Question

What is the molarity of a solution containing 7 g of NaOH in 500 mL of NaOH solution?

Answer 1

In this problem we need to find the molarity of the NaOH solution. For that we need the no. of moles of NaOH in 7 g of solid NaOH and the volume of the solution. If we are given these two pieces of information, we can find the molarity.

Complete Step By Step Answer:
Molarity is defined as the no. of moles of solute, in here it is NaOH, present in a given volume of solution ( in litres) . Mathematically it can be given as:
$molarity = \dfrac{{mole{s_{solute}}}}{{Volum{e_{solution}}(L)}}$
The units of molarity is mol/L or also as ‘M’.
Remember that the volume given to us is in millilitres, but we need to convert it to Litres. Also, the number of moles of solute is not given to us, we’ll have to find that too. Therefore, to find the molarity we need to find
- The volume of the solution in Litres
- The no. of moles of NaOH (solid) dissolved in the solution.
To find the no. of moles of NaOH we will use the formula: $moles = \dfrac{{mass(g)}}{{Molar{\text{ }}Mass(g/mol)}}$
Consider the Molar Mass of NaOH to be 40 g/mol. This is the amount of NaOH in 1 mol of it.
Hence the no. of moles of NaOH $= \dfrac{7}{{40}} = 0.175mol$ of NaOH
The volume of the solution in Litres will be $= \dfrac{{500}}{{1000}}L = 0.5L$
The molarity of the solution, on substituting the values will be $= \dfrac{n}{V} = \dfrac{{0.175}}{{0.5}} = 0.35M$
On rounding off the final value, we get the molarity of the solution to be $= 0.4M$
Therefore, the molarity of the solution containing 7g of NaOH will be 0.4M.

Note:
The molarity includes the volume of the solution, and not just the solvent in litres. The volume of the solution is the sum of both solute and solvent present in it. Molality includes the use of Mass of solvent which can be given as:
$Molality = \dfrac{{mole{s_{solute}}}}{{mas{s_{solvent}}(kg)}}$