Molarity of a Salt Solution

Easy

Problem

5.84 g of sodium chloride (NaCl) is dissolved in water and the solution is diluted to a total volume of 0.500 L. Calculate the molarity of the solution (M(NaCl) = 58.44 g/mol).

Given

Mass of NaCl = 5.84 g
Molar mass of NaCl = 58.44 g/mol
Total solution volume = 0.500 L (NaCl dissolved and diluted to this mark).

Find

The molarity of the NaCl solution.

Principle

Molarity is defined as moles of solute per liter of solution. Converting a weighed mass to moles requires the molar mass, and the volume used must be the total volume of the finished solution, not just the water added.

Formula

M = \frac{n_{\text{solute}}}{V_{\text{solution}}}

mol = mass / molar mass; M = mol solute / L solution

Solution

Convert grams to moles: n(NaCl) = 5.84 g / 58.44 g/mol = 0.09993 mol, about 0.0999 mol.
Divide by the total solution volume: M = 0.09993 mol / 0.500 L = 0.19986 mol/L.
Round to three significant figures (the data have three): M = 0.200 M.

0.200 M NaCl

Unit check

Grams divided by g/mol gives mol, and mol divided by L gives mol/L, the unit of molarity. Significant figures follow the least precise input (three figures in 5.84 g and 0.500 L).

What this means physically

A 0.200 M solution contains 0.200 mol of NaCl per liter — roughly twice the concentration of a 0.100 M standard. This two-step pattern (grams → moles → molarity) is the standard route for preparing solutions of a target concentration.

Common mistake

Students often divide grams directly by liters, forgetting to convert grams to moles first. Molarity is moles per liter, not grams per liter — the molar mass step is essential.