Question

What is the molarity of a KOH solution with relative density 0.0028 and %w/w=40%? The molar mass of KOH is 56.1056 g/mol.

Answer 1

Hint: The molarity of the solution is also known as the concentration of the solution and is given as the no. of moles of solute present in per unit volume of the solution. The volume of the solution should always be considered in litres.

Complete Step By Step Answer:
The formula for the molarity of a solution is: $ Molarity = \dfrac{{mole{s_{solute}}(mol)}}{{Vo\operatorname{l} um{e_{solution}}(L)}} $
The units of Molarity are often given as $ mol/L $ . The information given to us in the question is; $ {\rho _{solution}} = 0.0028,\% w/{w_{KOH}} = 40\% ,M.{M_{KOH}} = 56.1056g/mol $
The relative density is the density of the solution relative to the density of the water, which is often taken as $ 1g/mL $ . The relative density can be given as: $ density = \dfrac{{{\rho _{solution}}}}{{{\rho _{water}}}} = \dfrac{{0.0028}}{1}g/mL = 0.0028g/mL $
In g/L the density of the solution $ = 2.8g/L $
Now, we are given that the %w/w of the solution is 40%, which means that 40g of solute is present in 100g of solution. Hence the mass of the solution can be considered as 100 grams. The volume of the solution can be found out by its density by using the formula: $ density = \dfrac{{mass}}{{volume}} $
 $ volum{e_{solution}} = \dfrac{{mas{s_{solution}}}}{{density}} = \dfrac{{100}}{{2.8}} = 35.7L $
The volume of the solution is now known. The no. of moles of solute i.e. KOH can be found out by the equation: $ moles = \dfrac{{mas{s_{solute}}}}{{M.{M_{solute}}}} = \dfrac{{40g}}{{56.1056g/mol}} = 0.713mol $
Now, substituting these values in the formula for finding the Molarity we can find the concentration of the solution in mol/L
 $ Molarity = \dfrac{{mole{s_{solute}}(mol)}}{{Vo\operatorname{l} um{e_{solution}}(L)}} = \dfrac{{0.713mol}}{{35.7L}} = 0.02mol/L $
Hence the concentration of the solution is 0.02 M.

Note:
Specific gravity is the ratio of the density of an item to the density of the reference material. Besides, the specific gravity can tell us if the object will sink or float in the reference material. The reference material is mostly water as it has a consistent density of 1 gram per cubic centimetre.