Expressing Concentration of Solutions

Solution is a homogeneous mixture (homogeneous mixture is a mixture where throughout the solution the composition is uniform) of two or more chemically non-reacting substances whose composition can be varied within certain limits. Every solution is made up of solvent and one or more solutes. Any of the phases of matter (solid, liquid, gas) can be dissolved in other phases.

The component of a solution present in a large quantity is known as a solvent. One or more components present in the solution other than the solvent are called solutes.

A solution containing only one solute dissolved in a solvent is called a binary solution. Solutions in water are called aqueous solutions and the solution in which water is not present is called a non-aqueous solution. The solvents in nonaqueous solutions are benzene, carbon tetra chloride, ether, DMSO, etc.

Importance of Solution

Solutions are most important in everyday life. solutions can be a mixture of solid, liquid, or gaseous forms. solid, liquid, and gaseous solution chemistry is important because many chemical reactions occur in them. For example, the water we drink, and the air we breathe can consist of chemicals. The use of solutions can be understood by Water as the solvent used in making food, soaps, detergents, textiles, etc.  Alloy are solid solutions that are used in the manufacturing of aerospace, cars, and other vehicles as well as some utensils. For example – brass is a homogeneous mixture of copper and zinc. Fluoride ion is most important for teeth to prevent tooth decay. 1 part per million fluoride ions can prevent tooth decay and a 1.5ppm fluoride ion concentration can cause the teeth to become mottled and a higher concentration of fluoride ion can work as toxicity.

Expressing concentration of solutions

The concentration of a solution is the amount of the solute dissolved in a known amount of solvent. The concentration of the solution is expressed in various ways –

Percentage Strength

The percentage of a solution is usually expressed either as ‘percentage by mass’ or ‘percentage by volume’ or ‘mass by volume’

• Mass percentage (w/w): Mass percentage of any solution is useful to get an idea about the percentage of the mass of solute and solvent in a solution. For example – if a solution is described by 10% glucose in water by mass, it means that 10g glucose is dissolved in 90g of water resulting in a 100g solution.

Mass % of component = {(Mass of the component in the solution)/ (total mass of the solution)} × 100

• Volume percentage (v/v): For Example, 10%  (v/v) ethanol solution in water means that 10mL of ethanol is dissolved in water such that the total volume of the solution is 100mL.

Volume % of a component = [Volume of the component/Total Volume of the solution] ×100

• Mass by volume percentage (w/v) 

Mass by Volume % of a component = [Mass of the component/Total volume of the solution]× 100

Let us understand percentage strength with an example as follows

Example: A solution is prepared by adding 2g of substance A to 18gm of water. Calculate the mass percent of the solute.

Solution:

Mass of solution =( 2 + 18 ) = 20g

Mass percent of the solute =  [(Mass of the solute) / (Mass of solution)]  ×  100

                                             = [2g /20g] × 100  = 10%

Mole fraction

The mole fraction of any component in the solution is equal to the number of moles of that component divided by the total number of moles of all the components. The fraction obtained by dividing the number of moles of a component by the total number of moles of all the component present in the solution is called the Mole fraction.

Mole fraction of a component = [(Number of moles of the component) / (Total number of moles of all the components)]

For example: In a binary mixture, if the number of moles of A and b is n1 and n2 respectively, the mole fraction of A and B will be –

Mole fraction of A,   X1 = {(n1) / (n1 + n2)}

Mole fraction of B , X2 = {(n2) / (n1 + n2)}

Thus, the Mole fraction of a constitution is the fraction obtained by dividing the number of moles of that constant by the total number of moles of all the constituents present in the solution. It may be noted that the mole fraction is a dimensionless quantity. It has no unit. And the sum of mole fraction of component is equal to 1 i.e.

Sum of mole fraction of component is equal to 1 i.e.  x1 + x2 = 1

Strength

The strength of the solution is defined as the amount of solute in grams present in one liter  (one cubic decimeter) of the solution, and hence is expressed in g/liter or g/cubic decimeter. Its unit is g/L or g/cubic decimeter. The formula for calculation of strength may be written as : 

Strength of a solution (g/L or g/cubic decimeter) = [(Mass of solute in grams) / (volume of solution)]

Let us understand strength with an example as follows

Example: Calculate the strength of HCl solution if the molarity of HCl solution is 2mol/L

Solution:

Strength of HCl solution = Molarity of HCl × Molecular weight of HCl           (Molecular wt. of HCl = 36.5g/mol)

                                       = 2mol/L × 36.5g/mol  

                                       = 73.0g/L

Molarity

Molarity of a solution is defined as the amount of solute dissolved per liter (or per cubic decimeter) of solution. It is denoted by ‘M’. i.e. Molarity is the number of moles of the solute dissolved in one liter of solution. Its unit is mol/L or M.

Molarity = [(moles of the solute) / (volume of solution in liters)]

Moles of solute can be calculated as:

Moles   = [(mass of the solute) / (molar mass of the solute)]

Molarity can be calculated from the strength as

Molarity = [(Strength in grams per liter) / (Molar mass of solute in g/mole)]

Let us understand molarity with an example as follows:

Example: 27.25 gm of calcium chloride, dissolved in 250 mL of solution. Find the molarity of chloride ions in this solution.

Solution:

Molarity of chloride ions = 2 × Molarity of Calcium chloride

Given weight of Calcium Chloride = 27.25 gm , Molecular weight of calcium chloride = 111 g/mol , volume of solution = 250 mL

Molarity of Calcium chloride solution = [(Given wt. / Molecular weight) × (1000/volume of solution in mL)]

                                                           =[(27.25 gm/111 g/mol) × (1000/250 mL)]  = 1 mol/L

Molarity of chloride ions = 2 × 1 mol/L = 2 mol/L

Molality

Molality of a solution is defined as the number of moles of the solute dissolved in 1000 grams of the solvent. It is denoted by ‘m’. Units of molality are m or mol/kg. It is independent of temperature as it is a mass/mass relationship.

Molality =[(Number of moles of solute) / (Mass of solvent in kilogram)]

Molarity = [(Number of moles of solute) / (Mass of solvent in grams)] × 1000 

Let us understand molality with an example as follows:

Example: Calculate the molality of 2.5 gm ethanoic acid in 75gm of benzene.

Solution:

Given wt. (Mass of solute)of ethanoic acid = 2.5 gm, Molecular wt. of ethanoic acid = 60gm, Mass of solvent (benzene)= 75gm

The molality of ethanoic acid in benzene (m) = [(Given wt./Molecular wt. of ethanoic acid) × (1000/Mass of solvent)]

                                                                  = [(2.5 gm/60 g/mol) × (1000/75gm)] = 0.556 mol/kg

Normality

Normality of a solution is defined as the number of grams equivalents of the solute dissolved per liter ( or one cubic decimeter) of the given solution. It is denoted by ‘N’. Its unit is eq/L or N or meq/L

Normality = [(Number of gram equivalent of solute ) /  (Volume of  solution in liter)]

The number of grams equivalent to the solute is calculated as follows:

Number of grams equivalent = [(Mass of solute in grams) / Equivalent mass of the solute)]

The equivalent masses of acids, bases, and salts are calculated as follows

Equivalent mass of an acid = [(Molar mass of the acid ) / (Basicity)]

Equivalent mass of a base = [(Molar mass of the base) / (Acidity)]

Equivalent mass of a salt = [( Molar mass of the salt) / (Total positive valency of metal atoms)]

Basicity is the number of displaceable hydronium ions present in one molecule of acid. Acidity is the number of displaceable hydroxide ions present in one molecule of the base.

Gram equivalent is equal to the mass in grams equal to the equivalent weight (Equivalent weight refers to the mass of one equivalent of any material that is to be taken). Grams equivalent is the mass of an equivalent in the units of a gram. unit of measurement of gram equivalent is Grams. If the mass of any compound is given in grams then the given mass containing gram equivalent is equal to the no. of moles multiplied by valency.

Relation of gram equivalent with moles

Gram equivalent = a × no. of moles; (a can be valency for element, acidity for base and basicity for acid)

No. of moles = [Given wt. / Molecular wt.]

Example: Calculate normality of NaOH solution containing 5g of NaOH in 450 mL of solution.

Solution:

Normality = [(Number of gram equivalent of solute ) /  (Volume of  solution in liter)]

Number of grams equivalent = [(Mass of solute in grams) / Equivalent mass of the solute)]

Equivalent mass of a base = [(Molar mass of the base) / (Acidity)]

Molar mass of NaOH = 23 +16+1 = 40  ,    Acidity = 1 (as no. of displaceable hydroxide ion present in one molecule of base)

Equivalent mass of a base =  [( 40) / (1)] = 40

Mass of solute = 5g ;                     Number of grams equivalent = [(5)/(40)] = 0.125geq or eq

Volume of solution = 450mL ;       Normality of NaOH solution = [(0.125geq) / (1000/450mL)] = 0.27geq/L or eq/L

Difference between Molarity and Normality

	Molarity	Normality
1.	Molarity is the number of moles of solute dissolved present in per liter of the solution	Normality of a solution is the number of grams equivalent to the solute dissolved in 1L of a given solution
2.	The unit of measurement is mol/L	The unit of measurement is eq/L or meq/L
3.	Molarity is dependent on Temperature. As temperature changes can change the molarity of a solution by increasing the volume.	Normality is temperature independent. Normality has no effect on the normality of the solution.
4.	Molarity of a solution does not depend on the solute undergoing a reaction.	Normality of a solution depends on the solute undergoing a reaction.
5.	Symbol that represents Mortality is M.	Symbol that represents Normality is N.
6.	Molarity of a solution depends on the temperature, Volume, Addition of more solute, and the solubility of a solute.	Normality of a solution depends on the reactive species that are present in that solution.

Parts per million (ppm)

Mass of solute present in one million parts by mass of the solution is called parts per million. When a solute is present in trace quantities it is convenient to express concentration in parts per million (ppm). The mass of the solute present in one million parts by mass of the solution is called parts per million. It has no unit.

ppm = [(Number of parts of the component) / (Total number of parts of all components of the solution )]  × 1000000

Note: Saturated solution, a solution in which no more solute can be dissolved at the same temperature and pressure is called a saturated solution. 

Sample Problems based on Solutions

Problem 1: A solution is prepared by adding 2g of substance A to 20g of water. Calculate the mass percent of the solute.

Solution:

Mass of solution (solute + solvent) = 2 + 20g = 22g

Mass percent of the solute = [(Mass of the solute) / (Mass of solution)]  ×  100

                                          = 2 / 22 × 100 = 9.09%

Problem 2: A solution of Oxalic acid, is prepared by dissolving 0.63g of the acid in 250 cubic centimeters of the solution. Calculate the Normality of the solution.

Solution:

The molar mass of oxalic acid = 126 g/mol

Equivalent mass of oxalic acid = [(Molar mass of oxalic acid) / (Basicity)] = 126/2 = 63 equivalent

Grams equivalents = [(Mass in g) / (equivalent mass)] = 0.63g / 63equivalent  = 0.01 g equivalent

Normality of the solution = [(Grams equivalents of the solute) / ( Volume of the solution in L)]

                                        = 0.01gequivalent/0.250L = 0.04 geq/L

Problem 3: The density of the 3M solution of NaCl is 1.25 g/mL. Calculate the molality of the solution.

Solution:

Molality = [(Moles of the solute) / (Mass of the solvent in kg)]

3M NaCl solution means that 3 moles of NaCl are present in 1L of the solution 

Mass of 1L, i.e. 1000mL of the solution = Volume×Density = 1000mL×1.25g/mL = 1250g

Mass of 3 moles of solute (NaCl) = 3 mol × 58.5 g/mol = 175.5 g , Mass of solvent = 1250 – 175.5 = 1074.5g = 1.0745kg

Molality of the solution = [3mol/1.0745kg] = 2.79 mol/kg = 2.79m

Problem 4: Calculate the molarity of NaOH in the solution prepared by dissolving its 4g in enough water to form 250mL of the solution.

Solution:

The molar mass of NaOH = 40g/mol, Given wt. = 4g

Moles of the solute (NaOH) = 4g / 40 g/mol = 0.1 mol

Volume of solution = 250 mL = 0.25L

Molarity of the solution =  [(moles of the solute) / (volume of solution in liters)] = [0.1 mol/ 0.25L] = 0.4mol/L

Problem 5: How many grams of NaOH should be dissolved to make 100 centimeter cubic of 0.15M NaOH solution?

Solution: 

1000 cubic centimeter of 0.15M NaOH contain NaOH = 0.15 mole

100 cubic centimeter of 0.15M NaOH contain NaOH = 0.15/1000 × 100                  (Molar mass NaOH = 40g/mol)

                                                                                   = 0.015 mole 

                                                                                   = 0.015 × 40g = 0.6g

Problem 6: Calculate the mole fraction of benzene in a solution containing 30% by mass in carbon tetra chloride.

Solution:

30% of benzene in carbon tetrachloride by mass means that the solution contains 30g of benzene in 100gm of solution.

Mass of benzene = 30g , Mass of carbon tetrachloride = (100-30)g = 70g , Molar mass of benzene = 78g/mol , 

Molar mass of carbon tetrachloride = ( 12 + 4 × 35.5 ) g/mol = 154 g/mol

No. of moles of benzene ( solute) , x2 =[(30g)/(78g/mol)]= 0.385mol

No. of moles of tetra chloride (solvent), x1 =[(70g)/(154g/mol)] = 0.454 mol

Mole fraction of benzene = [( moles of benzene)/ (total moles in the solution)]

                                       = [(0.385) /( 0.385 + 0.454)] = 0.459 

And sum of mole fraction of component is equal to 1 i.e. x1 + x2 = 1

Mole fraction of carbon tetrachloride = 1-0.459 = 0.541

FAQs based on Concentration of Solutions

Question 1: What do you mean by the saturated and unsaturated solution?

Answer: 

• Saturated solution: A solution in which no more solute can be dissolved at the same temperature and pressure is called a saturated solution. 
• Unsaturated solution: A solution in which more solute can be dissolved at the same temperature and pressure is called an unsaturated solution.  

Question 2: What is a type of solution if the solute is gas and the solvent is solid? Give one example. 

Answer:

When gas is solute and solid is solvent, it is a solid solution. Example – Solution of hydrogen in palladium.

Question 3: What is a type of solution if Liquid acts as solute and gas as solvent? Give one example. 

Answer:

When liquid acts as solute and gas as a solvent, it is the gaseous solution.  Example – Chloroform mixed with nitrogen gas.