Question

How many grams of $NaOH$ are dissolved in 500 ml of a solution having a concentration of 0.2M?

Answer 1

Hint: Molarity of a solution is defined as the number of moles of solute dissolved in one liter or 1000 ml of solution. It is represented as a concentration term and its unit of molarity is mol/ltr.

Complete step by step answer:
The molarity of the solution is given as 0.2 M and the volume of the solution is given as 500 ml. The formula of molarity is given as:

${\text{Molarity}} = \dfrac{{{\text{no of moles of solute}}}}{{{\text{volume of solution (in ml)}}}} \times 1000$ (1)

And the number of moles is equal to the ratio of the given mass to the molecular mass. mathematically it is written as:

\[{\text{No}}{\text{. of moles}} = \dfrac{{{\text{given mass}}}}{{{\text{molecular mass}}}}\]

On putting the above in equation (1), we get:

\[{\text{Molarity}} = \dfrac{{{\text{given mass}}}}{{{\text{molecular mass}} \times {\text{volume of solution (in ml)}}}} \times 1000\] (2)

The molecular mass of the sodium hydroxide is equal to the sum of the molecular mass of sodium, the molecular mass of oxygen, and the molecular mass of hydrogen. The molecular mass of sodium is 23 and the molecular mass of oxygen and hydrogen is 16 and 1 g respectively. Thus the molecular mass of sodium hydroxide =$23 + 16 + 1 = 40g$
On putting the value in equation (2), we get:

\[0.2 = \dfrac{{{\text{given mass}}}}{{40 \times 500}} \times 1000\]

\[ \Rightarrow 0.2 = \dfrac{{{\text{given mass}}}}{{40}} \times 2\]

\[ \Rightarrow 0.2 = \dfrac{{{\text{given mass}}}}{{20}}\]

\[ \Rightarrow 0.2 \times 20 = {\text{given mass}}\]

\[ \Rightarrow {\text{given mass = 4g}}\]

Hence the amount of sodium hydroxide dissolved in 500 ml of a solution having a 0.2 M concentration is 4 gram.

Note: The reactions for the process such as precipitation and neutralization, involve the concept of molarity and it is used in stoichiometric calculations for the same. Another concept involving the concentration is molality and it is defined as the one kilogram of solvent for every one liter of solution. Also, the molarity and molality affects the rate of reaction and are important in reactions involving aqueous solution.