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Expressing Concentration

Mass percent, mole fraction, molarity and molality, and how to convert between them.

9 micro-lessons

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Mass %, ppm, and Mole Fraction

The basic ways to express concentration, and their formulas.

Expressing Concentration

There are several ways to describe the concentration of a solution quantitatively. The method you choose depends on the application.

Mass Percentage (w/w)

Used heavily in industrial chemistry, mass percentage tells you the mass of solute in 100 parts of solution by mass.

$\text{Mass \%} = \frac{\text{Mass of component in solution}}{\text{Total mass of solution}} \times 100$

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Example 1.1: Mole Fraction

Calculates the mole fraction of ethylene glycol in a 20% by mass aqueous solution.

Problem

Calculate the mole fraction of ethylene glycol ( $\text{C}_2\text{H}_6\text{O}_2$ ) in a solution containing $20\%$ of $\text{C}_2\text{H}_6\text{O}_2$ by mass.

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Solve it: Mole Fraction

Your turn: calculate a mole fraction (textbook Intext Question 1.2).

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Problem: Calculate the mole fraction of benzene in a solution containing 30% by mass in carbon tetrachloride.

Step 1: Assuming 100 g of total solution, the mass of benzene is 30 g and the mass of solvent ( $CCl_4$ ) is g.

Step 2: Next, determine the molar mass of each component. The molar mass of benzene ( $C_6H_6$ ) is 78 $g\ mol^{-1}$ and the molar mass of $CCl_4$ is $g\ mol^{-1}$ .

Step 3: Calculate the number of moles: moles of benzene = 0.385 mol, and moles of $CCl_4$ = 0.455 mol.

Step 4: Finally, determine the mole fraction of benzene by dividing its moles by the total moles, yielding $x_{benzene} =$ .

Volume of Solvent vs Volume of Solution

The one difference between molarity and molality.

imagePrompt: clean side-by-side comparison, consistent visual treatment for both sides, same scale and style, pastel color coding to distinguish categories, elegant typography, white background, generous whitespace. On the left side, show a beaker labeled 'Molarity (M)' containing exactly 1 Liter of a mixed solution (representing solute + solvent combined). On the right side, show a scale with a beaker containing exactly 1 kg of pure solvent, with a scoop of solute being added, labeled 'Molality (m)'.

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Molarity (M) vs. Molality (m)

Molarity measures moles per liter of total solution and is temperature-dependent due to thermal expansion. Molality measures moles per kilogram of pure solvent and remains constant regardless of temperature or pressure changes.

This distinction is critical for calculating colligative properties—like boiling point elevation—where temperature fluctuates.

Molarity vs Molality

Defines Molarity (M) and Molality (m) emphasizing temperature dependence.

While mass percentage and mole fraction are incredibly useful, in a chemistry lab, solutions are often measured by volume or by adding solute to a specific mass of pure solvent.

Molarity ( $M$ )

Molarity is defined as the number of moles of solute dissolved in one litre (or one cubic decimetre) of the overall solution.

$\text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in litre}}$

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Example 1.2: Calculating Molarity

Calculates Molarity of NaOH in solution.

Problem

Calculate the molarity of a solution containing $5\text{ g}$ of $\text{NaOH}$ in $450\text{ mL}$ solution.

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Example 1.3: Calculating Molality

Calculates Molality of ethanoic acid in benzene.

Problem

Calculate molality of $2.5\text{ g}$ of ethanoic acid ( $\text{CH}_3\text{COOH}$ ) in $75\text{ g}$ of benzene.

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Mass %, ppm, and Mole Fraction

The basic ways to express concentration, and their formulas.

Expressing Concentration

There are several ways to describe the concentration of a solution quantitatively. The method you choose depends on the application.

Mass Percentage (w/w)

Used heavily in industrial chemistry, mass percentage tells you the mass of solute in 100 parts of solution by mass.

$\text{Mass \%} = \frac{\text{Mass of component in solution}}{\text{Total mass of solution}} \times 100$

1 / 5

Example 1.1: Mole Fraction

Calculates the mole fraction of ethylene glycol in a 20% by mass aqueous solution.

Problem

Calculate the mole fraction of ethylene glycol ( $\text{C}_2\text{H}_6\text{O}_2$ ) in a solution containing $20\%$ of $\text{C}_2\text{H}_6\text{O}_2$ by mass.

1 / 5

Solve it: Mole Fraction

Your turn: calculate a mole fraction (textbook Intext Question 1.2).

0 of 3 blanks filled

Problem: Calculate the mole fraction of benzene in a solution containing 30% by mass in carbon tetrachloride.

Step 1: Assuming 100 g of total solution, the mass of benzene is 30 g and the mass of solvent ( $CCl_4$ ) is g.

Step 2: Next, determine the molar mass of each component. The molar mass of benzene ( $C_6H_6$ ) is 78 $g\ mol^{-1}$ and the molar mass of $CCl_4$ is $g\ mol^{-1}$ .

Step 3: Calculate the number of moles: moles of benzene = 0.385 mol, and moles of $CCl_4$ = 0.455 mol.

Step 4: Finally, determine the mole fraction of benzene by dividing its moles by the total moles, yielding $x_{benzene} =$ .

Molarity vs Molality

Defines Molarity (M) and Molality (m) emphasizing temperature dependence.

While mass percentage and mole fraction are incredibly useful, in a chemistry lab, solutions are often measured by volume or by adding solute to a specific mass of pure solvent.

Molarity ( $M$ )

Molarity is defined as the number of moles of solute dissolved in one litre (or one cubic decimetre) of the overall solution.

$\text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in litre}}$

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Example 1.2: Calculating Molarity

Calculates Molarity of NaOH in solution.

Problem

Calculate the molarity of a solution containing $5\text{ g}$ of $\text{NaOH}$ in $450\text{ mL}$ solution.

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Example 1.3: Calculating Molality

Calculates Molality of ethanoic acid in benzene.

Problem

Calculate molality of $2.5\text{ g}$ of ethanoic acid ( $\text{CH}_3\text{COOH}$ ) in $75\text{ g}$ of benzene.

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Expressing Concentration

Mass %, ppm, and Mole Fraction

Expressing Concentration

Mass Percentage (w/w)

Example 1.1: Mole Fraction

Problem

Solve it: Mole Fraction

Volume of Solvent vs Volume of Solution

Molarity vs Molality

Molarity (MMM)

Example 1.2: Calculating Molarity

Problem

Example 1.3: Calculating Molality

Problem

Mass %, ppm, and Mole Fraction

Expressing Concentration

Mass Percentage (w/w)

Example 1.1: Mole Fraction

Problem

Solve it: Mole Fraction

Volume of Solvent vs Volume of Solution

Molarity vs Molality

Molarity (MMM)

Example 1.2: Calculating Molarity

Problem

Example 1.3: Calculating Molality

Problem

Molarity ( $M$ )

Molarity ( $M$ )