Verified Answer :

  • Identify reactants and products to set up the chemical equation \(\text{aNa} + \text{bF}_2 \rightarrow \text{cNaF}\).
  • Use the Law of Conservation of Mass to create the system of equations \(\text{a} = \text{c}\) and \(2\text{b} = \text{c}\).
  • Assign a value to one coefficient and solve for the others to obtain \(\text{a}=2\), \(\text{b}=1\), and \(\text{c}=2\).
  • The final balanced equation is \(2\text{Na} + \text{F}_2 \rightarrow 2\text{NaF}\), with the coefficients \(\boxed{2, 1, 2}\).

Explanation

  1. Problem Analysis and Conservation of Mass

To balance the chemical equation, we must ensure that the number of atoms for each element is equal on both sides of the reaction. The given reaction is:
\[aNa + bF_2 \rightarrow cNaF\]
where \(a, b,\) and \(c\) are the stoichiometric coefficients we need to determine.
The law of conservation of mass states that matter cannot be created or destroyed in a chemical reaction. Therefore, the number of sodium (Na) atoms and fluorine (F) atoms must be the same in the reactants and products.

  1. Setting up and Solving the System of Equations

We set up the equations based on the number of atoms for each element:
For sodium (Na): The number of Na atoms in the reactants is \(a\), and in the products is \(c\). Thus, \(a = c\).
For fluorine (F): The number of F atoms in the reactants is \(2b\), and in the products is \(c\). Thus, \(2b = c\).
We can choose the simplest integer value for one of the coefficients to solve the system. Let's set \(b = 1\). Then, from the second equation, \(c = 2 \times 1 = 2\). Since \(a = c\), we also get \(a = 2\).

  1. Verification of the Balanced Equation

Using the coefficients we found (\(a=2, b=1, c=2\)), the balanced equation is:
\[2Na + 1F_2 \rightarrow 2NaF\]
Now, let's verify the atom counts:

  • Sodium (Na): 2 atoms on the left, 2 atoms on the right.
  • Fluorine (F): 2 atoms on the left (in \(F_2\)), 2 atoms on the right (in \(2NaF\)).

Since the number of atoms for each element is balanced on both sides, the equation is now correctly balanced.

Examples

Chemical balancing is essential in many fields, such as cooking, industrial manufacturing, and pharmaceuticals. For instance, when a baker adjusts a recipe to make a larger batch of bread, they use the same principles of stoichiometry to ensure that all ingredients are balanced correctly to maintain the quality of the product. Similarly, in a laboratory, knowing exactly how much of each reactant is needed for a specific yield prevents waste and ensures the reaction proceeds safely and efficiently.

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