Question

A solution of NaOH (molar mass 40g/mol) was prepared by dissolving 1.6g of NaOH in $500c{{m}^{3}}$ water. Calculate the molarity of the NaOH solution.

Answer 1

Hint: The concentration of solution which describes the composition of the solution either qualitatively or quantitatively. To describe the concentration of solution quantitatively more methods are available. There are mass percentage, volume percentage, ppm, mole fraction, normality, molarity, and molality.

Complete step by step solution:
 Molarity (M): it is defined as the number of moles of solute dissolved in one liter of solution. The value of molarity expressed in moles/liter which represents the concentration of a solution. The molarity of the solution can be calculated by using the below formula,
$Molarity(M)=\dfrac{n}{V(ml)}X1000$
Where n = moles of solute
V = volume of solution in ml.
In the given problem, solute = NaOH and the solution is water.
Let's calculate the number of moles of NaOH, ${{n}_{NaOH}}=\dfrac{weight\text{ }of\text{ }NaOH}{molar\text{ }mass\text{ }of\text{ }NaOH}$
Weight of NaOH (given) = 1.6 g
Molar mass of NaO = 40 g/mole
Substitute the values in the above formula in a number of moles of NaOH,
${{n}_{NaOH}}=\dfrac{weight\text{ }of\text{ }NaOH}{molar\text{ }mass\text{ }of\text{ }NaOH}=\dfrac{1.6g}{40g/mol}=0.04moles$
Given volume of solution = $500c{{m}^{3}}$ = volume of water = 500 mL
Substitute the number of moles of NaOH and volume of water in the above molarity formula,
Then, $M=\dfrac{0.04moles}{500mL}X1000=0.08moles/L$

Therefore, the molarity of NaOH = 0.08M.

Note: The volume of the solution may change with increasing or decreasing temperature of the solution when the moles of solute are constant. At lower concentrations with temperature independent then molarity and molality values will be equal.