Question

fluorine gas and water vapor react to form hydrogen fluoride gas and oxygen. what volume of oxygen would be produced by this reaction if 9.78 cm³ of fluorine were consumed? also, be sure your answer has a unit symbol, and is rounded to 3 significant digits.

Explanation:

To solve this problem, we first need to determine the balanced chemical equation for the reaction between fluorine gas ($\ce{F_2}$) and water vapor ($\ce{H_2O}$). The reaction is:

$$\ce{2F_2(g) + 2H_2O(g) -> 4HF(g) + O_2(g)}$$

Step 1: Analyze the stoichiometry of the reaction

From the balanced equation, the mole ratio (and thus the volume ratio, since all gases are at the same temperature and pressure) of $\ce{F_2}$ to $\ce{O_2}$ is $2:1$. This means the volume of $\ce{O_2}$ produced is $\frac{1}{2}$ the volume of $\ce{F_2}$ consumed.

Step 2: Calculate the volume of $\ce{O_2}$ produced

Given the volume of $\ce{F_2}$ consumed is $9.78\ \text{cm}^3$, we use the volume ratio:

$$\text{Volume of } \ce{O_2} = \frac{1}{2} \times \text{Volume of } \ce{F_2}$$

Substitute the given volume:

$$\text{Volume of } \ce{O_2} = \frac{1}{2} \times 9.78\ \text{cm}^3 = 4.89\ \text{cm}^3$$

Answer:

$4.89\ \text{cm}^3$