C03 relative masses of atoms and molecules

Relative Masses of Atoms and MoleculesChapter 3

LEARNING OUTCOMES

Define relative atomic mass, Ar

Define relative molecular mass, Mr

Relative Atomic Mass

The masses of atoms and molecules are very small and it very hard for us to compare them or use them in calculations.

For e.g. the mass of a hydrogen atom is 0.000 000 000 000 000 000 000 0014 or (1.4 x 10-24)g and the mass of a carbon atom is 1.68 x 10-23 g.


Relative Atomic Mass Instead of using the true masses of atoms, scientists compare the masses of atoms with the mass of a hydrogen atom, which is assigned a mass of one unit.

If we take the mass of a hydrogen atom to be 1, then the mass of a carbon atom will be 12, since a carbon atom is 12 times as heavy as a hydrogen atom.


Relative Atomic Mass The mass of a carbon atom is

12 times as heavy as a hydrogen atom, so we say that the relative atomic mass of carbon is 12.

C

12 H atoms

The relative atomic mass of an element is the average mass of an atom of the element compared to the mass of 1/12 of the mass of a carbon-12 atom.

Hence we define:

Scientists prefer to use the carbon atom instead of the hydrogen atom as a standard unit, so if we take 1/12 of the mass of a carbon atom, we will still get 1 unit.


Relative Atomic MassRelative atomic mass Mass of one atom of the element

(Ar) Mass of of an atom of carbon-12

The symbol for Relative Atomic Mass is Ar

Relative atomic mass has no units.

The relative atomic mass of an element can be obtained from the mass number (nucleon number) of the element in the Periodic Table.

Examples : 2311Na, 56

26Fe Hence, Ar of Na = 23, Ar of Fe = 56


= 112

Quick check 11. Define the relative atomic mass of an element.

2. Using the Periodic Table, find the relative atomic mass of the following:Mg, Ca, Cl, O, S, Ne, Br.

3. What is the mass of a calcium atom compared to the mass of a helium atom?

4. How many hydrogen atoms have the same mass as one potassium atom?

5. How many oxygen atoms have the same mass as one bromine atom?

Solution


Solution to Quick check 1

1. The relative atomic mass of an element is the average mass of an atom of the element compared to the mass of 1/12 of a carbon-12 atom.

2. Ar: Mg=24, Ca=40, Cl=35.5, O=16, S=32, Ne=20, Br=80.

3. Mass of a Ca atom =10 x Mass of a He atom

4. 39 hydrogen atoms

5. 5 oxygen atoms

Return


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Relative Molecular Mass The picture shows the mass of a molecule of water compared to the mass of hydrogen atoms.

It shows that one molecule of water is 18 times as heavy as one hydrogen atom.

Therefore, the relative molecular mass of water is 18.


99

Relative Molecular Mass

The relative molecular mass of a substance is the average mass of one molecule of the substance compared to the mass of 1/12 of a carbon-12 atom.

If we use the mass of a carbon-12 atom as the standard unit of comparison, then the relative molecular mass of a substance is defined as:


Relative molecular mass Mass of one molecule of a substance

(Mr) Mass of of a carbon-12 atom= 1

12

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Relative Molecular Mass The symbol for Relative Molecular Mass is Mr

The relative molecular mass of a molecule can be found by adding up the relative atomic masses of all the atoms present in the molecule.

E.g. Mr of water, H2O = Mass of 2 H atoms + mass of 1 O atom = 2 x 1 + 16 = 18


1111

Relative Formula Mass Ionic compounds (e.g. sodium chloride) are not made up of single molecules; instead they are made up of a crystal lattice consisting of many oppositely charged ions. Hence, instead of calculating the relative molecular mass of an ionic compound, we calculate the mass based on its formula (formula mass).

We can take the relative formula mass as equivalent to the relative molecular mass in our calculations.


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1. Find the relative molecular mass of carbon dioxide, CO2.

Mr of CO2 = 12 + 16 x 2 = 44

2. Find the relative molecular mass (formula mass) of copper(II) nitrate, Cu(NO3)2.

Mr of Cu(NO3)2 = 64 + (14 + 16x3 )x2 = 64 + 62x2 = 188

3. Find the relative molecular mass (formula mass) of ammonium sulphate, (NH4)2SO4.

Mr of (NH4)2SO4 = (14 + 1x4)x2 + 32 + 16x4 = 36 + 32 + 64 = 132


Finding Relative Molecular MassWorked examples

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Quick check 2

(a) Magnesium sulphate, MgSO4

(b) Calcium nitrate, Ca(NO3)2

(c) Ammonium carbonate, (NH4)2CO3

(d) Benzoic acid, C7H6O2

(e) Hydrated sodium carbonate, Na2CO3.10H2O

Solution


Find the relative molecular mass (or formula mass) of each of the following:

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Solution to Quick check 2

a) Mr of MgSO4 = 24 + 32 + 16x4 = 120

b) Mr of Ca(NO3)2 = 40 + 2(14 + 16x3) = 164

c) Mr of (NH4)2CO3 = 2(14+4) + 12 + 16x3 = 96

d) Mr of C7H6O2 = 12x7 + 6 + 16x2 = 122

e) Mr of Na2CO3.10H2O = 23x2 + 12 + 16x3 + 10(2x1 + 16) = 286

Return


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Percentage compositionWorked example 1What is the percentage composition of calcium carbonate, CaCO3?

Solution% of Ca = [Ca] x 100% = 40 x 100% [CaCO3] [40 + 12 + 16x3] = 40%

% of C = [ C ] x 100% = 12 x 100% [CaCO3] 100 = 12%

% of O = [ O3 ] x 100% = 16x3 x 100% [CaCO3] 100

= 48% Check %Ca + %C + %O = 40 + 12 + 48 = 100%


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Percentage compositionWorked example 2What is the percentage of sodium in sodium carbonate, Na2CO3?Solution

% of Na = [Na2] x 100% = 23x2 x 100% [Na2CO3] [23x2 + 12 + 16x3] = 43.4%

Worked example 3Find the mass of oxygen in 90 g of water.Solution

Mr of H2O = 1x2 + 16 = 18Mass of oxygen = 16 x 90 g = 80 g 18

Worked example 4What mass of magnesium oxide can be made from 6 g of magnesium?Solution

Mr of MgO = 24 + 16 = 40 Mass of MgO = 6 x 40 g = 10 g 24


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Percentage yieldThe percentage yield of a product is given by the formula:Percentage yield = Actual mass of product obtained x 100%

Theoretical mass of product obtained

Worked example 1

In an experiment to prepare magnesium sulphate, 2.4 g of magnesium was dissolved completely in dilute sulphuric acid. On crystallisation, 22.0 g of magnesium sulphate crystals, MgSO4.7H2O, were obtained. What is the percentage yield?


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Percentage yield

Percentage yield = Actual mass of product obtained x 100% Theoretical mass of product obtained

Write the chemical equation: Mg + H2SO4 MgSO4 + H2

Number of mole of Mg reacted = 2.4 = 0.1 mol 24

From equation, 1 mol of Mg 1 mol of MgSO4

Therefore, 0.1 mol of Mg 0.1 mol of MgSO4.7H2O

Mass of MgSO4.7H2O produced = 0.1 mol x 246 g/mol = 24.6 g

= 22.0 x 100 % 24.6

= 89.4 %

Solution


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Percentage purity The percentage purity tells us how pure a prepared product

is compared to the pure form of the substance. For example, the percentage purity of a gold bar may be

given as 99.99 %.


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Percentage purityWorked example 2

On analysis, 5.00 g of a sample of marble (calcium carbonate) was found to contain only 4.26 g of pure calcium carbonate. What is the percentage purity of the marble?

Percentage purity = 4.26 x 100 % 5.00

= 85.2 %

Solution


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Quick check 31. Find the percentage composition of each element in sulphuric acid, H2SO4.

2. Find the percentage of nitrogen in calcium nitrate, Ca(NO3)2.

3. Find the mass of calcium in 250 g of calcium carbonate, CaCO3.

4. What mass of iron can be obtained from 320 g of iron(III) oxide, Fe2O3?

5. 24 g of hydrogen combines with 192 g of oxygen to form water. What mass of hydrogen will combine with 24 g of oxygen?

6. In the Haber process to manufacture ammonia, it was reported that in a certain factory, 2.8 tonnes of nitrogen gas produced 0.80 tonne of ammonia. What is the percentage yield of ammonia? The equation for the Haber process is: N2(g) + 3H2(g) 2NH3(g) Solution


2222

Solution to Quick check 31. % composition of H2SO4 :

H =2.04 %, S =32.7 %, O = 65.3 %2. % of nitrogen in Ca(NO3)2 = 17.1 %

3. Mass of calcium = 40 x 250 = 100 g 100

4. Mass of iron = 112 x 320= 224 g 160

5. Mass of hydrogen = 24 x 24 = 3 g 192

6. Percentage yield = 0.8 x 100 % 3.4

= 23.5 % Return


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http://www.ch.cam.ac.uk/magnus/MolWeight.html

To learn more about Relative Atomic and Molecular Mass, click on the link below!


ReferencesReferences

Chemistry for CSEC Examinations by Mike Taylor and Tania Chung

Longman Chemistry for CSEC by Jim Clark and Ray Oliver

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C03 relative masses of atoms and molecules