Calculating Molar Concentration

Molar concentration is the number of moles contained in one litre of a substance. The concentration of a solution is expressed in |\text {mol/L}.|

|C=\dfrac{n}{V}| 
where
|C| stands for molar concentration |\text {(mol/L or M)}|
|n| stands for the number of moles |\text {(mol)}|
|V| stands for the volume of the solution |\text {(L)}|

What is the molar concentration of a solution if |20\ \text {g}| of |CaCO_{3}| were dissolved in |500\ \text {mL}| of solution?

Here are the given values of the problem.
||\begin{align} m &= \text {20 g} &V &= \text {500 mL = 0.500 L} \\ M &= \text {100.09 g/mol} &C&= \text {?} \end{align}||
First the mass must be converted into moles.
||\begin{align} n= \dfrac{m}{M} \quad \Rightarrow \quad n &= \dfrac{\text {20 g}}{\text {100.09 g/mol}} \\ &= \text {0.2 mol} \end{align}||
It is then possible to determine the concentration of  |\text {mol/L}| using the formula.
||\begin{align} C =\dfrac{n}{V} \quad \Rightarrow \quad
C&=\dfrac {\text {0.2 mol}}{\text{0.5 L}} \\ &= \text {0.4 mol/L = 0.4 M} \end{align}||

In this video, we assume that adding the solute (NaCl) to the solvent (water) does not change the volume of the solution. In the first example, 250 mL of water corresponds to V, the volume of the solution. In the second example, 0.7 L of water corresponds to V, the volume of the solution.

When adding a solute to a solvent causes the volume of the solution to vary, the volume of the resulting solution must be carefully selected for concentration calculations.