Amount of substance

Welcome to the "Amount of Substance"!

Ever wondered how chemists count something as tiny as an atom? Since we can't pick them up with tweezers, we use a special system of "chemical counting." In this chapter, you will learn how to measure out exact amounts of chemicals for reactions, how to predict how much product you'll make, and how to master the "mole"—the chemist’s most important tool. Don't worry if the math seems a bit much at first; we will break it down step-by-step!

1. Relative Mass: The Chemical Scale

Atoms are too light to weigh in grams individually. Instead, we compare their weights to a standard: the Carbon-12 isotope.

Relative Atomic Mass (\(A_r\))

The average mass of an atom of an element compared to 1/12th of the mass of one atom of Carbon-12.

Relative Molecular Mass (\(M_r\))

The average mass of a molecule compared to 1/12th of the mass of one atom of Carbon-12. To find the \(M_r\), simply add up the \(A_r\) values of all the atoms in the formula.
Example: For \(H_2O\), \(M_r = (2 \times 1.0) + 16.0 = 18.0\).

Relative Formula Mass

We use this term for ionic compounds (like \(NaCl\)) because they don't exist as simple individual molecules, but the calculation is exactly the same as \(M_r\).

Quick Review: Everything is compared to Carbon-12. If you see \(A_r\), think "single atom." If you see \(M_r\), think "the whole formula."

2. The Mole and Avogadro

A mole is just a specific number, like a "dozen" means 12. In chemistry, a mole is the amount of substance that contains as many particles as there are atoms in 12g of Carbon-12.

The Avogadro Constant (\(L\))

This is the number of particles in one mole. You don't need to memorize the number (it's roughly \(6.022 \times 10^{23}\)), but you need to know how to use it.

The Formula:
\(Number\ of\ particles = moles \times Avogadro\ constant\)

Linking Moles and Mass

This is the most common calculation you will do. Use this simple formula:
\(moles\ (n) = \frac{mass\ (m)}{relative\ mass\ (M_r)}\)

Memory Aid: Think of the "n-m-Mr" triangle. Cover the one you want to find with your finger to see the formula!

Common Mistake: Always make sure your mass is in grams (g). If the question gives you kilograms (kg) or milligrams (mg), convert them to grams first!

3. Concentration and Solutions

When chemicals are dissolved in water, we measure how "crowded" the particles are. This is called concentration.

The Formula:
\(moles\ (n) = concentration\ (c) \times volume\ (V)\)

Important Unit Warning!

Concentration is measured in \(mol\ dm^{-3}\). Volume is usually given in \(cm^3\), but for this formula, it must be in \(dm^3\).
To convert: \(dm^3 = \frac{cm^3}{1000}\)

Key Takeaway: Always check your units! If you see \(cm^3\), divide by 1000 before you do anything else.

4. The Ideal Gas Equation

For gases, the relationship between pressure, volume, and temperature is given by:
\(pV = nRT\)

Where:
p = Pressure in Pascals (Pa)
V = Volume in \(m^3\)
n = Number of moles
R = Gas constant (provided in the exam)
T = Temperature in Kelvin (K)

The "Unit Trap"

This equation is where most students lose marks because of units. Use this checklist:
1. Is Pressure in \(Pa\)? (If \(kPa\), multiply by 1000).
2. Is Volume in \(m^3\)? (If \(dm^3\), divide by 1000. If \(cm^3\), divide by 1,000,000).
3. Is Temperature in \(K\)? (Add 273 to the Celsius value: \(K = ^\circ C + 273\)).

5. Empirical and Molecular Formulas

Empirical Formula: The simplest whole-number ratio of atoms in a compound.
Molecular Formula: The actual number of atoms of each element in a molecule.

How to calculate Empirical Formula:

1. List the mass (or %) of each element.
2. Divide each mass by the element's \(A_r\) to find the moles.
3. Divide all the results by the smallest number of moles to get the ratio.
4. If you get a decimal like 1.5, multiply everything by 2 to get whole numbers.

Did you know? Hydrazine's molecular formula is \(N_2H_4\), but its empirical formula is just \(NH_2\). It's like simplifying a fraction in math!

6. Balanced Equations and Yield

A balanced equation is like a recipe. It tells you exactly how much of "Ingredient A" reacts with "Ingredient B."

Percentage Yield

In real life, we never make 100% of the product. Some gets lost on the filter paper or doesn't react fully.
\(Percentage\ Yield = \frac{Actual\ yield}{Theoretical\ yield} \times 100\)

Atom Economy

This measures how "green" or efficient a reaction is. It looks at how much of the starting mass ends up in the desired product rather than waste.
\(Percentage\ atom\ economy = \frac{molecular\ mass\ of\ desired\ product}{sum\ of\ molecular\ masses\ of\ all\ reactants} \times 100\)

Key Takeaway: High atom economy is better for the environment and cheaper for companies because it produces less waste!

7. Required Practical 1: Titrations

You will need to know how to make a volumetric solution (an accurate concentration) and perform a titration to find an unknown concentration.

Step-by-Step for Titration:

1. Use a pipette to add a fixed volume of one solution to a flask.
2. Add a few drops of indicator (like phenolphthalein).
3. Add the other solution from a burette drop-by-drop until the color just changes (the end point).
4. Record the volume used (the titre).
5. Repeat until you have concordant results (results within \(0.10\ cm^3\) of each other).

Don't worry if this seems tricky at first! Titrations require practice and a steady hand. The key is to be precise and always read the burette from the bottom of the meniscus.

Summary: The "Big Ideas"

• Moles allow us to count atoms by weighing them.
• Concentration is moles per \(dm^3\).
• \(pV=nRT\) requires very specific SI units.
• Atom economy tells us how efficient a reaction is, while yield tells us how much we actually made.