Mass Percent in Solutions: Concepts and Calculations

Mass Percent in Solutions

Definition and Formula

Mass percent (also called weight percent) is a way to express the concentration of a component in a solution. It represents the percentage of a given element or compound within the total mass of the solution.

• Mass Percent is calculated using the following formula:

$\text{Mass Percent} = \frac{\text{Mass Component}}{\text{Total Mass}} \times 100$

• Mass Component: The mass of the solute (the substance being dissolved).

• Total Mass: The mass of the entire solution (solute + solvent).

Example Calculation: Mass Percent of NaOH

Suppose we are given a solution with 23.0% NaOH by mass. This means:

• 23.0 grams NaOH are present in every 100 grams of solution.

• The remaining mass (77 grams) is the solvent, typically water.

$\text{23.0\% NaOH} = \frac{23.0\,\text{g NaOH}}{100\,\text{g Solution}} \times 100$

• Calculation: 100 g solution - 23 g NaOH = 77 g H2O (solvent)

Example 1: Calculating Mass of Water Added

Calculate the amount of water (in kilograms) that must be added to 12.0 g of urea, (NH2)2CO, to prepare a solution with 18.3 percent by mass urea. The molar mass of urea is 60.055 g/mol.

• Step 1: Set up the mass percent equation:

$\text{Mass percent} = \frac{\text{g solute}}{\text{g solution}} \times 100$

• Step 2: Substitute values:

$18.3 = \frac{12.0}{12.0 + x} \times 100$

• Step 3: Solve for x (mass of water):

$18.3(12.0 + x) = 1200$ $219.6 + 18.3x = 1200$ $18.3x = 980.4$ $x = 53.6$ g

• Step 4: Convert to kilograms:

$x = 0.0536$ kg

Example 2: Calculating Mass Percent of KBr

A solution is prepared by dissolving 51.0 g of KBr in 310 mL of water. Calculate the mass percent of KBr in the solution.

• Step 1: Find total mass of solution:

$\text{Total mass} = 51.0\,\text{g KBr} + 310\,\text{g H}_2\text{O} = 361.0\,\text{g solution}$

• Step 2: Calculate mass percent:

$\text{Mass percent} = \frac{51.0}{361.0} \times 100 = 14.1\%$

Summary Table: Mass Percent Calculations

Component	Mass of Solute (g)	Mass of Solvent (g)	Total Mass (g)	Mass Percent (%)
NaOH	23.0	77.0	100.0	23.0
Urea	12.0	53.6	65.6	18.3
KBr	51.0	310.0	361.0	14.1

Key Points

• Mass percent is a useful way to express solution concentration, especially in laboratory settings.

• Always ensure units are consistent (grams or kilograms) when performing calculations.

• Mass percent can be used to determine how much solvent to add to achieve a desired concentration.