Mole Concept and Molar Mass with Example Problems

Mole concept

While carrying out reaction we are often interested in knowing the number of atoms and molecules. Some times, we have to take the atoms or molecules of different reactants in a definite ratio.

Eg. Consider the following reaction

2 H₂ + O₂ + 2H₂O

In this reaction one molecule of oxygen reacts with two molecules of hydrogen. So it would be desirable to take the molecules of H2 and oxygen in the ratio 2:1, so that the reactants are completely consumed during the reaction. But atoms and molecules are so small in size that is not possible to count them individually.

In order to overcome these difficulties, the concept of mole was introduced. According to this concept number of particles of the substance is related to the mass of the substance.

Definition

The mole may be defined as the amount of the substance that contains as many specified elementary particles as the number of atoms in 12g of carbon - 12 isotope.

(i.e) one mole of an atom consists of Avogadro number of particles.

One mole    =   6.023 x 1023 particles

One mole of oxygen molecule  =   6.023 x x 10²³ oxygen molecules

One mole of oxygen atom       =       6.023 x x 10²³ oxygen atoms

One mole of ethanol       =       6.023 x x 10²³ ethanol molecules

In using the term mole for ionic substances, we mean the number of formula units of the substance. For example, a mole of sodium carbonate, Na₂CO₃ is a quantity containing 6.023 x 10²³ Na₂CO₃ units. But each

formula unit of Na₂CO₃ contains 2 x 6.023 x 10²³ Na⁺ ions and one CO₃^2-ions and 1 x 6.023 x 10²³ CO₃^2- ions.

When using the term mole, it is important to specify the formula of the unit to avoid any misunderstanding.

Eg. A mole of oxygen atom (with the formula O) contains 6.023 x 10²³ Oxygen atoms. A mole of oxygen molecule (formula O₂) contains 6.023 x 10²³ O2 molecules (i.e) 2 x 6.023 x 10²³ oxygen.

Molar mass

The molar mass of a substance is the mass of one mole of the substance. The mass and moles can be related by means of the formula.

Molar mass = Mass / mole

Eg. Carbon has a molar mass of exactly 12g/mol.

Problems

Solved Problems

What is the mass in grams of a chlorine atom, Cl?

What is the mass in grams of a hydrogen chloride, HCl?

Solution

The atomic weight of Cl is 35.5 amu, so the molar mass of Cl is g/mol. Dividing 35.5 g (per mole) by 6.023 x 10²³ gives the mass of one atom.

Mass of a Cl atom =      35.5 g/ 6.023 x 1023 = 5.90 x 10-23 g

The molecular weight of HCl equal to the atomic weight of H, plus the atomic weight of Cl, (ie) (1.01 + 35.5) amu = 36.5 amu. Therefore 1 mol of HCl contains 36.5 g HCl

Mass of an HCl molecule = 36.5 g / 6.02 x1023 = 6.06x10-23g

Problems For Practice

What is the mass in grams of a calcium atom, Ca?

What is mass in grams of an ethanol molecule, C₂H₅OH?

Calcualte the mass (in grams) of each of the following species. a. Na atom b. S atom c. CH₃Cl molecule d. Na₂SO₃ formula unit

Mole Calculations

To find the mass of one mole of substance, there are two important things to know.

1.    How much does a given number of moles of a substance weigh?

2.    How many moles of a given formula unit does a given mass of substance contain.

Both of them can be known by using dimensional analysis.

To illustrate, consider the conversion of grams of ethanol, C₂H₅OH, to moles of ethanol. The molar mass of ethanol is 46.1 g/mol, So, we write

1 mol C₂H₅OH = 46.1 g of C₂ H₅OH

Thus, the factor converting grams of ethanol to moles of ethanol is 1mol C₂H₅OH/46.1g C₂H₅OH. To covert moles of ethanol to grams of ethanol, we simply convert the conversion factor (46.1 g C₂H₅OH/1 mol C₂H₅OH).

Again, suppose you are going to prepare acetic acid from 10.0g of ethanol, C2H5OH. How many moles of C2H5OH is this? you convert 10.0g C2H5OH to moles C2H5OH by multiplying by the appropriate conversion factor.

10.0g C2H5 OH x          ( 1 mol C2H5OH/46.1 g C2H5OH ) = 0.217 mol C2H5 OH

Converting Moles of Substances to Grams Solved Problems

ZnI₂, can be prepared by the direct combination of elements. A chemist determines from the amounts of elements that 0.0654 mol ZnI₂ can be formed.

Solution

The molar mass of ZnI2 is 319 g/mol. (The formula weight is 319 amu, which is obtained by summing the atomic weight in the formula) Thus

0.0654 mol ZnI2    x (319 g ZnI2/ 1 mol ZnI2 ) =   20.9 gm ZnI2

Problems for Practice

H₂O₂ is a colourless liquid. A concentrated solution of it is used as a source of oxygen for Rocket propellant fuels. Dilute aqueous solutions are used as a bleach. Analysis of a solution shows that it contains 0.909 mol H₂O₂ in 1.00 L of solution. What is the mass of H₂O₂ in this volume of solution?.

Boric acid, H₃BO₃ is a mild antiseptic and is often used as an eye wash. A sample contains 0.543 mol H₃BO₃. What is the mass of boric acid in the sample?.

CS₂ is a colourless, highly inflammable liquid used in the manufacture of rayon and cellophane. A sample contains 0.0205 mol CS₂. Calculate the mass of CS₂ in the sample.

Converting Grams of Substances to Moles

In the preparation of lead(II)chromate PbCrO4, 45.6 g of lead(II)chromate is obtained as a precipitate. How many moles of PbCrO4 is this?

The molar mass of PbCrO4 is 323 g/mol (i.e) 1 mol PbCrO4 = 323 g PbCrO4

Therefore,

45.6 g PbCrO4 x (1 mol.PbCrO4 / 323 g PbCrO4) =    0.141 mol PbCrO4

Problems for Practice

Nitric acid, HNO₃ is a colourless, corrosive liquid used in the manufacture of Nitrogen fertilizers and explosives. In an experiment to develop new explosives for mining operations, a 28.5 g sample of HNO₃ was poured into a beaker. How many moles of HNO₃ are there in this sample of HNO₃?

Obtain the moles of substances in the following.

1.     3.43 g of C 

2.     76g C4 H10

3.     e. 2.57 g As g.

_4.        41.4 g N₂H₄

5.     7.05 g Br2

6.     35.4 g Li2 CO3

7.     7.83 g P4

_8.        153 g Al₂ (SO₄)₃

Calculation of the Number of Molecules in a Given Mass Solved Problem

How many molecules are there in a 3.46 g sample of hydrogen chloride, HCl?

Note: The number of molecules in a sample is related to moles of compound (1 mol HCl = 6.023 x 10²³ HCl molecules). Therefore if you first convert grams HCl to moles, then you can convert moles to number of molecules).

Solution

3.46g HClx ( 1molHCl/36.5g HCl ) x ( 6.023x1023 HClmolecules / 1molHCl) = 5.71 x 1022 HCl molecules

Problems for Practice

How many molecules are there in 56mg HCN?

Calculate the following

 Number of molecules in 43g NH3

 Number of atoms in 32.0 g Br₂

 Number of atoms in 7.46 g Li