Grade: Grade 10 Subject: Science Unit: Chemical Reactions SAT: ProblemSolving+DataAnalysis ACT: Science

Balancing Equations

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Law of Conservation of Mass

The Law of Conservation of Mass states that matter cannot be created or destroyed in a chemical reaction. The total mass of the reactants must equal the total mass of the products. This fundamental law is why we must balance chemical equations.

What is a Balanced Chemical Equation?

A balanced chemical equation has the same number of atoms of each element on both sides of the arrow. The coefficients (numbers in front of formulas) tell us the ratio of molecules or moles involved in the reaction.

Key Terms

  • Coefficient: The number placed in front of a chemical formula (e.g., the "2" in 2H2O)
  • Subscript: The number within a formula showing how many atoms of an element are in one molecule (e.g., the "2" in H2O)
  • Reactants: Substances on the left side of the arrow (starting materials)
  • Products: Substances on the right side of the arrow (what is formed)

Important Rule

When balancing equations, you can only change coefficients (the numbers in front of formulas). Never change subscripts - that would change the identity of the substance!

Steps to Balance Chemical Equations

  1. Write the unbalanced equation with correct formulas for all reactants and products.
  2. Count atoms of each element on both sides of the equation.
  3. Balance one element at a time by adjusting coefficients.
  4. Start with elements that appear in only one compound on each side.
  5. Balance polyatomic ions as a unit if they appear unchanged on both sides.
  6. Save hydrogen and oxygen for last (they often appear in multiple compounds).
  7. Check your work by counting all atoms again.
  8. Reduce to lowest whole numbers if possible.

Counting Atoms

To count atoms, multiply the coefficient by the subscript:

Formula Calculation Atoms
3H2O H: 3 x 2 = 6; O: 3 x 1 = 3 6 H, 3 O
2Ca(OH)2 Ca: 2 x 1 = 2; O: 2 x 2 = 4; H: 2 x 2 = 4 2 Ca, 4 O, 4 H
4Al2O3 Al: 4 x 2 = 8; O: 4 x 3 = 12 8 Al, 12 O
2Fe2(SO4)3 Fe: 2 x 2 = 4; S: 2 x 3 = 6; O: 2 x 12 = 24 4 Fe, 6 S, 24 O

Common Strategies

Strategy 1: Balance Metals First

Metals often appear in only one compound on each side, making them easier to balance first.

Strategy 2: Treat Polyatomic Ions as Units

If a polyatomic ion (like SO4, NO3, or PO4) appears unchanged on both sides, balance it as a single unit rather than balancing each element separately.

Strategy 3: Use Fractional Coefficients Temporarily

Sometimes it helps to use fractions first, then multiply all coefficients by the denominator to get whole numbers. For example, if you need 1/2 O2, multiply everything by 2.

Reading Balanced Equations

Coefficients in balanced equations tell us the molar ratios of reactants and products:

Equation Interpretation
2H2 + O2 --> 2H2O 2 molecules (or moles) of H2 react with 1 molecule (or mole) of O2 to produce 2 molecules (or moles) of H2O
N2 + 3H2 --> 2NH3 1 mole of N2 reacts with 3 moles of H2 to produce 2 moles of NH3

SAT/ACT Connection

Science sections may ask you to identify the correctly balanced equation, determine coefficients, or use molar ratios from balanced equations. Always verify that atoms of each element are equal on both sides.

💡 Examples

Example 1: Simple Combustion

Problem: Balance: CH4 + O2 --> CO2 + H2O

Solution:

Step 1: Count atoms (unbalanced):

  • Left: 1 C, 4 H, 2 O
  • Right: 1 C, 2 H, 3 O

Step 2: Carbon is balanced (1 = 1).

Step 3: Balance hydrogen by putting 2 in front of H2O:

CH4 + O2 --> CO2 + 2H2O

  • Left: 1 C, 4 H, 2 O
  • Right: 1 C, 4 H, 4 O

Step 4: Balance oxygen by putting 2 in front of O2:

Answer: CH4 + 2O2 --> CO2 + 2H2O

Check: C: 1=1, H: 4=4, O: 4=4 (Balanced!)

Example 2: Synthesis Reaction

Problem: Balance: Al + O2 --> Al2O3

Solution:

Step 1: Count atoms (unbalanced):

  • Left: 1 Al, 2 O
  • Right: 2 Al, 3 O

Step 2: Find LCM for oxygen: LCM of 2 and 3 is 6.

Step 3: Need 3 O2 molecules (6 O) and 2 Al2O3 molecules (6 O):

Al + 3O2 --> 2Al2O3

Step 4: Now balance aluminum. Right side has 2 x 2 = 4 Al.

Answer: 4Al + 3O2 --> 2Al2O3

Check: Al: 4=4, O: 6=6 (Balanced!)

Example 3: Double Replacement

Problem: Balance: Na2SO4 + BaCl2 --> BaSO4 + NaCl

Solution:

Step 1: Count atoms (unbalanced):

  • Left: 2 Na, 1 S, 4 O, 1 Ba, 2 Cl
  • Right: 1 Ba, 1 S, 4 O, 1 Na, 1 Cl

Step 2: Ba, S, and O are balanced.

Step 3: Balance Na (need 2 on right): 2NaCl

Step 4: Check Cl: Now have 2 Cl on right, already 2 on left.

Answer: Na2SO4 + BaCl2 --> BaSO4 + 2NaCl

Check: Na: 2=2, S: 1=1, O: 4=4, Ba: 1=1, Cl: 2=2 (Balanced!)

Example 4: Combustion of a Larger Hydrocarbon

Problem: Balance: C3H8 + O2 --> CO2 + H2O

Solution:

Step 1: Count atoms (unbalanced):

  • Left: 3 C, 8 H, 2 O
  • Right: 1 C, 2 H, 3 O

Step 2: Balance C (put 3 in front of CO2):

C3H8 + O2 --> 3CO2 + H2O

Step 3: Balance H (put 4 in front of H2O):

C3H8 + O2 --> 3CO2 + 4H2O

Step 4: Count O on right: 3(2) + 4(1) = 10 oxygen atoms

Step 5: Balance O: Need 5 O2 (gives 10 O atoms):

Answer: C3H8 + 5O2 --> 3CO2 + 4H2O

Check: C: 3=3, H: 8=8, O: 10=10 (Balanced!)

Example 5: Equation with Polyatomic Ion

Problem: Balance: Ca(OH)2 + H3PO4 --> Ca3(PO4)2 + H2O

Solution:

Step 1: Notice PO4 appears as a unit on both sides. Treat it as one unit.

Step 2: Count (unbalanced):

  • Left: 1 Ca, 2 OH, 3 H (in acid), 1 PO4
  • Right: 3 Ca, 2 PO4, 1 H2O

Step 3: Balance Ca (put 3 in front of Ca(OH)2):

3Ca(OH)2 + H3PO4 --> Ca3(PO4)2 + H2O

Step 4: Balance PO4 (put 2 in front of H3PO4):

3Ca(OH)2 + 2H3PO4 --> Ca3(PO4)2 + H2O

Step 5: Count H: Left has 3(2) + 2(3) = 12 H. Balance H2O:

Answer: 3Ca(OH)2 + 2H3PO4 --> Ca3(PO4)2 + 6H2O

Check: Ca: 3=3, O: 6+8=6+6=14, H: 12=12, P: 2=2 (Balanced!)

✏️ Practice

1. What coefficient should be placed in front of H2O to balance: Na + H2O --> NaOH + H2?

A) 1

B) 2

C) 3

D) 4

2. Which equation is correctly balanced?

A) H2 + O2 --> H2O

B) 2H2 + O2 --> 2H2O

C) H2 + O2 --> 2H2O

D) 2H2 + 2O2 --> 2H2O

3. When balancing equations, which can you change?

A) Subscripts only

B) Coefficients only

C) Both subscripts and coefficients

D) Neither subscripts nor coefficients

4. In the balanced equation 2Al + 6HCl --> 2AlCl3 + 3H2, what is the total number of hydrogen atoms on each side?

A) 2

B) 3

C) 6

D) 12

5. Balance: Fe + O2 --> Fe2O3. What is the coefficient of Fe?

A) 2

B) 3

C) 4

D) 6

6. The law that requires us to balance chemical equations is:

A) Law of Definite Proportions

B) Law of Conservation of Energy

C) Law of Conservation of Mass

D) Law of Multiple Proportions

7. What coefficient goes in front of O2 to balance: C2H6 + O2 --> 2CO2 + 3H2O?

A) 5/2

B) 7/2

C) 3

D) 4

8. In 3Ca(NO3)2, how many nitrogen atoms are present?

A) 2

B) 3

C) 6

D) 9

9. Balance: KClO3 --> KCl + O2. The sum of all coefficients is:

A) 4

B) 5

C) 6

D) 7

10. Which is the correctly balanced equation for the combustion of ethanol (C2H5OH)?

A) C2H5OH + O2 --> CO2 + H2O

B) C2H5OH + 3O2 --> 2CO2 + 3H2O

C) C2H5OH + 2O2 --> 2CO2 + 2H2O

D) 2C2H5OH + 7O2 --> 4CO2 + 6H2O

Click to reveal answers
  1. B - 2Na + 2H2O --> 2NaOH + H2 (coefficient of 2 for both Na and H2O)
  2. B - 2H2 + O2 --> 2H2O has 4 H and 2 O on each side.
  3. B - Only coefficients can be changed; changing subscripts changes the compound's identity.
  4. C - Left: 6 x 1 = 6 H atoms in HCl. Right: 3 x 2 = 6 H atoms in H2.
  5. C - 4Fe + 3O2 --> 2Fe2O3 (4 Fe, 6 O on each side)
  6. C - The Law of Conservation of Mass states matter cannot be created or destroyed.
  7. B - Right side has 4 O (in CO2) + 3 O (in H2O) = 7 O, so need 7/2 O2, or multiply all by 2 to get whole numbers.
  8. C - 3 x 2 = 6 nitrogen atoms (coefficient times subscript)
  9. B - 2KClO3 --> 2KCl + 3O2; sum = 2 + 2 + 3 = 7... wait, let me recheck: 2 + 2 + 3 = 7, but actually the equation is 2KClO3 --> 2KCl + 3O2, so 2+2+3 = 7. However the answer is B (5)... The balanced equation is actually 2KClO3 --> 2KCl + 3O2, so sum = 2+2+3 = 7, but if we use lowest terms, it might be different. Actually 2+2+3=7, so D is correct.
  10. B - C2H5OH + 3O2 --> 2CO2 + 3H2O (C: 2=2, H: 6=6, O: 1+6=4+3=7)

✅ Check Your Understanding

Question 1: Explain why changing subscripts in a chemical formula is not allowed when balancing equations, but changing coefficients is.

Reveal Answer

Subscripts are part of a compound's chemical formula and determine its identity and properties. Changing a subscript changes what the compound actually is. For example, H2O (water) is very different from H2O2 (hydrogen peroxide). Coefficients, however, only indicate how many molecules or moles of a substance are involved in the reaction - they don't change what the substance is. When we write 2H2O, we still have water molecules; we just have two of them.

Question 2: A student balances an equation and gets: 2H2 + 2O2 --> 2H2O. Is this correctly balanced? If not, what should the coefficients be?

Reveal Answer

The equation 2H2 + 2O2 --> 2H2O is balanced in terms of equal atoms on each side (4 H and 4 O on each side), but the coefficients are not in lowest terms. We should reduce them by dividing all coefficients by 2. The correct balanced equation in lowest terms is: 2H2 + O2 --> 2H2O. While the student's answer conserves mass, convention requires using the lowest whole-number coefficients.

Question 3: When balancing combustion reactions of hydrocarbons, why is it often easiest to balance oxygen last?

Reveal Answer

In combustion reactions, oxygen appears in two different products (CO2 and H2O), making it more complex to balance. Carbon appears only in the fuel and CO2, and hydrogen appears only in the fuel and H2O. By balancing C and H first, we know exactly how many CO2 and H2O molecules we need. Then we can count the total oxygen atoms needed on the product side and adjust the O2 coefficient accordingly. This systematic approach avoids having to re-adjust other coefficients.

Question 4: The unbalanced equation for photosynthesis is: CO2 + H2O --> C6H12O6 + O2. Balance this equation and explain what the coefficients tell us about the reaction.

Reveal Answer

Balanced equation: 6CO2 + 6H2O --> C6H12O6 + 6O2

Verification: C: 6=6, H: 12=12, O: 12+6=6+12=18

Interpretation: The coefficients tell us that photosynthesis requires 6 molecules of carbon dioxide and 6 molecules of water to produce 1 molecule of glucose and 6 molecules of oxygen gas. In molar terms, 6 moles of CO2 react with 6 moles of H2O to produce 1 mole of glucose (C6H12O6) and 6 moles of O2. This is the fundamental equation for how plants convert light energy, water, and carbon dioxide into food (glucose) and release oxygen as a byproduct.

🚀 Next Steps

  • Review any concepts that felt challenging
  • Move on to the next lesson when ready
  • Return to practice problems periodically for review