PYTR Class

Learning Objectives

This section focuses on:

1. Relative atomic atomic mass and relative formula mass
2. Empirical and molecular formula
3. The mole as the unit of amount
   • Molar mass
   • Molar concentration
   • Avogadro’s Law

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Part 1: Relative Atomic Mass

Relative Atomic Mass (Ar) is the weighted average mass of an atom of an element compared to 1/12th the mass of a carbon-12 atom. It takes into account the different isotopes of the element and their abundances.

From the above, it is noted that hydrogen has a unit mass of 1 whilst magnesium has a unit mass of 24. This was then used as the standard i.e starting point of assigning mass for all atoms. Carbon unit mass is 12. This number now is used. Therefore, when comparing with magnesium mass, two moles of carbon would balance a scale with one mole of magnesium. Since carbon weighs 12 units, magnesium is 12 * 2 = 24.

Modern atomic studies is now using mass spectrometer which gives the relative abundances of isotopes of an element.

It is often found on the periodic table and is not necessarily a whole number because it accounts for isotope distribution.

Part 2: Empirical and molecular formula

Example Calculation of Empirical

Step 1: Find the Empirical Formula

Let’s say a compound contains 40% carbon (C), 6.7% hydrogen (H), and 53.3% oxygen (O) by mass.

• Step 1: Convert mass percentages to moles:

• Step 2: Divide by the smallest number of moles:

• Step 3: Rewrite the elements as a compouns with its subscript ratio:

So, the empirical formula is CH₂O.

Example Calculation of Empirical

Suppose the molecular mass of the compound is 180 g/mol.

Step 1: Find the molar mass of the empirical formula (CH₂O):

Step 2: Determine the multiple:

Step 3: Multiply the empirical formula by 6:

Step 4: Rewrite the elements as a compound with its molecular ratio:

So, the molecular formula is C₆H₁₂O₆ (which is glucose).

Part 3: Mole Concept

Concept 1: Mass and moles

Activity 1: Watch this video answer the following questions together with the video

• Example 1: Find the amount of 30.0 g of Li₃TaO₄ 
• Example 2: Find the mass of 0.003 mol of KMnO₄

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Concept 2: Number of particles and moles

Avogadro’s Constant (NA​):

This means that 1 mole of any substance contains 6.02×10²³ particles (atoms, molecules, or ions).

Question: Find the number of molecules in 2 moles of water (H₂O)

Answer:

Concept 3: Concentration (solution) and moles

Concentration of solution is expressed in many different units including:

• Molarity (mol / dm3)
• Molality (mol / Kg)
• Part per million (ppm)
• Density (g/cm3)

In the IB, molarity is the one that is used.

• Molarity = the amount of solute (in moles) in 1 dm3 of solvent (pure water)

Note that the unit of volume is L or dm3. These two are the same factor i.e 1 L = 1 dm3

Activity 2: Watch this video to explore further about finding the limiting reactant

• Example: Find the mass of CO₂ produed when 250 cm3 of 0.1 mol/dm3 of HCl reacts with 1.8 g of CaCO₃  

Concept 4: Volume of gas at STP and moles

Volume of Gas at STP and Moles

At Standard Temperature and Pressure (STP):

• Temperature = 0°C (273.15 K)
• Pressure = 1 atm (101.3 kPa)
• 1 mole of any ideal gas occupies 22.4 liters (L or dm³)
• Formula: Volume of gas (L or dm³) = Moles × 22.4

Formula to Find Moles from Volume at STP:

Question: Find the volume of 3 moles of oxygen (O₂) gas at STP

Volume of Gas at SATP and Moles

At Standard Ambient Temperature and Pressure (SATP):

• Temperature = 25°C (298.15 K)
• Pressure = 1 atm (101.3 kPa)
• 1 mole of any ideal gas occupies 24 liters (dm³)

This has the same concept as STP but with different volume occupied by the gas. This is consistent with the relation of temperature and volume. Higher temperature would increase air pressure hence a gas in a container would occupy a larger volume

Activity 3: Use Ideal Gas equation, PV = nRT

• Example: Find the volume of CO₂ produced when 250 cm3 of 0.1 mol/dm3 of HCl reacts with 1.8 g of CaCO₃  at 100 kPa and 280 K