Sure, let's go through the solution step-by-step:
1. Understand the chemical reaction:
The decomposition of potassium iodide (KI) can be represented by the balanced chemical equation:
[tex]\[
2 \text{KI} \rightarrow 2 \text{K} + \text{I}_2
\][/tex]
This equation tells us that 2 moles of potassium iodide (KI) decompose to produce 1 mole of iodine (I₂) and 2 moles of potassium (K).
2. Identify the given data and required result:
- We are given 7.0 moles of potassium iodide (KI).
- We need to find out how many moles of iodine (I₂) are produced.
3. Analyze the stoichiometry:
According to the balanced equation, 2 moles of KI produce 1 mole of I₂. Hence, there is a stoichiometric ratio of 2:1 between KI and I₂.
4. Calculate the number of moles of iodine (I₂) produced:
- Since 2 moles of KI yield 1 mole of I₂, we can determine the moles of I₂ by dividing the moles of KI by 2.
[tex]\[
\text{moles of I}_2 = \frac{\text{moles of KI}}{2}
\][/tex]
- Substitute the number of moles of KI (7.0 moles) into the equation:
[tex]\[
\text{moles of I}_2 = \frac{7.0 \text{ moles}}{2}
\][/tex]
[tex]\[
\text{moles of I}_2 = 3.5 \text{ moles}
\][/tex]
5. Express the result with the correct number of significant figures:
- The given value (7.0 moles of KI) has two significant figures.
- Therefore, the calculated number of moles of I₂ should also be expressed with two significant figures.
Thus, the number of moles of iodine (I₂) produced in the decomposition of 7.0 moles of potassium iodide (KI) is [tex]\(3.5\)[/tex] moles.
