#= "mass solute + mass solvent"/"volume solution"#

#-= (m_"solute" + m_"solvent")/V_"soln"#

#= (n_"solute"M_"solute" + n_"solvent"M_"solvent")/V_"soln"#

where the volume of the solution is not necessarily the volume of the solute plus solvent, but tends to be assumed so. #M# is molar mass in #"g/mol"# and #n# is #"mol"#s.

The total volume is given by:

#V = n_1barV_1 + n_2barV_2#,

where #barV_i = V_i/n# is the molar volume of component #i#.

With one component in the solution with water, we have:

#bb(D = (n_"solute"M_"solute" + n_"solvent"M_"solvent")/(n_"solute"barV_"solute" + n_"solvent"barV_"solvent")#

The molar volume of water is known from its density at some temperature #T# and #"1 atm"# pressure. Simply do some unit conversion to get from #"g/mL"# to #"mol/L"#, then reciprocate it.

So:

  • By knowing the density of your solute at your temperature #T# and #"1 atm"# pressure, you can get #barV_"solute"#.
  • By knowing the masses of both the solute and solvent individually before mixing the solution, as well as their molar masses, you can determine the total mass of the solution.
  • Knowing their masses and their molar masses, you can also then determine the total volume of the solution.
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