Solutions & concentration
The idea
Dissolving salt in water gives a solution — solute dispersed uniformly through solvent — but chemistry needs to know how much is in there, not just that it dissolved. The workhorse measure is molarity: M = moles of solute per liter of solution. A 0.200 M solution carries 0.200 mol of solute in every liter, which makes molarity a direct bridge between a volume you can measure with glassware and a mole count you can feed into stoichiometry.
Read the definition carefully: the denominator is liters of final solution, not liters of water added. That is why solutions are prepared by dissolving the solute first and then adding solvent up to the target volume mark. Dilution follows from one conserved idea — adding solvent changes the volume but not the moles of solute — which is exactly the content of M₁V₁ = M₂V₂: the same moles spread through more liquid.
The misconception to dodge is thinking dilution removes solute or that concentration is an amount. Concentration is a density of particles, amount is the particle count; pouring half a solution down the drain halves the moles but leaves the molarity untouched, while adding water leaves the moles untouched and lowers the molarity.
Worked example
You need 250.0 mL of a 0.200 M sodium chloride solution. What mass of NaCl should you weigh out? Use Na = 23.0, Cl = 35.5 g/mol.
- Convert the volume into the units molarity speaks: 250.0 mL = 0.2500 L of final solution.
- Find the moles the solution must contain, straight from the definition M = n/V rearranged: n = M × V = 0.200 mol/L × 0.2500 L = 0.0500 mol of NaCl.
- Convert moles to a weighable mass: M(NaCl) = 23.0 + 35.5 = 58.5 g/mol, so mass = 0.0500 mol × 58.5 g/mol = 2.93 g.
- Sanity-check: a full liter of 0.200 M NaCl would need 0.200 × 58.5 = 11.7 g, and a quarter of a liter should need a quarter of that — 11.7 ÷ 4 = 2.93 g. Consistent.
- Note the technique the definition forces: dissolve the 2.93 g in less water first, then fill up to the 250.0 mL mark — adding 250 mL of water to the solid would overshoot the final volume and undershoot the concentration.
Answer. Weigh out 2.93 g of NaCl and dilute to a final volume of 250.0 mL.
Check your understanding
- Why is molarity defined per liter of solution rather than per liter of solvent, and how does that change lab procedure?
- How does the dilution equation M₁V₁ = M₂V₂ follow from the fact that moles of solute are conserved?
- If a solution warms up and expands slightly, what happens to its molarity even though nothing was added?
- How would you use a known molarity and a measured volume to feed a reaction calculation, and why is that pairing so useful?
Build the foundations first
Solutions & concentration builds on these concepts. If any feel shaky, start there.