Balancing Chemical Equations: Principles, Steps, and Practice Problems

Balancing Chemical Equations

Introduction to Balancing Equations

Balancing chemical equations is a fundamental skill in general chemistry, essential for understanding chemical reactions and stoichiometry. A balanced equation ensures that the same number of each type of atom appears on both sides of the reaction, reflecting the law of conservation of mass.

• Balanced Equation: An equation is "balanced" when the number of atoms of each element is the same on both the reactant and product sides.

• Chemical Arrow: The arrow in a chemical equation (→) separates reactants from products.

• Coefficients: Numbers placed in front of chemical formulas to indicate the number of molecules or moles involved.

Steps to Balancing a Chemical Equation

Follow these steps to systematically balance any chemical equation:

1. Step 1: Write the Unbalanced Equation

   • List all reactants and products, ensuring chemical formulas are correct.

   • Example: The reaction of zinc metal with hydrochloric acid produces zinc chloride and hydrogen gas.

   $\mathrm{Zn}(s) + \mathrm{HCl}(aq) \rightarrow \mathrm{ZnCl}_2(aq) + \mathrm{H}_2(g)$

2. Step 2: Adjust Coefficients

   • Change coefficients to ensure the same number of each atom on both sides.

   • Do not alter subscripts in chemical formulas.

   • If no coefficient is written, it is assumed to be 1.

   Example (balanced): $\mathrm{Zn}(s) + 2\mathrm{HCl}(aq) \rightarrow \mathrm{ZnCl}_2(aq) + \mathrm{H}_2(g)$

Note: Chemists prefer the lowest whole-number coefficients when writing balanced equations.

Practical Tips for Balancing Equations

• Polyatomic Ions: Balance polyatomic ions as a group if they appear unchanged on both sides.

• Hydrogen and Oxygen: Leave H and O until last, especially in complex or combustion reactions.

Practice Problems: Balancing Equations

Balance the following chemical equations. For each, ensure the number of atoms of each element is equal on both sides.

1. $\mathrm{Mg(OH)_2} + \mathrm{HBr} \rightarrow \mathrm{MgBr_2} + \mathrm{H_2O}$

2. $\mathrm{Mg(OH)_2} + \mathrm{HI} \rightarrow \mathrm{MgI_2} + \mathrm{H_2O}$

3. $\mathrm{Ca(OH)_2} + \mathrm{HCl} \rightarrow \mathrm{CaCl_2} + \mathrm{H_2O}$

4. $\mathrm{Al_2O_3} + \mathrm{H_2SO_4} \rightarrow \mathrm{Al_2(SO_4)_3} + \mathrm{H_2O}$

5. $\mathrm{Li_2CO_3} + \mathrm{H_2SO_4} \rightarrow \mathrm{Li_2SO_4} + \mathrm{H_2O} + \mathrm{CO_2}$

6. $\mathrm{C_2H_4} + \mathrm{O_2} \rightarrow \mathrm{CO_2} + \mathrm{H_2O}$

7. $\mathrm{H_2O_2} \rightarrow \mathrm{H_2O} + \mathrm{O_2}$ (Decomposition of hydrogen peroxide)

8. $\mathrm{Na_2SO_3} + \mathrm{Cl_2} + \mathrm{HCl} \rightarrow \mathrm{NaHSO_4} + \mathrm{HCl}$

9. $\mathrm{KClO_3} \rightarrow \mathrm{KCl} + \mathrm{O_2}$

10. $\mathrm{C_6H_{12}O_6} + \mathrm{O_2} \rightarrow \mathrm{CO_2} + \mathrm{H_2O}$

11. $\mathrm{C_4H_{10}} + \mathrm{O_2} \rightarrow \mathrm{CO_2} + \mathrm{H_2O}$

12. $\mathrm{NH_4} + \mathrm{H_2O} \rightarrow \mathrm{HNO_3} + \mathrm{H_2O}$

13. $\mathrm{ClO_2} + \mathrm{H_2O} \rightarrow \mathrm{HClO_3} + \mathrm{HCl}$

14. $\mathrm{PCl_3} + \mathrm{H_2O} \rightarrow \mathrm{H_3PO_3} + \mathrm{HCl}$

15. $\mathrm{Al} + \mathrm{Fe_2O_3} \rightarrow \mathrm{Al_2O_3} + \mathrm{Fe}$

16. $\mathrm{Cu} + \mathrm{H_2SO_4} \rightarrow \mathrm{CuSO_4} + \mathrm{SO_2} + \mathrm{H_2O}$

Reference Materials

• Flowers, Paul, Theobold, Klaus, Langley, Richard, & Robinson, W. R. (2019). Chemistry 2e.

• Jespersen, N. D., Hyslop, Alison, & Brady, J. E. (2015). Chemistry: The molecular nature of matter.

• Zumdahl, Steven, Zumdahl, Susan, DeCoste, Donald J. (n.d.). Chemistry.

Summary Table: Steps for Balancing Equations

Step	Description
1	Write the unbalanced equation with correct formulas
2	Adjust coefficients to balance atoms
3	Check that all atoms are balanced
4	Use lowest whole-number coefficients

Additional info: The above notes expand on the worksheet instructions and provide academic context for balancing equations, including practical tips and references for further study.