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?
You probably mean
#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"#
The total volume is given by:
#V = n_1barV_1 + n_2barV_2#,
#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
- 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.