To determine the ratio of atoms of potassium (K) to atoms of oxygen (O) in the chemical equation for potassium oxide, let's break down the equation step by step. The given chemical equation is:
[tex]\[
4 K + O_2 \rightarrow 2 K_2O
\][/tex]
### Step 1: Identify the quantity of each element on the left-hand side (reactants)
On the left-hand side of the equation, we have:
- 4 atoms of potassium (K)
- 1 molecule of oxygen gas (O2), which contains 2 atoms of oxygen (O)
### Step 2: Count the total number of atoms for each element
- Potassium (K): There are 4 atoms of potassium in the reactants.
- Oxygen (O): Since one molecule of O2 contains 2 oxygen atoms, there are 2 atoms of oxygen in the reactants.
### Step 3: Determine the ratio
We are asked for the ratio of potassium atoms to oxygen atoms. The quantities are:
- 4 potassium atoms
- 2 oxygen atoms
To express this ratio in its simplest form, we divide both quantities by their greatest common divisor (GCD).
The GCD of 4 and 2 is 2.
### Step 4: Simplify the ratio
[tex]\[
\frac{4}{2} = 2 \quad \text{(potassium atoms)}
\][/tex]
[tex]\[
\frac{2}{2} = 1 \quad \text{(oxygen atoms)}
\][/tex]
Thus, the simplified ratio of potassium atoms to oxygen atoms is:
[tex]\[
2:1
\][/tex]
### Final Answer
The ratio of atoms of potassium to atoms of oxygen is [tex]\( \boxed{2:1} \)[/tex].
