DAT General Chemistry: Writing and Balancing Chemical Equations

DAT High-Yield Concept

Law of Conservation: Chemical equations must conserve both mass (atoms) and net charge between reactants and products.
Coefficients vs. Subscripts: Balancing is achieved exclusively by changing stoichiometric coefficients, never chemical subscripts.
State Symbols: Specify physical phases— $\ce{(s)}$ , $\ce{(l)}$ , $\ce{(g)}$ , and $\ce{(aq)}$ —to differentiate solids, pure liquids, gases, and aqueous solutions.
Polyatomic Ion Shortcut: Polyatomic ions that remain unchanged on both sides of a reaction should be balanced as intact units to save time on the DAT.

Reactants, Products, and State Symbols

A chemical equation provides a symbolic quantitative representation of a chemical change. The starting substances, known as reactants, are placed on the left side of the reaction arrow $\ce{->}$ . The newly formed substances, known as products, are placed on the right side. Stoichiometric coefficients placed in front of chemical formulas indicate the relative molar ratios of all species involved.

Physical states are designated using parenthetical state symbols immediately following each formula: $\ce{(s)}$ for solid, $\ce{(l)}$ for liquid, $\ce{(g)}$ for gas, and $\ce{(aq)}$ for an aqueous solution dissolved in water.

The term refers to the relationship between the amounts of substances that react together in a particular chemical reaction, and the amounts of products that are formed. The general stoichiometric equation: aA+bB+...→...+yY+zZ provides the information that a moles of A reacts with b moles of B to produce y moles of Y and z moles of Z. The stoichiometry of a reaction may be unknown, or may be very complex. (Source: International Union of Pure and Applied Chemistry (IUPAC) · CC BY-SA 4.0 · Wikimedia Commons)

Key Concept: Coefficients vs. Subscripts

Subscripts define the molecular identity and atom ratios within a specific compound (e.g., $\ce{H2O}$ vs. $\ce{H2O2}$ ). Altering a subscript changes the substance entirely. Coefficients multiply the entire chemical formula, altering only the total quantity of that substance without changing its chemical identity.

Feature	Stoichiometric Coefficients	Chemical Subscripts
Location	In front of the entire chemical formula	To the lower right of individual element symbols
What it represents	Relative mole or molecule ratio in reaction	Atom ratio within a single chemical compound
Adjustable when balancing?	Yes (sole mechanism for balancing)	No (changing alters molecular identity)

Conservation of Atoms and Charge

According to the Law of Conservation of Mass, matter is neither created nor destroyed during an ordinary chemical reaction. Therefore, the total number of atoms of each element on the reactant side must exactly equal the total number of atoms of that same element on the product side.

In ionic or electrochemical processes, reactions must also adhere to the Law of Conservation of Charge: the net electrical charge of all reactants must equal the net electrical charge of all products.

నీరు ఏర్పడుటకు తుల్య సమీకరణం (Source: Kvr.lohith · CC BY-SA 4.0 · Wikimedia Commons)

Worked Example 1: Verifying Mass and Charge Conservation

Question: Verify whether the following aqueous redox equation conserves both mass and electrical charge: $\ce{Fe^{2+}(aq) + Ce^{4+}(aq) -> Fe^{3+}(aq) + Ce^{3+}(aq)}$

Reasoning:
1. Atom count: Reactants contain $1\, \ce{Fe}$ and $1\, \ce{Ce}$ . Products contain $1\, \ce{Fe}$ and $1\, \ce{Ce}$ . Atom counts are balanced.
2. Net charge: Reactant charge = $(+2) + (+4) = +6$ . Product charge = $(+3) + (+3) = +6$ . Net charge is conserved.

DAT Exam Trap: Students often balance atom counts successfully but forget to check net electrical charge when balancing ionic or redox reactions.

Balancing Chemical Equations

To balance a chemical equation, systematically adjust coefficients until the atom inventory for every element is identical on both sides. A proven strategy is to balance elements appearing in only one reactant and product first, balance polyatomic ions as single units if they remain intact, and balance free uncombined elements (such as $\ce{O2(g)}$ ) last.

Balancing by atom inventory: carbon, then hydrogen, then oxygen — A balanced equation is a statement that atoms are neither created nor destroyed, so every element must appear the same number of times on both sides. The only thing you are allowed to adjust is the coefficient in front of a formula, because changing a subscript changes the substance itself. A workable order for a combustion is carbon first, then hydrogen, and oxygen last, since oxygen usually turns up in more than one product and is easiest to fix once everything else is settled. For propane, three carbons force a 3 on carbon dioxide and eight hydrogens force a 4 on water; those two choices demand ten oxygen atoms on the right, which five O2 molecules supply.

DAT Mnemonic: Use MINOH to prioritize balancing order:
Metals → Ions (polyatomic) → Nonmetals → Oxygen → Hydrogen.

Worked Example 2: Combustion Reaction Balancing

Question: Write the balanced chemical equation for the complete combustion of propane gas ( $\ce{C3H8}$ ).

Step-by-Step Solution:
1. Write the unbalanced equation with state symbols: $\ce{C3H8(g) + O2(g) -> CO2(g) + H2O(g)}$ 2. Balance Carbon: Reactants have $3$ C atoms. Place coefficient $3$ before $\ce{CO2}$ : $\ce{C3H8(g) + O2(g) -> 3CO2(g) + H2O(g)}$ 3. Balance Hydrogen: Reactants have $8$ H atoms. Place coefficient $4$ before $\ce{H2O}$ : $\ce{C3H8(g) + O2(g) -> 3CO2(g) + 4H2O(g)}$ 4. Balance Oxygen: Products contain $(3 \times 2) + (4 \times 1) = 10$ O atoms. Place coefficient $5$ before $\ce{O2}$ : $\ce{C3H8(g) + 5O2(g) -> 3CO2(g) + 4H2O(g)}$

Final Answer: $\ce{C3H8(g) + 5O2(g) -> 3CO2(g) + 4H2O(g)}$ . (Verification: $3\, \ce{C}$ , $8\, \ce{H}$ , $10\, \ce{O}$ on both sides).

ప్రోపేన్ దహన చర్య - తుల్య సమీకరణం (Source: Kvr.lohith · CC BY-SA 4.0 · Wikimedia Commons)

Critical Thinking Questions

Why is changing subscripts to balance an equation scientifically incorrect, even if it results in equal atom counts on both sides?
In the net ionic precipitation reaction $\ce{Ba^{2+}(aq) + SO4^{2-}(aq) -> BaSO4(s)}$ , demonstrate how both atom count and net charge are conserved.
When balancing combustion reactions with an odd number of oxygen atoms on the product side, how can fractional coefficients be converted to the lowest whole-number integer ratio required for standard stoichiometric equations?

References

Sources returned by Google Search grounding during lesson verification.

Stoichiometry and Balancing Reactions - Chemistry LibreTexts — chem.libretexts.org
4.1 Writing and Balancing Chemical Equations - OpenStax — openstax.org

Writing and Balancing Chemical Equations

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Practice Questions

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