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Calculate the Molar Concentration of a Solution

Concept: A solution is made up of one or many solutes dissolved in a solvent. To know how much solute is present in a solvent we use the term molar concentration. Molar concentration means the number of moles of solute present is one litre of solution and we all know number of moles is

equal to (given mass of solute)/( molar mass of solute).

Therefore molar concentration is (no. of moles of solute)/(volume of solution).

Applications of Molar Concentration of a Solution: Numerical Problems

1) What is the molar concentration of a solution containing 3 moles of sugar in 5 litres of sugar solution?

Ans: Molar concentration = moles of solute (sugar) / Volume of solution in litres

= 3 moles/ 5 l

= 0.6 M

2) If 2.75 moles of KOH is dissolved in 4 litres of water what is the molar concentration of the resulting solution?

Ans: Assuming the volume of the solution to be 4 l we can write

Molar concentration of KOH = No. of moles of KOH / Volume of solution in litres

= 2.75moles/4l

= 0.6875 M

These were numericals based on a direct relationship between number of moles of solute and volume of solution in litres.

Type II: Given the mass of solute and volume of solvent, how can we express the molar concentration of solution?

Examples:

1) If a mass of 0.2g NaCl is dissolved in 100ml of water what is the molar concentration of the resulting solution?

Ans: Molar concentration = No. of moles of solute /

Volume of solution in litres

Mass of 1 mole NaCl = molecular or formula mass of NaCl

= 23+35.45= 58.45

We know no. of moles= given mass /

Molecular mass

= 2/ 58.45 moles of solute

= 0.034 moles

Now 0.034 moles of NaCl is dissolved in 100 ml of water

1000 ml = 1 litre

100 ml = 100/1000=0.1litre

Assuming total volume of solution = 0.1 litre

We can express the molar concentration as 0.034 moles / 0.1 litre

= 0.34 moles/ litre

= 0.34 M

When the volume of solvent is not equal to the volume of solution

2) Calculate the molar concentration of a solution of sodium thiosulphate having 474 g of sodium thuosulphate in a given volume of solvent. Given: density of thiosulphate solution = 1.25g/ml

Ans: Density = mass/ volume

Volume = mass/ density

=474/1.25 ml

= 379.2ml

Molarity = moles of solute/

Volume of solution in litres

Moles of Na2S2O3 = (23X2) + (32X2) + (16X3)

= 46 + 64 + 48

= 158

Molarity = (158/379.2) X 1000

= 4.166 X 102 M

3) 2.68 g of copper sulphate penta hydrate is dissolved in water and the solution is made to 200 cc in a volumetric flask. Calculate the molarity.

Ans: Moles of CuSO4. 5H2O = 63.54 + 32 + (16X4) + (5X18)

= 63.54 + 32 + 64 + 90

= 249.54g

No. of moles = given mass /

Molecular mass

= 2. 68g/249.54g

= 0.0107 moles

Volume = 200cc = 200 ml

Molarity = moles of solute/

Volume in litres of solution

= (.0107/ 200) X 1000

= 5.35X10-5 X103

= 5.35 X 10-2 M

Type III: To Calculate the Moles from Molarity.

1) Find the number of moles of HCl in 250ml of 0.01 molar of HCl solution.

Ans: Given: Molar concentration of Hcl solution = 0.01M

So in 1000ml no. of moles of HCl = 0.01 M

So in 250 ml no. of moles of HCl = ?

= (250 X 0.01)/1000

= 2.5 X 10-3 moles.

2) Calculate the number of moles of KNO3 in 50ml of 0.001 M solution.

Ans: Given: Molar concentration of KNO3 = 0.001M

So in 1000ml number of moles of KNO3 = 0.001 M

So in 50 ml number of moles of KNO3 =?

= (50X0.001)/1000

= 5.0 X 10-5 moles

Type IV: Diluted Solution

1) 150 ml of water is added to 200ml of 0.02 M HCl. Calculate the molar concentration of the resulting solution.

Ans: First we calculate number of moles of HCl in 200ml solution.

In 1000ml of solution no. of moles of HCl is 0.02 M

In 200ml of solution no. of moles of HCl is?

= [0.02 X 200 ]/ 1000

= 4 X10-3

Total volume of water and HCl = 150 + 200 ml

= 350ml

No. of moles of HCl in 350ml = 4 X10-3

Therefore molar concentration of 350 ml solution = [4 X 10-3 ]/

[350 X 10-3]

= 0.0114 M

2) What is the molar concentration of pure water?

Ans: Molar concentration = No. of moles /

Volume of solution in litres

Density of water = 1g/ml

= 1g/10-3l

Mass of 1 litre of water = mass of 1000ml of water

= volume X density

= 1000ml X 1g/ml

= 1000g

Moles of water = 1000g/18

=55.55moles

Molarity of water = 55.55 M

Type V: Relationship between Molar Concentration and Molal Concentration.

Molality= moles of solute / Mass of solvent in kg.

Please express your views of this topic oxidation of alcohols to aldehydes by commenting on article.

1)Molality of a solution of ethyl alcohol in water is 1.55m. Calculate how many grams of ethyl alcohol is dissolved in 2 kg of water. Hence calculate the molarity of the solution.

Ans: Molality of ethyl alcohol is 1.55m

i.e. 1.55 moles in 1000g

Moles of ethyl alcohol = (12X2) + 5 + 16 +1

= 46

Therefore 1 mole of ethyl alcohol = 46

So 1.55moles of ethyl alcohol = 1.55 X 46

= 71.3 g

71.3 g is present in 1 kg water

? g is present in 2 kg water

= 71.3 X 2= 142.6 g

Density of water = 1g/ml=1kg/l

2 kg of water have volume 2l

No. of moles =142.6/46 = 3.1 mole

Molarity = No. of moles/

Volume

= 3.1/2 = 1.55M



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