- Analyze the reaction: Identify the atoms present on both sides.
- Set up a system of linear equations: Equate the count of Fe, O, Pd, and F atoms on both sides.
- Solve the system: Assign the value 1 to the first coefficient to find the others.
- Verify: Confirm that all atoms are balanced, yielding the equation: \(\boxed{1FeO + 1PdF_2 \rightarrow 1FeF_2 + 1PdO}\).
Explanation
- Problem Analysis
The objective is to balance the chemical equation \(FeO + PdF_2 \rightarrow FeF_2 + PdO\). Balancing an equation requires that the number of atoms of each element is identical on both sides of the reaction. We identify the elements involved as Iron (Fe), Oxygen (O), Palladium (Pd), and Fluorine (F). We seek the smallest positive integer coefficients \(a, b, c, d\) such that \(aFeO + bPdF_2 \rightarrow cFeF_2 + dPdO\).
- System of Equations Construction
To maintain the law of conservation of mass, we set up equations based on the number of atoms for each element:
- For Iron (Fe): \(a = c\)
- For Oxygen (O): \(a = d\)
- For Palladium (Pd): \(b = d\)
- For Fluorine (F): \(2b = 2c\) (which simplifies to \(b = c\))
- Solving the System
We start by assigning the simplest value to the first coefficient, \(a = 1\).
- Since \(a = c\), it follows that \(c = 1\).
- Since \(a = d\), it follows that \(d = 1\).
- Since \(b = d\), it follows that \(b = 1\).
Given these values, all coefficients are \(a=1, b=1, c=1, d=1\). This results in the balanced equation: \(1FeO + 1PdF_2 \rightarrow 1FeF_2 + 1PdO\).
- Final Verification and Conclusion
Checking the atom counts:
- Left side: 1 Fe atom, 1 O atom, 1 Pd atom, 2 F atoms.
- Right side: 1 Fe atom, 2 F atoms, 1 Pd atom, 1 O atom.
The atoms are balanced on both sides. Thus, the coefficients are 1 for each substance. The equation is \(\boxed{1FeO + 1PdF_2 \rightarrow 1FeF_2 + 1PdO}\).
Examples
Balancing chemical equations is essential in fields like pharmacology and environmental science. For instance, when designing a drug or analyzing pollutant removal from water, scientists must know exactly how much of each reactant is needed to produce a target quantity of product. Just like in this problem, ensuring the conservation of mass allows researchers to accurately predict chemical yields and maintain safety in industrial and lab-scale processes. Understanding this balance is the foundation for stoichiometry, which guides the efficient use of materials.