Mass (weight) fraction is the ratio of the mass of one component of a solution to the total mass of the solution.

Mass fraction_{(a)} = mass_{(a)} ÷ (mass_{(a)} + mass_{(b)} + mass_{(c)} + ...)
mass_{(a)} = mass of component a
mass_{(b)} = mass of component b
mass_{(c)} = mass of component c

mass fraction_{(a)} + mass fraction_{(b)} + mass fraction_{(c)} + .... = 1

Masses (weights) can be any units as long as they are the same units for all components.

Percent by mass (weight) is the percent of the total mass of the solution that is one component.

Percent by mass (weight) = mass (weight) fraction x 100

mass % a (wt. % a) = mass_{(a)} ÷ (mass_{(a)} + mass_{(b)} + mass_{(c)} + ...) x 100

mass % a + mass % b + mass % c + .... = 100

Mass (weight) Percent of solute is usually abbreviated as w/w .

Mass Fraction Calculations

1. What is the mass (weight) fraction of sodium chloride in an aqueous solution containing 560mg of sodium chloride and 10.4g of water?

Convert all mass units to the same units:
mass_{(NaCl)} = 560mg = 560 x 10^{-3}g = 0.560g
mass_{(H2O)} = 10.4g

Calculate the mass (weight) fraction:
mass fraction_{(NaCl)} = mass_{(NaCl)} ÷ (mass_{(NaCl)} + mass_{(H2O)})
mass fraction_{(NaCl)} = 0.560 ÷ (0.560 + 10.4) = 0.051

2. If 500g of an aqueous solution of sucrose contains a mass fraction of water of 0.65, what mass of sucrose is present?

Calculate the mass fraction of sucrose:
mass fraction_{(sucrose)} = 1 - mass fraction_{(water)} = 1 - 0.65 = 0.35

Calculate the mass of sucrose present:
mass fraction_{(sucrose)} = mass_{(sucrose)} ÷ total mass_{(solution)} mass_{(sucrose)} = mass fraction_{(sucrose)} x mass_{(solution)} = 0.35 x 500 = 175g

Percent by Mass (weight) Calculations

1. An aqueous solution of potassium chloride has a mass % water of 78%. What is the mass percent potassium chloride?

Re-arrange the equation to find mass % KCl:
mass %_{(KCl)} + mass %_{(H2O)} = 100
mass %_{(KCl)} = 100 - mass %_{(H2O)}

Subsitute in the values:
mass %_{(KCl)} = 100 - 78 = 22%

2. An aqueous solution contains 700g water and 45g sodium hydroxide. What is the percent by mass of sodium hydroxide?

Write the equation:
mass % NaOH = mass_{(NaOH)} ÷ (mass_{(NaOH)} + mass_{(H2O)}) x 100

Substitute in the values (all masses must have the same units):
mass_{(NaOH)} = 45g
mass_{(H2O)} = 700g
mass % NaOH = 45 ÷ (45 + 700) x 100 = 6.04%

3. An aqueous solution contains 42% by mass ethanol. What mass of ethanol is present in 250g of solution?

Re-arrange the equation to find mass of ethanol:
mass % ethanol = mass_{(ethanol)} ÷ mass_{(solution)} x 100
mass_{(ethanol)} = mass % ethanol ÷ 100 x mass_{(solution)}

Substitute in the values:
mass_{(ethanol)} = 42 ÷ 100 x 250 = 105g

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