- Identify the product as potassium oxide with the formula \(K_2O\).
- Observe the subscripts: 2 for potassium (K) and 1 for oxygen (O).
- Determine the ratio of atoms by relating the K and O counts, which is \(2:1\).
- Final answer: \(\boxed{2:1}\).
Explanation
- Analyzing the Chemical Formula
The chemical formula for potassium oxide, which is the product of the reaction \(4K + O_2 \rightarrow 2K_2O\), is \(K_2O\). To determine the ratio of the number of atoms of potassium to the number of atoms of oxygen in this compound, we examine the subscripts in the chemical formula. The subscript '2' following the symbol 'K' indicates that there are 2 atoms of potassium, and the absence of a subscript following the symbol 'O' indicates there is 1 atom of oxygen. Therefore, the ratio of potassium atoms to oxygen atoms within a single unit of the compound is \(2:1\).
- Verifying with Stoichiometry
Even when considering the stoichiometric coefficient provided in the balanced equation, which indicates 2 formula units of \(K_2O\), the total number of atoms of each element in the product side is 4 atoms of potassium (\(2 \times 2 = 4\)) and 2 atoms of oxygen (\(2 \times 1 = 2\)). The ratio of these total counts is \(4:2\), which simplifies to \(2:1\). Thus, the ratio of potassium atoms to oxygen atoms in the product remains constant.
- Conclusion
Based on the analysis of the chemical formula, we have determined that for every 2 potassium atoms, there is 1 oxygen atom. This corresponds to a ratio of \(2:1\). Comparing this result to the given options, we identify that the correct ratio is \(2:1\).
Examples
In chemistry, knowing the ratio of atoms in a compound is essential for understanding its properties and reactivity. For instance, in an industrial setting, knowing that the ratio of potassium to oxygen in potassium oxide is \(2:1\) allows engineers to calculate exactly how much potassium metal is required to react with a specific mass of oxygen, ensuring that no excess reactant is wasted and the process is efficient. This same principle applies to many other industrial synthesis processes where stoichiometry guides production.