Concentration describes how much solute is dissolved in a given amount of solution. A spoonful of sugar in a small cup of water tastes much sweeter than the same spoonful in a large pitcher. The amount of solute is the same, but the concentration is different.

Molarity (M) is the most common way to express concentration in chemistry. It tells you how many moles of solute are dissolved per liter of solution:

$M = \frac{\text{moles of solute}}{\text{liters of solution}}$

If you dissolve 0.5 moles of NaCl in enough water to make 1.0 L of solution, the molarity is 0.5 M. Notice that molarity is based on the volume of the solution, not the volume of the solvent alone. That distinction trips people up on tests.

Because liquid volume expands and contracts with temperature, molarity can shift slightly as temperature changes. For most classroom and lab work at constant temperature, this isn't a concern.

Understanding Concentration and Molarity, Molarity | General Chemistry

Exploring Molal Concentration and Parts per Million

Molality (m) is an alternative concentration unit based on mass instead of volume:

$m = \frac{\text{moles of solute}}{\text{kilograms of solvent}}$

The key difference from molarity: molality uses kilograms of solvent (not solution), and since mass doesn't change with temperature, molality stays constant regardless of heating or cooling. This makes it useful for colligative property calculations like boiling point elevation and freezing point depression.

Parts per million (ppm) is used for extremely dilute concentrations, like trace contaminants in drinking water:

$\text{ppm} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 10^6$

A concentration of 1 ppm means there is 1 mg of solute in 1 kg of solution. For context, the EPA's action level for lead in drinking water is 15 ppb (parts per billion), which equals 0.015 ppm.

Molarity vs. Molality quick comparison:

Molarity = moles of solute / liters of solution (changes with temperature)

Molality = moles of solute / kilograms of solvent (stays constant with temperature)

Understanding Concentration and Molarity, 6.1 Solution Concentration and Molarity – Introduction to Chemistry

Moles and Solutions

Understanding Moles and Stock Solutions

The mole is chemistry's counting unit. One mole equals $6.022 \times 10^{23}$ particles (Avogadro's number). You convert between mass and moles using molar mass:

$\text{number of moles} = \frac{\text{mass of substance (g)}}{\text{molar mass (g/mol)}}$

The molar mass of NaCl is about 58.44 g/mol. If you have 29.22 g of NaCl, that's $\frac{29.22}{58.44} = 0.500 \text{ mol}$ .

A stock solution is a pre-made concentrated solution that you dilute to whatever working concentration you need. Labs keep stock solutions on hand because it's more practical to dilute a single concentrated batch than to weigh out fresh solute every time. To prepare one, you dissolve a precisely measured amount of solute in solvent and bring the total volume up to a specific mark, usually using a volumetric flask.

Dilution Techniques and Calculations

Dilution means adding more solvent to lower a solution's concentration. The total amount of solute doesn't change; it just gets spread through a larger volume. This relationship is captured by the dilution equation:

$M_1 V_1 = M_2 V_2$

$M_1$ and $V_1$ = the molarity and volume before dilution
$M_2$ and $V_2$ = the molarity and volume after dilution

Example: You have 50.0 mL of a 2.0 M HCl solution and need to dilute it to 0.50 M. What total volume do you need?

Write down what you know: $M_1 = 2.0 \text{ M}$ , $V_1 = 50.0 \text{ mL}$ , $M_2 = 0.50 \text{ M}$
Plug into the equation: $(2.0)(50.0) = (0.50)(V_2)$
Solve for $V_2$ : $V_2 = \frac{(2.0)(50.0)}{0.50} = 200 \text{ mL}$
You'd add enough water to bring the total volume to 200 mL. That means adding 150 mL of water to your original 50.0 mL.

Note that $V_1$ and $V_2$ just need to be in the same units. You can use mL for both or L for both. Just don't mix them.

A serial dilution repeats this process multiple times, creating a series of solutions with progressively lower concentrations. The dilution factor for each step is:

$\text{Dilution Factor} = \frac{\text{Final Volume}}{\text{Initial Volume}}$

For example, if you transfer 1 mL of solution into 9 mL of solvent, your final volume is 10 mL, giving a dilution factor of 10. Each step reduces the concentration by that factor. Serial dilutions are common in biology and environmental science when you need a wide range of concentrations for testing.

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