Molarity

Molarity is the concentration unit that counts moles per liter: M = n / V. A 0.25 M sodium chloride solution holds 0.25 mol of NaCl in every liter of solution. The n is the solute, the V is the whole solution, not the solvent alone. The liter measures the final solution after the solute has been dissolved. The unit tells you the story: moles in the numerator and liters in the denominator.

The common mistake is dividing the wrong way. For 0.50 mol in 2.0 L, liters divided by moles gives 4.0, which makes no sense as a concentration here. Moles divided by liters gives 0.25 mol/L, and the definition is written with moles on top. Check the units of the answer to catch the flip. The definition itself is the best check of the answer's units.

Molarity rearranges like any other equation. If you need the volume, V = n / M. Finding 0.100 mol in a 0.50 M solution means 0.100/0.50 = 0.20 L. Finding moles given V and M means multiplying: n = M x V. Choose the rearrangement that leaves the wanted unit standing alone. All three re-arrangements are the same relationship, just solved for a different letter.

Watch the volume unit: liters only. A volume in milliliters must be converted before dividing. The result, in mol/L, is the molarity and is written with an M, so 0.25 M is 0.25 mol/L. The letter M means molarity; the unit means moles per liter. Dividing by 1000 turns milliliters into liters before the molarity step, and forgetting it changes the answer by a factor of a thousand.