13.2 Units of Concentration
PRE-HEALTH PREP
Molarity, Molality & Concentration Unit Conversions
General Chemistry 13.2
Lesson Overview
Concentration units—molarity, molality, mole fraction, and mass percent—each express the amount of solute in a solution using different reference quantities. A detailed worked example converts a 20% sulfuric acid solution between all four units, demonstrating the step-by-step process and the role of density and molar mass in these conversions. The comparison between molarity and molality clarifies why the two values diverge at higher concentrations and when each unit is most appropriate.
What Are Concentration Units in Chemistry?
Concentration describes how much solute is dissolved in a given amount of solution or solvent. In general chemistry, four concentration units are commonly used because different situations call for different ways of expressing this relationship. This lesson reviews molarity and mole fraction from earlier chapters, introduces molality as a new unit, and revisits mass percent along with its relatives—parts per million (ppm) and parts per billion (ppb).
| UNITS OF CONCENTRATION |
|---|
| Molarity |
| Molality |
| Mole Fraction |
| Mass Percent, ppm, etc. |
Molality is particularly important because it serves as the foundation for colligative properties covered in the next lesson. Understanding how to convert between concentration units—specifically how to convert molarity to molality and how to convert mass percent to molarity—is an essential skill for any general chemistry student.
Why So Many Concentration Units?
Each concentration unit has a specific advantage. Molarity is convenient for volumetric lab work, molality is temperature-independent and ideal for colligative property calculations, mole fraction appears in gas law applications, and mass percent is intuitive for everyday solution composition descriptions.
Molarity (M): Moles of Solute per Liter of Solution
Molarity (symbol: M) is defined as the moles of solute divided by the total volume of the solution in liters. It is the most common concentration unit in general chemistry.
Molarity is the most commonly used concentration unit in general chemistry, particularly for reactions carried out in aqueous solution. If you have been working with solution stoichiometry since chapter four, you are already well acquainted with this unit.
Quick Example
A solution containing 0.50 moles of NaCl dissolved in enough water to produce 1.0 L of total solution has a molarity of 0.50 M NaCl.
Mole Fraction (χ): A Dimensionless Concentration Unit
Mole fraction expresses the fraction of total moles belonging to a particular component. It is a dimensionless quantity (no units) and always falls between 0 and 1.
You may recall mole fractions from Dalton's law of partial pressures in the chapter on gases, where the mole fraction of each gas determined its partial pressure. The same concept applies to solutions: you can express the mole fraction from either the solvent's or the solute's perspective, depending on what the problem requires.
Looking Ahead to Colligative Properties
Certain colligative properties require the mole fraction of the solvent rather than the solute. Keep this distinction in mind as you work through these calculations.
Molality (m): Moles of Solute per Kilogram of Solvent
Molality (symbol: lowercase m) is defined as the moles of solute divided by the kilograms of solvent—not the total solution. This is the key distinction between molality and molarity.
Molarity vs. Molality: The Critical Difference
Students frequently confuse these two concentration units because their names are nearly identical. The key difference lies in the denominator:
- Molarity (M): moles of solute per liter of total solution
- Molality (m): moles of solute per kilogram of solvent only
This distinction matters because adding solute to a solution changes its total volume, but the mass of the solvent remains constant. As a result, molality does not change with temperature (since mass is unaffected by thermal expansion), making it the preferred concentration unit for several colligative property calculations.
Why Molality Is Used for Colligative Properties
Since volume expands or contracts with temperature while mass stays constant, molality provides a temperature-independent measure of concentration. This property makes it especially useful for boiling point elevation and freezing point depression calculations.
Mass Percent, Parts Per Million & Parts Per Billion: 3 Related Units
Mass percent expresses the mass of solute as a percentage of the total mass of the solution. It is one of the most intuitive concentration units and connects directly to ppm and ppb.
The concept extends naturally to more dilute concentrations. "Percent" literally means "per hundred," so mass percent is simply parts per hundred. For much smaller concentrations, chemists use parts per million (ppm) and parts per billion (ppb).
| Unit | Formula | Multiplication Factor | Typical Use |
|---|---|---|---|
| Mass Percent | (mass solute / mass solution) × 100 | 102 | Everyday solutions |
| Parts Per Million (ppm) | (mass solute / mass solution) × 106 | 106 | Water quality, trace contaminants |
| Parts Per Billion (ppb) | (mass solute / mass solution) × 109 | 109 | Atmospheric gases, toxicology |
The Universal Pattern for All 3 Units
Regardless of the unit, the calculation always follows the same structure: mass of solute divided by total mass of solution, multiplied by the appropriate factor. The only difference is the scaling factor—100 for percent, 106 for ppm, and 109 for ppb.
Worked Example: Converting a 20% H2SO4 Solution Between All 4 Concentration Units
Consider a 20% sulfuric acid (H2SO4) solution by mass with a density of 1.14 g/mL. Starting from this mass percent, we will convert to molarity, molality, and mole fraction—demonstrating that you can move between any concentration unit when given sufficient information.
The Intensive Property Shortcut
Concentration is an intensive property, meaning it does not depend on sample size. When a problem provides concentration without specifying a particular amount, you are free to choose any convenient sample size. The answer will be the same regardless of the amount you select.
Choosing a Convenient Sample Size
Since we are working with a 20% solution by mass, choosing a 100-gram sample makes the arithmetic straightforward: 20% of 100 grams is simply 20 grams of H2SO4. No calculator required for that step.
Our Starting Point
Total solution: 100 g
H2SO4 (solute): 20 g
Water (solvent): 80 g
Density: 1.14 g/mL
How to Convert Mass Percent to Molarity: 3-Step Method
Converting mass percent to molarity requires moles of solute and liters of total solution. We need to convert both from our chosen 100-gram sample.
Step 1: Find Moles of Solute
First, determine the molar mass of H2SO4 from the periodic table:
1 S = 32 g/mol
4 O = 4(16) = 64 g/mol
Molar mass = 2 + 32 + 64 = 98 g/mol
Now convert grams to moles:
Step 2: Find Total Volume of Solution
Use the density to convert the total mass to volume. Rearranging density = mass / volume gives volume = mass / density:
87.7 mL × (1 L / 1000 mL) = 0.0877 L
Step 3: Calculate Molarity
Result
The 20% H2SO4 solution has a molarity of 2.33 M. Notice how the intensive property shortcut saved work: by choosing 100 grams, the percent-to-mass conversion was trivial.
How to Convert Mass Percent to Molality: 2-Step Method
Converting mass percent to molality requires moles of solute and kilograms of solvent. We already know the moles of solute from our molarity calculation, so the only new piece is expressing the solvent mass in kilograms.
Step 1: Find Kilograms of Solvent
From our 100-gram sample: 20 grams are solute, leaving 80 grams of water (the solvent).
Step 2: Calculate Molality
Result
The 20% H2SO4 solution has a molality of 2.55 m (read as "2.55 molal"). Notice that the molality (2.55 m) is slightly higher than the molarity (2.33 M)—this pattern is typical and becomes more pronounced with increasing concentration.
How to Convert Mass Percent to Mole Fraction: 2-Step Method
Calculating the mole fraction of the solute requires the moles of solute and the total moles (solute plus solvent combined).
Step 1: Find Moles of Solvent
We already have the moles of H2SO4 (0.204 mol). Now convert the 80 grams of water to moles using water's molar mass (18 g/mol):
Step 2: Calculate Mole Fraction
χH2SO4 = 0.204 ÷ 4.644 = 0.044
Result
The mole fraction of H2SO4 in this solution is 0.044. This means that roughly 4.4% of all molecules in the solution are sulfuric acid molecules, while the remaining ~95.6% are water molecules.
Solvent vs. Solute Mole Fraction
This example calculates χsolute, but some colligative property equations require χsolvent instead. The two always sum to 1, so χsolvent = 1 − χsolute = 1 − 0.044 = 0.956.
Molarity vs. Molality: 5 Key Differences
An important pattern emerges when comparing molarity and molality for the same solution. For dilute aqueous solutions, the two concentration values are nearly identical because one kilogram of water occupies approximately one liter. However, as concentration increases, the values diverge—with molality typically being higher than molarity.
| Feature | Molarity (M) | Molality (m) |
|---|---|---|
| Unit | mol / L solution | mol / kg solvent |
| Denominator includes | Solute + solvent (total) | Solvent only |
| Temperature dependent? | Yes (volume changes) | No (mass is constant) |
| Requires density? | Sometimes (for conversions) | No |
| Best used for | Lab work, stoichiometry | Colligative properties |
Why Molality Is Higher Than Molarity
Molarity divides by the total solution volume (solvent plus solute), while molality divides by the solvent mass alone. Since the denominator in molality excludes the solute, it is smaller, producing a larger numerical result. The more concentrated the solution, the more pronounced this difference between molarity and molality becomes.
7 Key Takeaways: Concentration Units & Conversions
- Molarity (M) equals moles of solute per liter of total solution—the most common concentration unit in general chemistry lab work.
- Molality (m) equals moles of solute per kilogram of solvent and is temperature-independent, making it essential for colligative property calculations.
- Mole fraction (χ) expresses the proportion of moles belonging to one component. The mole fractions of solute and solvent always sum to 1.
- Mass percent, ppm, and ppb all follow the same pattern: mass of solute divided by total mass, multiplied by 100, 106, or 109 respectively.
- Concentration is an intensive property. When no sample size is given, choose a convenient amount (e.g., 100 g for mass percent problems) to simplify calculations.
- For dilute aqueous solutions, molarity and molality are approximately equal; they diverge as concentration increases, with molality typically yielding a higher value.
- You should be prepared to convert between any two concentration units when given sufficient information (typically density and/or molar masses).