FORMULAE, STOICHIOMETRY AND MOLE CONCEPT

FORMULAE, STOICHIOMETRY AND MOLE CONCEPT

By the end of this chapter, you should be able to:

• Understand the concepts of relative atomic mass and relative molecular mass.
• Analyze the relationship between the number of moles and the number of particles.
• Analyze the relationship between the number of moles of a substance and its mass.
• Analyze the relationship between the number of moles of a gas and its volume.
• Synthesize chemical formulae
• Interpret chemical equations
• Practice scientific attitudes and values investigating matter.

Keywords

• Relative atomic mass
• Relative formula mass
• Moles
• Molar gas volume
• Empirical formula
• Molecular formula

Competency: you will be able to use formulae and equations to determine quantities of matter.

Introduction

An equation for a reaction provides quantitative data relating to reactants and products involved. So, it is possible to relate the weights and volumes of the substances taking part in the chemical change. A reaction involves the interaction between a specific number of reactant molecules, moles or volumes and also an integral number of product species. There is always a simple relationship between the masses, the moles and the volumes of reactants and products. The methods of analyzing and measuring of reactants and products at the present time, have become more advanced in terms of precision and variety. Humans have become dependent on them in all the fields of life including the environment, food, health, agriculture, industry and others. The importance of measurement in chemistry is due to the fact that it provides us with necessary information and quantitative data to allow us to use the required procedures and the appropriate practices.

In this chapter you will learn how to use relationships between chemical reactions molecules to determine quantities of matter.

1. Relative atomic mass and relative molecular mass.

Relative atomic mass

The mass of a single atom is so tiny that it would be impossible to use it in calculations. To solve this problem, we use a much simpler way of thinking about the masses of atoms. Instead of working with real masses of atoms, we in stead focus on the relative masses of atoms of elements. We call these relative atomic masses.

We use the atom of carbon (C) as the standard atom. We give carbon the mass of 12 because it has 6 protons and 6 neutrons. Then we compare the masses of all other elements with the mass of carbon-12 to obtain their relative masses.

The relative atomic mass (A) of an element is the mass of one atom of that element relative to the mass of carbon-12.

Consider figure 3.1, you will notice that the mass of magnesium relative to the mass of carbon-12 is 24.

The relative atomic mass of an element is always equal or very similar to the mass number of the element. However, unlike the mass number, it caters for any isotopes of the element. In activity 3.1, you will explore the relative atomic masses of different elements.

Figure 3.1: Relating the mass of carbon -12 and the mass of magnesium1

Activity 3.1 Writing the relative atomic masses of the first 20 elements.

What you need

1. In your groups, study the periodic table and note the relative atomic masses of the first 20 elements.
2. Using the periodic table, calculate the mass numbers of the different elements basing on proton and nuclear numbers.

Discussion

1. Tabulate your findings showing the element, symbol, mass number and relative atomic mass.
2. How do the relative numbers compare with the relative atomic numbers?
3. Why do the relative atomic masses have no units?
4. What can you table with the rest of the class by pinning it in the classroom.

Relative formula mass

You normally use different substances but many of them are not elements. Indeed, the majority of substances used in everyday life are actually compounds. How can we fine the relative masses of elements to work out the relative formula masses of the compounds. This is true regardless of whether the substances are made up of molecules or a collection of ions.

The relative formula mass of a substance is the relative atomic masses of all the formula.

It is often just called formula mass. In the activity, you will calculate the formula masses of different compounds.

Worked example 3.1 Calculating formula masses of different substances.

Calculate the formula mass of water.

Solution

The formula of water is H2O and so the relative formula mass is the sum of the relative atomic mass of two hydrogen atoms (2×1) and one oxygen atom (16) which up to 18.

Exercise 3.1

Calculate the relative formula mass of the following compounds.

1. Ammonium chloride (NH4CL)
2. Calcium carbonate (CaCO3)
3. Magnesium nitrate (Mg(NO3 )3
4. Sulphuric acid (H2SO4)
5. Lead (ii) Hydroxide (Pb(OH)2)

(C=12, S=32, PB=205, H=1, O=16, Mg =24, N=14, Ca =40, C =35.5)

2. The mole

Relative atomic masses and relative formula masses are useful. However, they are bulky to use in comparing different substances. Amounts of substances are often measured in moles.  This makes it much easier to work out how much of a substance is required in a reaction. In figure 3.2, the basket of oranges contains the same number of fruits as a basket of mangoes. However, the two baskets have different weights because the weight of a mango is not the same as that of an orange.

Figure 3.2: Mole of mangoes has the same number of particles as a mole of oranges but they differ in mass. 

The equivalent of 12g of carbon-12 is a mole. it is that amount of substance containing 6.23×1023 particles. The number 6.02×1023 is a very special number and s known as the Avogadro constant.

We can also say that one mole is simply equal to the relative formula mass expressed in grams. The value of the Avogadro constant was chosen so that the mass of one mole of that substance is equal to the relative formula mass in grams. In the next activity, you will relate the mole, number of particles and the mass of substances.

Worked example 3.2 Relating the mole, number of particles and mass.

Worked example

Calculate the number of particles in 2 moles of sodium.

Solution

1 mole =6.23×1023 particles

2 moles =6.231023× 2 = 12.46×1023 particles

Exercise 3.2

1. Calculate the number of particles in the following;

1. 0.1 moles of sodium atoms
2. 0.5 moles of chlorine atoms
3. 0.3 moles of calcium atoms;
4. Calculate the mass of each of the following; (Zn =65, Ne =20, O=16)

1. 3.011023 atoms of zinc
2. 12.04×1023 atoms of neon
3. 24.08×1023 atoms of oxygen
4. Converting masses to moles

Look at the beautiful bungalow in figure 3.3 below. There are a number of ways to look at the house.

Figure 3.3: The bungalow can be looked at in different ways 

Would the person looking from the front see the same features as one who approaches it from the side or back? Definitely, someone looking in front would see the front door the windows and pillars which may not be present in the back view of the house. Similarly, we can look at substances in the perspective of mass or the perspective of numbers of particles which in this case are the moles. For atoms, 1 mole is equivalent to relative atomic mass (RAM) in grams. For example: 1 mole of Cu =64g; 1 mole of S =32g; 1 mole of H =1g.

In case of molecules, 1 mole is equivalent to relative molecular mass (RMM) or relative formula mass (RFM). For example: 1 mole of H2O = 18g; 1 mole of CaCO3 =100g; 1 mole of H2SO4 =98g. Hence, we can convert mass into moles and vice versa. The In activity 3.4 you will convert moles to mass and vice versa.

Worked example 3.3 Relating mass with moles.

1. Calculating the number of moles of in 4g of oxygen molecule (O2) (O =16)

Solution

RMM = (2×16) = 32

32g are contained in 1 mole of O2

1g is contained in 1/32 moles of O2

4g are contained in 1/32×4 moles of O2

                             = 0.125 moles of O2

Worked example 3.3 Relating mass with moles

2. Given (Na = 23) calculate the mass in 0.23 moles of sodium

Solution

1 mole of sodium weights 23g

0.23 moles of sodium weigh 23/1×0.23g      

                                                  = 5.29g.

Exercise

1. Calculate the number of moles in;

1. 19.8g of silver
2. 14g of magnesium
3. 34g of ammonium chloride
4. 0.9g of sodium carbonate
5. 24.2g of calcium chloride

(O=16, Ca=40, C=12, S=32, H=1, Cu =64, Ag =108, Mg =24)

2. Calculate the mass of;

1. 0.1 moles of sodium atom
2. 0.3 moles of chlorine molecules
3. 0.05 moles of calcium atoms
4. 0.05 moles of copper (II) carbonate
5. Chemical fprmulae

A chemical formula shows the number and kind of atoms in the formula of a compound. We know from Dalton’s atomic theory that elements exist in a given fixed ratio in compounds.

Percentage composition and formulae

The percentage composition of an element in a compound is the ratio of the mass of the element to the formula mass expressed as a percentage.