Solutions & Molarity — Reference Sheet

Solute, Solvent, and Solution

Every solution is a homogeneous mixture built from two parts. The solute is the substance being dissolved, and it's normally the smaller amount. The solvent does the dissolving and is normally the larger amount. Together they make the solution. When water is the solvent, chemists call the result an aqueous solution, written with the state symbol (aq) after the formula.

Term	Definition	Example (salt water)
Solute	Substance being dissolved	NaCl (table salt)
Solvent	Substance doing the dissolving	H₂O (water)
Solution	Solute + solvent, mixed evenly	Salt water
Aqueous (aq)	A solution where water is the solvent	NaCl(aq)

Not every mixture is a solution

A true solution is homogeneous, meaning the composition looks identical throughout, down to the particle level, and it never settles out. Muddy water is a mixture, but it isn't a solution because the dirt eventually settles.

Molarity: M = mol / L

Molarity (M) is the most common way chemists express concentration. It's defined as moles of solute per liter of total solution, not per liter of solvent added.

Symbol	Meaning	Unit
M	Molarity	mol/L, also written mol·L⁻¹
n	Moles of solute	mol
V	Volume of solution	L

The formula: M = n ÷ V. Rearranged forms you'll need constantly: n = M × V and V = n ÷ M.

Volume of solution, not solvent

The volume in molarity is the total volume of the finished solution, after the solute is dissolved and the mixture is brought up to the mark. It is not the volume of water you started with, since adding solute changes the total volume slightly.

Worked Molarity Examples

Example 1. What is the molarity of a solution made by dissolving 0.500 mol of NaCl in enough water to make 2.00 L of solution? M = n ÷ V = 0.500 mol ÷ 2.00 L = 0.250 M

Example 2. How many grams of NaCl are needed to make 500. mL of a 1.50 M solution? Molar mass of NaCl = 58.44 g/mol. Step 1, find moles: n = M × V = 1.50 mol/L × 0.500 L = 0.750 mol Step 2, convert to grams: 0.750 mol × 58.44 g/mol = 43.8 g NaCl

Convert mL to L first

Molarity is always mol per liter. If a volume is given in mL, divide by 1000 before plugging it into M = n ÷ V. Forgetting this conversion is the single most common molarity mistake.

Dilution: M₁V₁ = M₂V₂

Diluting a solution means adding more solvent, which lowers the concentration but does not change the number of moles of solute present. That's the whole idea behind the dilution equation: moles before equal moles after.

Symbol	Meaning
M₁	Initial (concentrated, stock) molarity
V₁	Initial (stock) volume
M₂	Final (diluted) molarity
V₂	Final (diluted) volume

Example. You have a 6.00 M HCl stock solution. How many mL of stock are needed to prepare 250. mL of 0.500 M HCl? M₁V₁ = M₂V₂ (6.00 M)(V₁) = (0.500 M)(250. mL) V₁ = (0.500 × 250.) ÷ 6.00 = 20.8 mL of stock You'd measure out 20.8 mL of the 6.00 M stock, then add water until the total volume reaches 250. mL.

Any consistent volume unit works

M₁V₁ = M₂V₂ works with mL on both sides or L on both sides, as long as V₁ and V₂ use the same unit as each other. You don't need to convert to liters first the way you do for M = n ÷ V.

Preparing a Solution of Known Molarity

To make a solution of a specific molarity from a solid solute, chemists use a volumetric flask, which is calibrated to hold one exact, precise volume.

Step	Action
1	Calculate the mass of solute needed (M × V, then convert mol to g)
2	Weigh out that mass on a balance
3	Add the solute to a volumetric flask of the target volume
4	Add solvent partway, swirl to dissolve the solute completely
5	Add solvent until the bottom of the meniscus sits exactly on the calibration line
6	Stopper and invert to mix thoroughly

Dissolve before filling to the line

Never fill straight to the calibration mark and then try to dissolve the solute. Dissolving changes the total volume, so you'll overshoot. Dissolve most of the way first, then top off to the line as the last step.

Concentration Vocabulary

Molarity is a precise number, but chemists also use qualitative and alternative terms to describe how much solute a solution holds.

Term	Meaning
Dilute	Relatively little solute per unit of solvent
Concentrated	Relatively large amount of solute per unit of solvent
Saturated	Holds the maximum solute that will dissolve at that temperature; excess solute would not dissolve
Unsaturated	Holds less solute than the maximum that could dissolve at that temperature
Supersaturated	Holds more dissolved solute than a saturated solution normally would, an unstable state that can crystallize if disturbed
Molality (m)	Moles of solute per kilogram of solvent, mol/kg, different from molarity and independent of temperature
ppm	Parts per million, used for extremely dilute solutions, roughly 1 mg solute per 1 L of water

Dilute/concentrated vs. saturated/unsaturated

Dilute and concentrated are relative comparisons between two solutions. Saturated and unsaturated describe a solution relative to its own maximum solubility limit at a given temperature. A solution can be both concentrated and unsaturated at the same time.

Try it yourself

Download molarity-lab-trials.csvmolarity-lab-trials.csv

Six lab trials, each dissolving a measured mass of a solute in a measured final volume of solution.

Open it as a spreadsheet

Open molarity-lab-trials.csv in Google Sheets or Excel. Add a column for molar mass and a column for molarity so you can compute all six trials at once, the same way you'd check a lab partner's math.

Using the values in the file, answer these. Atomic masses (g/mol): Na 22.99, Cl 35.45, Ca 40.08, K 39.10, N 14.01, O 16.00, Mg 24.31, S 32.07, C 12.01, H 1.01. Round every molarity to 3 significant figures. 1. Calculate the molarity of the KNO₃ solution in trial 3. 2. Which trial produced the most concentrated (highest molarity) solution? 3. Rank all six trials from highest molarity to lowest.