To solve this problem, let’s break it down step-by-step:
1. Understanding the problem:
- We start with 3.45 moles of [tex]\( \text{KMnO}_4 \)[/tex].
- For each 2 moles of [tex]\( \text{KMnO}_4 \)[/tex], 8 moles of [tex]\( \text{H}_2\text{O} \)[/tex] are produced.
2. Setting up the ratio:
- The ratio of [tex]\( \text{H}_2\text{O} \)[/tex] to [tex]\( \text{KMnO}_4 \)[/tex] is given by [tex]\( \frac{8 \, \text{mol} \, \text{H}_2\text{O}}{2 \, \text{mol} \, \text{KMnO}_4} \)[/tex].
- Simplifying this ratio, [tex]\( \frac{8 \, \text{mol} \, \text{H}_2\text{O}}{2 \, \text{mol} \, \text{KMnO}_4} = 4 \, \text{mol} \, \text{H}_2\text{O} / 1 \, \text{mol} \, \text{KMnO}_4 \)[/tex].
3. Calculating the amount of [tex]\( \text{H}_2\text{O} \)[/tex] produced:
- We need to multiply the given moles of [tex]\( \text{KMnO}_4 \)[/tex] by the simplified ratio.
- Calculation: [tex]\( 3.45 \, \text{mol} \, \text{KMnO}_4 \times 4 \, \text{mol} \, \text{H}_2\text{O} / 1 \, \text{mol} \, \text{KMnO}_4 \)[/tex].
4. Performing the multiplication:
- This yields [tex]\( 3.45 \times 4 = 13.8 \, \text{mol} \, \text{H}_2\text{O} \)[/tex].
In summary, your initial setup was correct:
- You correctly used the ratio [tex]\( \frac{8 \, \text{mol} \, \text{H}_2\text{O}}{2 \, \text{mol} \, \text{KMnO}_4} \)[/tex].
- Simplified it to [tex]\( 4 \, \text{mol} \, \text{H}_2\text{O} \)[/tex] per [tex]\( 1 \, \text{mol} \, \text{KMnO}_4 \)[/tex].
- Correctly multiplied [tex]\( 3.45 \, \text{mol} \, \text{KMnO}_4 \)[/tex] by [tex]\( 4 \)[/tex] to get [tex]\( 13.8 \, \text{mol} \, \text{H}_2\text{O} \)[/tex].
Therefore, you set up the equation correctly and executed the calculation correctly, obtaining the correct answer.
