Question

On passing silent electric discharge through oxygen in an ozonizer, 5.5 mol % of oxygen is converted to ozone. How many moles of O$_2$ and O$_3$ result when 35 moles of O$_2$ is originally present?

• A. 33.0
• B. 34.4
• C. 35.0
• D. 31.8
• E. 31.0

Hint:

In gas conversion problems, always subtract the reacted moles from the initial reactant amount and use the stoichiometric ratios to find the product moles before summing them up.

Answer 1

The Correct Option is B

Concept: The conversion of oxygen to ozone is represented by the balanced chemical equation: $$3O_2 \rightarrow 2O_3$$ This stoichiometry indicates that 3 moles of oxygen produce 2 moles of ozone. The percentage conversion tells us how much of the initial reactant actually undergoes this change.

Step 1: {Calculate the number of moles of O$_2$ converted.}
The total initial moles of $O_2$ is $35$. Given that $5.5\%$ is converted: $$\text{Moles of } O_2 \text{ converted} = 35 \times \frac{5.5}{100} = 1.925 \text{ moles}$$

Step 2: {Calculate the remaining moles of O$_2$.}
The moles of oxygen that did not react is the initial amount minus the amount converted: $$\text{Remaining } O_2 = 35 - 1.925 = 33.075 \text{ moles}$$

Step 3: {Calculate the moles of O$_3$ produced.}
From the stoichiometry $3O_2 \rightarrow 2O_3$, $3$ moles of $O_2$ give $2$ moles of $O_3$. Thus, $1.925$ moles of $O_2$ produce: $$\text{Moles of } O_3 = 1.925 \times \frac{2}{3} \approx 1.283 \text{ moles}$$

Step 4: {Find the total resulting moles.}
Total resulting moles = Remaining $O_2$ + Produced $O_3$: $$\text{Total moles} = 33.075 + 1.283 = 34.358 \approx 34.4 \text{ moles}$$