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Balancing to Solve Systems

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Balancing to Solve Systems

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Balance to solve systems equations by balancing (chemistry)

Created by

Okpara Goodness
Okpara Goodness
Nigeria

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Balancing to Solve Systems
 

Balancing to Solve SystemsOnline version

Balance to solve systems equations by balancing (chemistry)

by Okpara Goodness
1

Slide 1: What balancing does

Balancing a chemical equation creates a system of linear equations based on conservation of atoms. Coefficients are unknowns to determine.

2

Slide 2: Gather information

List all elements involved and count atoms on both sides. Identify which coefficients will balance each element.

3

Slide 3: Assign variables

Assign a variable to each compound’s coefficient, e.g., a, b, c. These are the unknowns we must solve for.

4

Slide 4: Write balance equations

For each element, write an equation equating its total on the left and right using the variables.

5

Slide 5: Build the system

Assemble the equations into a linear system suitable for elimination or bookkeeping.

6

Slide 6: Solve the system

Use algebraic methods (substitution, elimination) to find relationships between coefficients.

7

Slide 7: Find a consistent set

Look for a solution with whole-number coefficients. If needed, scale the solution.

8

Slide 8: Check balance

Substitute the coefficients back into the equation to verify each element is balanced.

9

Slide 9: Common strategies

Start with a difficult element, use lowest common multiples, and handle polyatomic groups to simplify.

10

Slide 10: Practice example

Balance: Fe + O2 → Fe2O3. Use balancing to determine the smallest integers for coefficients.
 
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