Moles and Masses

This section explains moles and masses, covering, the mole and Avogadro’s constant, moles and relative formula mass and the empirical formula.

The Mole and Avogadro’s Constant

In chemistry, the mole is a fundamental unit used to measure the amount of substance. One mole of any substance contains exactly the same number of particles (atoms, molecules, ions, etc.), and this number is called Avogadro's constant.

• Avogadro's constant is $6.022 \times 10^{23}$, meaning that one mole of any substance contains $6.022 \times 10^{23}$ particles.

The mole allows chemists to count particles by weighing them. Instead of dealing with enormous numbers of atoms or molecules, we can work with moles, making calculations easier.

Moles and Relative Formula Mass (Mr)

The relative formula mass (Mr) of a compound is the sum of the relative atomic masses (Ar) of all the atoms in the compound’s formula.

For example, the relative formula mass of water (H₂O) is:

• Hydrogen (H) has an atomic mass of 1.
• Oxygen (O) has an atomic mass of 16.

So, the Mr of H₂O = (2 × 1) + (1 × 16) = 18 g/mol.

Using the mole concept, you can relate the mass of a substance to the number of moles it contains. The formula to calculate the number of moles from the mass and relative formula mass is:

$$\text{Number of moles} = \frac{\text{Mass}}{\text{Relative formula mass (Mr)}}$$

Amounts of Substances in Equations

The coefficients in a balanced chemical equation show the ratio of moles of each substance involved in the reaction. This allows chemists to calculate the amount of reactants and products in terms of moles.

For example, consider the balanced equation for the reaction between magnesium and hydrochloric acid:

$$\text{Mg (s)} + 2\text{HCl (aq)} \rightarrow \text{MgCl₂ (aq)} + \text{H₂ (g)}$$ 

The mole ratio of magnesium to hydrogen gas is 1:1, meaning 1 mole of magnesium produces 1 mole of hydrogen gas. If you know the number of moles of one substance, you can use this ratio to calculate the amount of other substances in the reaction.

Empirical Formula

The empirical formula of a compound shows the simplest whole-number ratio of atoms of each element in the compound. It is determined by finding the relative amounts of each element in a compound, often expressed as a percentage by mass, and then converting these amounts to a ratio.

Steps to Calculate the Empirical Formula:

1. Find the mass of each element in the compound.
2. Convert the masses to moles using the relative atomic mass (Ar) of each element.
3. Determine the simplest whole-number ratio of moles of each element.
4. Write the empirical formula based on the ratio.

Example: Empirical Formula of a Compound

A compound contains 4.8 g of carbon, 1.6 g of hydrogen, and 6.4 g of oxygen. To find the empirical formula:

1. Convert masses to moles:

• Carbon (C): $\frac{4.8}{12} = 0.4 \, \text{mol}$
• Hydrogen (H): $\frac{1.6}{1} = 1.6 \, \text{mol}$
• Oxygen (O): $\frac{6.4}{16} = 0.4 \, \text{mol}$

2. Find the simplest ratio:

• Divide each number of moles by the smallest number (in this case, 0.4).
• Carbon: $\frac{0.4}{0.4} = 1$
• Hydrogen: $\frac{1.6}{0.4} = 4$
• Oxygen: $\frac{0.4}{0.4} = 1$

3. Write the empirical formula: The empirical formula is CH₄O.

Examples of Calculations Using Moles and Mass

Example 1: Finding the Number of Moles of a Substance

Suppose you have 36 grams of water (H₂O). To find the number of moles of water:

1. Calculate the relative formula mass (Mr) of H₂O:
2. Use the formula for moles:

$$\text{Mr of H₂O} = (2 \times 1) + (1 \times 16) = 18 \, \text{g/mol}$$ 

$$\text{Number of moles} = \frac{\text{Mass}}{\text{Relative formula mass}} = \frac{36 \, \text{g}}{18 \, \text{g/mol}} = 2 \, \text{mol}$$ 

So, 36 grams of water contains 2 moles of water molecules.

Example 2: Using Moles in a Chemical Equation

Consider the reaction between zinc and sulfuric acid to form zinc sulfate and hydrogen gas:

$$\text{Zn (s)} + \text{H₂SO₄ (aq)} \rightarrow \text{ZnSO₄ (aq)} + \text{H₂ (g)}$$ 

If 0.5 moles of zinc react with excess sulfuric acid, how many moles of hydrogen gas are produced?

From the balanced equation, the mole ratio of zinc to hydrogen gas is 1:1. Therefore, 0.5 moles of zinc will produce 0.5 moles of hydrogen gas.

Understanding moles and masses is essential in chemistry, as it allows you to quantify substances involved in chemical reactions. By using Avogadro’s constant, the mole concept, and relative formula mass, you can calculate the amounts of substances required or produced in reactions and determine empirical formulas to understand the simplest ratios of atoms in compounds.