To determine the ratio of atoms of potassium (K) to atoms of oxygen (O) in the given chemical equation, we'll analyze the chemical reaction provided:
[tex]\[ 4K + O_2 \rightarrow 2K_2O \][/tex]
1. Identify the number of potassium atoms in the reactants:
- According to the equation, there are 4 atoms of potassium (K) on the reactant side.
2. Identify the composition of the product:
- The product of the reaction is potassium oxide ([tex]\( K_2O \)[/tex]).
- Each [tex]\( K_2O \)[/tex] molecule contains 2 potassium atoms and 1 oxygen atom.
3. Calculate the total number of atoms in the product:
- The equation produces 2 molecules of [tex]\( K_2O \)[/tex].
- Therefore, the total number of potassium atoms in the products is [tex]\( 2 \times 2 = 4 \)[/tex].
- The total number of oxygen atoms in the products is [tex]\( 2 \times 1 = 2 \)[/tex].
4. Determine the ratio of potassium atoms to oxygen atoms:
- From the quantities calculated, we have 4 potassium atoms and 2 oxygen atoms.
- To find the simplest ratio, we divide both numbers by their greatest common divisor, which is 2.
[tex]\[ \text{Ratio} = \frac{4 \text{ potassium atoms}}{2 \text{ oxygen atoms}} = 2:1 \][/tex]
Therefore, the ratio of atoms of potassium to atoms of oxygen is 4:1.
