Quantitative Chemistry: Balancing Equations and Conservation of Mass

Key Principles of Balancing Chemical Equations

The Law of Conservation of Mass is the fundamental principle underpinning chemical reactions, stating that matter cannot be created or destroyed. Consequently, in a balanced chemical equation, the number of atoms for each specific element must be identical on both the reactant side and the product side.

When adjusting chemical equations, it is imperative to modify only the coefficients, which are the numbers placed in front of chemical formulas. One must never change the subscripts within a formula; doing so alters the chemical identity of the substance itself. For instance, changing $H_2O$ to $H_2O_2$ transforms water into hydrogen peroxide, regardless of the desired balance.

A reliable strategy for balancing involves starting with elements that appear in only one reactant and one product. Additionally, polyatomic ions should be balanced as single, discrete units if they remain unchanged on both sides of the reaction arrow. If a coefficient is 1, it is mathematically implied and may be left blank or explicitly written as '1'.

Balanced Chemical Equations: Practice and Solutions

1. Magnesium oxidation: $2Mg(s) + O_2(g) \rightarrow 2MgO(s)$

2. Decomposition of hydrogen peroxide: $2H_2O_2(aq) \rightarrow 2H_2O(l) + O_2(g)$

3. Zinc and hydrochloric acid reaction: $Zn(s) + 2HCl(aq) \rightarrow ZnCl_2(aq) + H_2(g)$

4. Combustion of methane: $CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)$

5. Displacement of aluminum and copper(II) sulfate: $2Al(s) + 3CuSO_4(aq) \rightarrow Al_2(SO_4)_3(aq) + 3Cu(s)$

6. Sodium carbonate and nitric acid reaction: $Na_2CO_3(s) + 2HNO_3(aq) \rightarrow 2NaNO_3(aq) + H_2O(l) + CO_2(g)$

7. Combustion of propane: $C_3H_8(g) + 5O_2(g) \rightarrow 3CO_2(g) + 4H_2O(g)$

8. Lead(II) nitrate and potassium iodide reaction: $Pb(NO_3)_2(aq) + 2KI(aq) \rightarrow PbI_2(s) + 2KNO_3(aq)$

9. Reduction of iron(III) oxide with carbon monoxide: $Fe_2O_3(s) + 3CO(g) \rightarrow 2Fe(s) + 3CO_2(g)$

10. Combustion of octane: $2C_8H_{18}(l) + 25O_2(g) \rightarrow 16CO_2(g) + 18H_2O(g)$

Relative Atomic, Molecular, and Formula Masses

In quantitative chemistry, relative mass provides the sum of atomic masses within a chemical unit. Relative Molecular Mass ($M_r$) is defined as the sum of the relative atomic masses of the atoms in a molecule, specifically for covalent compounds. In contrast, Relative Formula Mass represents the sum of the relative atomic masses of the atoms within the formula unit of an ionic compound.

Calculations for standard substances (using atomic masses to 2 decimal places):

• Ammonia ($NH_3$): $14.01 + (3 \times 1.008) = 17.03$
• Glucose ($C_6H_{12}O_6$): $(6 \times 12.01) + (12 \times 1.008) + (6 \times 16.00) = 180.16$
• Magnesium Nitrate ($Mg(NO_3)_2$): $24.31 + 2 \times [14.01 + (3 \times 16.00)] = 148.33$
• Aluminium Sulfate ($Al_2(SO_4)_3$): $(2 \times 26.98) + 3 \times [32.06 + (4 \times 16.00)] = 342.14$
• Copper(II) Sulfate Pentahydrate ($CuSO_4 \cdot 5H_2O$): $63.55 + 32.06 + (4 \times 16.00) + 5 \times (18.016) = 249.69$
• Calcium Phosphate ($Ca_3(PO_4)_2$): $(3 \times 40.08) + 2 \times [30.97 + (4 \times 16.00)] = 310.18$
• Ethanol ($C_2H_5OH$): $(2 \times 12.01) + (6 \times 1.008) + 16.00 = 46.07$
• Ammonium Carbonate ($(NH_4)_2CO_3$): $2 \times [14.01 + (4 \times 1.008)] + 12.01 + (3 \times 16.00) = 96.09$
• Potassium Permanganate ($KMnO_4$): $39.10 + 54.94 + (4 \times 16.00) = 158.04$
• Iron(III) Oxide ($Fe_2O_3$): $(2 \times 55.85) + (3 \times 16.00) = 159.70$

Theoretical Reflection and Terminology

The distinction between relative molecular mass and relative formula mass lies in the nature of the chemical bonding. We use Relative Molecular Mass for substances like $NH_3$ (ammonia) because they consist of discrete, individual molecules held together by covalent bonds. Conversely, for substances like $NaCl$ (sodium chloride), which form a continuous giant ionic lattice rather than individual molecules, we use the term Relative Formula Mass to represent the simplest ratio of ions in the structure.

Quantitative Proofs of the Law of Conservation of Mass

To quantitatively demonstrate the Law of Conservation of Mass, a four-step process is followed: balancing the equation, calculating the total relative mass of reactants, calculating the total relative mass of products, and verifying their equality.

Problem 1: Combustion of Methane

• Balanced Equation: $CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O$
• Total Mass of Reactants: $16.04 + 2(32.00) = 80.04\,u$
• Total Mass of Products: $44.01 + 2(18.016) = 80.04\,u$
• Concluding Statement: Since the total mass of reactants ($80.04\,u$) equals the total mass of products ($80.04\,u$), the Law of Conservation of Mass is demonstrated.

Problem 2: Reaction of Magnesium with Oxygen

• Balanced Equation: $2Mg + O_2 \rightarrow 2MgO$
• Total Mass of Reactants: $2(24.31) + 32.00 = 80.62\,u$
• Total Mass of Products: $2(24.31 + 16.00) = 80.62\,u$
• Concluding Statement: The mass is conserved as the sum of atomic masses of reactants equals the sum of atomic masses of products.

Problem 3: Decomposition of Hydrogen Peroxide

• Balanced Equation: $2H_2O_2 \rightarrow 2H_2O + O_2$
• Total Mass of Reactants: $2(2 \times 1.008 + 2 \times 16.00) = 68.03\,u$
• Total Mass of Products: $2(18.016) + 32.00 = 68.03\,u$
• Concluding Statement: Mass is conserved; the total relative mass remains constant at $68.03\,u$ throughout the reaction.

Problem 4: Displacement Reaction (Aluminum and Copper(II) Sulfate)

• Balanced Equation: $2Al + 3CuSO_4 \rightarrow Al_2(SO_4)_3 + 3Cu$
• Total Mass of Reactants: $2(26.98) + 3(63.55 + 32.06 + 64.00) = 532.79\,u$
• Total Mass of Products: $342.14 + 3(63.55) = 532.79\,u$
• Concluding Statement: The total mass of reactants equals the total mass of products, satisfying the Law of Conservation of Mass.

Problem 5: Reduction of Iron(III) Oxide

• Balanced Equation: $Fe_2O_3 + 3CO \rightarrow 2Fe + 3CO_2$
• Total Mass of Reactants: $159.70 + 3(12.01 + 16.00) = 243.73\,u$
• Total Mass of Products: $2(55.85) + 3(44.01) = 243.73\,u$
• Concluding Statement: Mass is conserved as the total relative mass of $243.73\,u$ is identical for both reactants and products.

NESA Preliminary Chemistry Marking Philosophy

In NESA Preliminary Chemistry, marks are systematically awarded for demonstrating clear working, utilizing correct units ($u$), and providing logical concluding statements. For all mass calculations, it is an academic requirement to use atomic masses to at least 2 decimal places as specified by the provided Periodic Table to ensure quantitative accuracy.