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.
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 CO32-ions and 1 x 6.023 x 1023 CO32- 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.
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.
What is the mass in grams of a chlorine atom, Cl?
What is the mass in grams of a hydrogen chloride, HCl?
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
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.
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
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).
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