Balance Each Of The Following Chemical Equations

Balancing chemical equations is a fundamental skill in chemistry. It ensures that the law of conservation of mass is obeyed, meaning that atoms are neither created nor destroyed in a chemical reaction. This article will guide you through the principles, methods, and practical steps required to balance chemical equations effectively. We'll cover various techniques, from simple inspection to more complex algebraic methods, and provide numerous examples to solidify your understanding.

Understanding Chemical Equations

A chemical equation is a symbolic representation of a chemical reaction. It shows the reactants (the substances that combine or react) on the left side and the products (the substances formed) on the right side, separated by an arrow (→) that indicates the direction of the reaction.

For example, the reaction of hydrogen gas (H₂) with oxygen gas (O₂) to form water (H₂O) can be written as:

H₂ + O₂ → H₂O

However, this equation is unbalanced because the number of oxygen atoms is not the same on both sides. To balance it, we need to ensure that the number of atoms of each element is equal on both the reactant and product sides.

Key Terms in Chemical Equations

• Reactants: Substances that participate in a chemical reaction and are present at the beginning.
• Products: Substances that are formed as a result of the chemical reaction.
• Coefficients: Numbers placed in front of chemical formulas in an equation to indicate the relative number of moles of each substance involved in the reaction.
• Subscripts: Numbers written below and to the right of an element symbol in a chemical formula to indicate the number of atoms of that element in a molecule.
• Balanced Equation: A chemical equation in which the number of atoms of each element is the same on both sides of the equation.

The Law of Conservation of Mass

The law of conservation of mass states that matter cannot be created or destroyed in a chemical reaction. In other words, the total mass of the reactants must equal the total mass of the products. Balancing chemical equations ensures that this law is upheld by making sure the number of atoms of each element remains constant throughout the reaction.

Methods for Balancing Chemical Equations

There are several methods for balancing chemical equations, ranging from simple inspection to more systematic approaches. Here, we will discuss the following methods:

1. Balancing by Inspection (Trial and Error)
2. Algebraic Method

1. Balancing by Inspection (Trial and Error)

This is the most common method for balancing simple chemical equations. It involves adjusting the coefficients of the reactants and products until the number of atoms of each element is the same on both sides.

Steps for Balancing by Inspection:

1. Write the unbalanced equation: Start with the chemical formulas of the reactants and products.
2. Identify the elements present: List all the elements that appear in the equation.
3. Count the atoms of each element on both sides: Determine the number of atoms of each element on the reactant and product sides.
4. Balance the elements one at a time: Start with the element that appears in the fewest chemical formulas. Adjust the coefficients to balance the number of atoms of that element.
5. Continue balancing other elements: Proceed to balance the remaining elements, one at a time, adjusting coefficients as needed.
6. Check your work: Make sure that the number of atoms of each element is the same on both sides of the equation. If not, repeat the process.
7. Write the balanced equation: Once all elements are balanced, write the final balanced equation with the correct coefficients.

Example 1: Balancing the Formation of Water

Unbalanced equation: H₂ + O₂ → H₂O

1. Elements present: Hydrogen (H) and Oxygen (O)
2. Count atoms:
   • Reactants: H = 2, O = 2
   • Products: H = 2, O = 1
3. Balance oxygen: To balance oxygen, place a coefficient of 2 in front of H₂O: H₂ + O₂ → 2H₂O
4. Count atoms again:
   • Reactants: H = 2, O = 2
   • Products: H = 4, O = 2
5. Balance hydrogen: To balance hydrogen, place a coefficient of 2 in front of H₂: 2H₂ + O₂ → 2H₂O
6. Check:
   • Reactants: H = 4, O = 2
   • Products: H = 4, O = 2
7. Balanced equation: 2H₂ + O₂ → 2H₂O

Example 2: Balancing the Combustion of Methane

Unbalanced equation: CH₄ + O₂ → CO₂ + H₂O

1. Elements present: Carbon (C), Hydrogen (H), and Oxygen (O)
2. Count atoms:
   • Reactants: C = 1, H = 4, O = 2
   • Products: C = 1, H = 2, O = 3
3. Balance hydrogen: To balance hydrogen, place a coefficient of 2 in front of H₂O: CH₄ + O₂ → CO₂ + 2H₂O
4. Count atoms again:
   • Reactants: C = 1, H = 4, O = 2
   • Products: C = 1, H = 4, O = 4
5. Balance oxygen: To balance oxygen, place a coefficient of 2 in front of O₂: CH₄ + 2O₂ → CO₂ + 2H₂O
6. Check:
   • Reactants: C = 1, H = 4, O = 4
   • Products: C = 1, H = 4, O = 4
7. Balanced equation: CH₄ + 2O₂ → CO₂ + 2H₂O

Example 3: Balancing the Reaction of Nitrogen and Hydrogen to form Ammonia

Unbalanced equation: N₂ + H₂ → NH₃

1. Elements present: Nitrogen (N) and Hydrogen (H)
2. Count atoms:
   • Reactants: N = 2, H = 2
   • Products: N = 1, H = 3
3. Balance nitrogen: To balance nitrogen, place a coefficient of 2 in front of NH₃: N₂ + H₂ → 2NH₃
4. Count atoms again:
   • Reactants: N = 2, H = 2
   • Products: N = 2, H = 6
5. Balance hydrogen: To balance hydrogen, place a coefficient of 3 in front of H₂: N₂ + 3H₂ → 2NH₃
6. Check:
   • Reactants: N = 2, H = 6
   • Products: N = 2, H = 6
7. Balanced equation: N₂ + 3H₂ → 2NH₃

2. Algebraic Method

The algebraic method is a more systematic approach to balancing chemical equations, especially useful for complex equations where balancing by inspection may be difficult.

Steps for the Algebraic Method:

1. Write the unbalanced equation: Start with the chemical formulas of the reactants and products.
2. Assign algebraic variables: Assign a variable (e.g., a, b, c, d) to each chemical formula in the equation.
3. Write equations for each element: For each element, write an equation that equates the number of atoms on the reactant side to the number of atoms on the product side, using the assigned variables as coefficients.
4. Solve the system of equations: Solve the system of equations to find the values of the variables. If the system has infinite solutions, assign a convenient value (usually 1) to one of the variables and solve for the others.
5. Write the balanced equation: Substitute the values of the variables into the equation as coefficients. If necessary, multiply all coefficients by a common factor to obtain whole numbers.

Example 1: Balancing the Reaction of Iron(III) Oxide with Carbon Monoxide

Unbalanced equation: Fe₂O₃ + CO → Fe + CO₂

1. Assign variables: aFe₂O₃ + bCO → cFe + dCO₂
2. Write equations for each element:
   • Iron (Fe): 2a = c
   • Oxygen (O): 3a + b = 2d
   • Carbon (C): b = d
3. Solve the system of equations:
   • Let a = 1.
   • From the iron equation, c = 2a = 2(1) = 2.
   • From the carbon equation, b = d.
   • Substitute b for d in the oxygen equation: 3a + b = 2b, so 3a = b. Since a = 1, b = 3.
   • Since b = d, d = 3.
4. Balanced equation: 1Fe₂O₃ + 3CO → 2Fe + 3CO₂
   • Or simply: Fe₂O₃ + 3CO → 2Fe + 3CO₂

Example 2: Balancing the Reaction of Potassium Permanganate with Hydrochloric Acid

Unbalanced equation: KMnO₄ + HCl → KCl + MnCl₂ + H₂O + Cl₂

1. Assign variables: aKMnO₄ + bHCl → cKCl + dMnCl₂ + eH₂O + fCl₂
2. Write equations for each element:
   • Potassium (K): a = c
   • Manganese (Mn): a = d
   • Oxygen (O): 4a = e
   • Hydrogen (H): b = 2e
   • Chlorine (Cl): b = c + 2d + 2f
3. Solve the system of equations:
   • Let a = 1.
   • From the potassium and manganese equations, c = 1 and d = 1.
   • From the oxygen equation, e = 4a = 4(1) = 4.
   • From the hydrogen equation, b = 2e = 2(4) = 8.
   • From the chlorine equation, 8 = 1 + 2(1) + 2f, so 2f = 5, and f = 2.5.
4. Since we need whole numbers, multiply all coefficients by 2:
   • a = 2, b = 16, c = 2, d = 2, e = 8, f = 5
5. Balanced equation: 2KMnO₄ + 16HCl → 2KCl + 2MnCl₂ + 8H₂O + 5Cl₂

Tips and Tricks for Balancing Chemical Equations

• Start with the most complex molecule: Begin by balancing the element that appears in the most complex molecule first. This can simplify the process.
• Balance polyatomic ions as a unit: If a polyatomic ion (e.g., SO₄²⁻, NO₃⁻) appears on both sides of the equation and remains unchanged, balance it as a single unit.
• Avoid changing subscripts: Never change the subscripts in a chemical formula when balancing an equation. Changing subscripts changes the identity of the substance.
• Check your work: After balancing the equation, double-check that the number of atoms of each element is the same on both sides.
• Use fractions as temporary coefficients: If you encounter a situation where you need a fractional coefficient to balance an element, use it temporarily and then multiply the entire equation by the denominator to obtain whole numbers.
• Practice regularly: The more you practice balancing chemical equations, the easier it will become.

Common Mistakes to Avoid

• Changing Subscripts: As mentioned earlier, never change the subscripts in a chemical formula. This changes the identity of the substance.
• Forgetting to Check: Always double-check your work to ensure that the equation is balanced correctly.
• Getting Discouraged: Balancing chemical equations can be challenging, but don't get discouraged. Keep practicing, and you will improve.
• Not Simplifying Coefficients: Ensure that the coefficients are in the simplest whole-number ratio. If all coefficients can be divided by a common factor, do so.

Examples and Practice Problems

Let's work through some additional examples to further solidify your understanding of balancing chemical equations.

Example 1: Balancing the Reaction of Aluminum with Copper(II) Chloride

Unbalanced equation: Al + CuCl₂ → AlCl₃ + Cu

1. Elements present: Aluminum (Al), Copper (Cu), and Chlorine (Cl)
2. Count atoms:
   • Reactants: Al = 1, Cu = 1, Cl = 2
   • Products: Al = 1, Cu = 1, Cl = 3
3. Balance chlorine: Place a coefficient of 3 in front of CuCl₂ and a coefficient of 2 in front of AlCl₃: Al + 3CuCl₂ → 2AlCl₃ + Cu
4. Count atoms again:
   • Reactants: Al = 1, Cu = 3, Cl = 6
   • Products: Al = 2, Cu = 1, Cl = 6
5. Balance aluminum: Place a coefficient of 2 in front of Al: 2Al + 3CuCl₂ → 2AlCl₃ + Cu
6. Balance copper: Place a coefficient of 3 in front of Cu: 2Al + 3CuCl₂ → 2AlCl₃ + 3Cu
7. Check:
   • Reactants: Al = 2, Cu = 3, Cl = 6
   • Products: Al = 2, Cu = 3, Cl = 6
8. Balanced equation: 2Al + 3CuCl₂ → 2AlCl₃ + 3Cu

Example 2: Balancing the Reaction of Iron with Oxygen to form Iron(III) Oxide

Unbalanced equation: Fe + O₂ → Fe₂O₃

1. Elements present: Iron (Fe) and Oxygen (O)
2. Count atoms:
   • Reactants: Fe = 1, O = 2
   • Products: Fe = 2, O = 3
3. Balance iron: Place a coefficient of 2 in front of Fe: 2Fe + O₂ → Fe₂O₃
4. Balance oxygen: Place a coefficient of 3/2 in front of O₂: 2Fe + (3/2)O₂ → Fe₂O₃
5. To remove the fraction, multiply the entire equation by 2: 4Fe + 3O₂ → 2Fe₂O₃
6. Check:
   • Reactants: Fe = 4, O = 6
   • Products: Fe = 4, O = 6
7. Balanced equation: 4Fe + 3O₂ → 2Fe₂O₃

Conclusion

Balancing chemical equations is a crucial skill in chemistry that ensures the conservation of mass in chemical reactions. Whether using the inspection method or the algebraic method, the goal is to adjust coefficients until the number of atoms of each element is the same on both sides of the equation. By understanding the principles, following the steps, and practicing regularly, you can master this skill and apply it to more complex chemical reactions. Remember to avoid common mistakes such as changing subscripts and always double-check your work. With patience and practice, balancing chemical equations will become a natural and intuitive process.