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# Percent by Mass (Weight) and Mass Fraction (w/w)

## Key Concepts

• 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?

1. Convert all mass units to the same units:
mass(NaCl) = 560mg = 560 x 10-3g = 0.560g
mass(H2O) = 10.4g

2. 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?

1. Calculate the mass fraction of sucrose:
mass fraction(sucrose) = 1 - mass fraction(water) = 1 - 0.65 = 0.35

2. 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?

1. Re-arrange the equation to find mass % KCl:
mass %(KCl) + mass %(H2O) = 100
mass %(KCl) = 100 - mass %(H2O)

2. 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?

1. Write the equation:
mass % NaOH = mass(NaOH) ÷ (mass(NaOH) + mass(H2O)) x 100

2. 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?

1. 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)

2. Substitute in the values:
mass(ethanol) = 42 ÷ 100 x 250 = 105g
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