Monday, August 26, 2013

Calculate Mole Fractions Using Mass Percent

According to basic definitions, a solute (e.g. sodium chloride) dissolves in solvent (e.g. water) to make a solution. Concentration indicates how much of a compound (solute) is dissolved in the solution, and can be expressed in multiple ways. Mole fraction refers to the ratio between number of moles of solute and the total number of moles in a solution. As an example, consider calculation of mole fractions in the solution of sodium hydroxide (NaOH) in water (H2O) if NaOH mass percent equals to 10.


1. Calculate molecular mass (M) of all compounds (including solvent) that compose the solution. Generally, for a compound with chemical formula AnBm:

Molecular mass (M) = n x M(A) + m x M(B), where M(A) or M(B) are atomic weights of the corresponding elements, which can be taken from the periodic table of the chemical elements.

In our example

M(NaOH)=M(Na)+M(O)+M(H)=23+16+1=40 g/mole.

M(H2O)=2xM(H)+M(O)=2 x 1+16=18 g/mole.

2. Calculate masses of solute and solvent in the solution. Mass percent (solute)=100percent x[mass(solute)/(mass(solution)). Abbreviate mass(solution) as "m" for simplicity and obtain: mass(solute)= m x [mass percent (solute)/100percent], and mass(solvent)= m-mass(solute).

In our example:

mass(NaOH)=m x [10 percent/100 percent]= 0.10m


3. Calculate amount of solute and solvent in Moles: amount =mass/molecular mass (mole)

In our example:

amount (NaOH)=0.1m/40 (mole)=0.0025m (mole)

amount(H2O)=0.90m/18 (mole)=0.05m (mole)

4. Calculate mole fractions. The mole fraction of the component X of the solution is

Mole fraction (X)=amount(X)/[Total amount (sum) of all components]

In our example, NaOH and H2O are only two components i.e.

Mole fraction(NaOH)=0.0025m/(0.0025m+0.05m)= 0.0025/0.0525=0.048

Mole fraction(H2O)=0.05m/(0.0025m+0.05m)= 0.05/0.0525=0.952

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