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Question: A solution contains 410.3 g of \(H_2SO_4\) per liter of solution at 20 ° C. If the density is 1.243g...

A solution contains 410.3 g of H2SO4H_2SO_4 per liter of solution at 20 ° C. If the density is 1.243g/mL, what will be its molarity and molality?

Explanation

Solution

Sulfuric acid or Sulphuric acid also known as oil of vitriol, is a mineral acid of the elements sulfur, oxygen and hydrogen with molecular formula H2SO4H_2SO_4. It is a colorless, odorless and viscous liquid that is soluble in water and is synthesized in reactions that are highly exothermic.
Molarity (M) is the amount of substance in a certain volume of solution. Molality is defined as the moles of a solute per kilogram of a solvent.

Complete Step-by-Step Solution:
Molarity is the ratio of the moles of solute to the total liters of solution. The solution includes both solute and solvent. Molarity is also known as molar concentration of a solution. The unit of molarity is M or mol/L. A 1M solution is said to be “one molar”.

So, molarity equation is given by:
M=Moles of soluteVolume of solution in litresM = \dfrac{{Moles\,of\,solute}}{{Volume\,of\,solution\,in\,litres}}

Molality is the ratio of the moles of solute to the kilogram of a solvent.
m=Moles solutekg solventm = \dfrac{{Moles\,solute}}{{kg\,solvent}}

For molarity:
Molecular mass of H2SO4H_2SO_4=98
Number of moles of H2SO4H_2SO_4= 410.398\dfrac{{410.3}}{98} = 4.186

Molarity of H2SO4 solution=No. of moles of H2SO4Volume of solution in litersMolarity\,of\,H_2SO_4\,solution=\dfrac{{No.\,of\,moles\,of\,H_2SO_4}}{{Volume\,of\,solution\,in\,liters}}

                                                         = $\dfrac{{4.186}}{1}$  
                                                         = $4.186M$

For Molality:
Mass of 1 liter H2SO4H_2SO_4solution = 1000 ×\times 1.243 = 1234g

Mass of water= (1243 - 410.3) = 832.7g
= 832.71000kg\dfrac{{832.7}}{{1000}}kg

Molality of solution=No. of moles of H2SO4Mass of water in kgMolality\, of\, solution = \dfrac{{No.\,of\,moles\,of\,H_2SO_4}}{{Mass\,of\,water\,in\,kg}}

                                        = $\dfrac{{4.186}}{{832.7}} \times 1000$  

                                          = $5.027m$

Hence the molarity will be 4.186 M and molality will be 5.027m

Note: Molarity and molality both are the measure of concentration.
Unit of molarity is (M) and the unit of molality is (m). Molarity is the ratio of moles to volume (in liters) and molality is the ratio of moles to mass (in kilogram).