Question

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

Answer 1

The concentration of the solution can be expressed in different units. Molarity is one of the measures of the concentration term. It is represented by $M$ . A concentration is said to be $1M$ when one mole of solute is dissolved in one liter of the solution.

Formula Used:
Molarity of solution, $M = \dfrac{n}{V}$
Where, $M$ is the molarity of the solution in which $n$ moles of solute are dissolved in $V$ liters of the solution.

Complete step by step answer:
First, we will start with the basic definition or meaning of molarity. It is defined as the ratio of the number of moles of solute to the volume of solution in liters. Now let’s go back to our question. First, we will understand and write the given quantities from the question. So, in the question, we have given that sodium hydroxide is dissolved in $500$ ml of solution and the concentration of the solution is given $0.2M$ . Now we need to calculate the amount of sodium hydroxide dissolved in the solution. So, let us consider that $x$ gram of sodium hydroxide is dissolved in the solution. The molar mass of sodium hydroxide is ${M_{NaOH}} = 23 + 16 + 1 = 40g/mol$ . Therefore, the number of moles of $NaOH$ will be calculated as $n = \dfrac{x}{{40}}$ . To find the amount $NaOH$ can be calculated by substituting the quantities $n = \dfrac{x}{{40}},V = 500ml = 0.5L$ in the formula $M = \dfrac{n}{V}$ .
So, $\Rightarrow 0.2 = \dfrac{x}{{40 \times 0.5}}$
$\Rightarrow x = 4g$
Therefore, we can conclude that $4g$ of $NaOH$ will dissolve in $500$ ml of a solution having molarity $0.2M$ .

Note:
The molarity of a solution is a temperature-dependent quantity because the molarity of a solution is based on the mass-volume relationship. Its unit is represented in moles per liter. Molality is also a concentration term but it is independent of temperature.