Question

Define molarity. Calculate the molarity of a solution containing $5g$ of $NaOH$ in $500ml$ of solution.

Answer 1

Hint: A mole of a solute is the amount of solute that contains Avogadro’s number of solute particles in it, now Molarity is defined as the number of moles of solute dissolved per liter of the solution, It is represented by the symbol $\left( M \right)$ and is calculated by knowing the molar mass and given mass of a species, alongside the volume of the entire solution.

Complete step-by-step answer:As already known, Molarity is defined as the number of moles of solute dissolved per liter of the solution
i.e. $Molarity(M) = \frac{{number\,of.moles.of\,solute}}{{volume\,of\,solution(L)}} \times 1000$
\[\therefore M = \frac{n}{{V(L)}} \times 1000\]
Unit of molarity is mol/liter
If the number of moles of solute remain constant, then molarity is inversely proportional to volume. It changes with change in volume.
i.e. $M \propto \frac{1}{V}$ (when n is constant)
$M \times V = cons\tan t$
$\therefore {M_1}{V_1} = {M_2}{V_2}$ (Molarity equation)
Given: Weight of $NaOH = 5g$
Molecular weight of $NaOH = (1 \times atomic\,\,mass\,\,of\,\,Na + 1 \times atomic\,\,mass\,\,of\,\,O + 1 \times atomic\,\,mass\,\,of\,\,H)$
$\begin{gathered}
 = (1 \times 23 + 1 \times 16 + 1 \times 1) \\
 = (23 + 16 + 1) \\
= 40g \\
\end{gathered} $ (Where atomic mass of $Na,O,H\,\,are\,\,23g,16g\,\,and\,\,1g)$
Volume of solution$ = 500ml$.
To calculate the molarity of $NaOH$solution.
Now, by using formula, \[Molarity(M) = \frac{{number\,\,of\,\,moles\,\,of\,\,NaOH}}{{volume\,\,of\,\,solution(ml)}}\]
\[\therefore Molarity(M) = \frac{{weight\,\,of\,\,NaOH \times 1000}}{{molecular\,\,weight\,\,of\,\,NaOH \times Volume\,\,of\,\,solution(ml)}}\]
By putting the value of weight of$NaOH$, molecular weight of $NaOH$ and volume of solution then,
\[Molarity\left( M \right) = \frac{{5 \times 1000}}{{40 \times 500}}\]
$ = 0.25$
Hence, molarity of $NaOH$solution$ = 0.25M$.

Note:Molarity depends upon temperature because volume of solution is temperature dependent. When a concentrated solution is diluted by adding more solvent, the number of moles of solute in the solution remains unchanged however the volume still changes.