Some older emergency oxygen masks contains potassium superoxide `KO_2` which reacts with `CO_2` and water present in exhaled air to produce oxygen according to the given equation. If a person exhales `0.667 g` of `CO_2` per minute, how many gram of `KO_2` are consumed in `5.0` minutes ?

Options

A. 10.7
B. 0.0757
C. 1.07
D. 5.38

Answer

To solve the problem step by step, we need to determine how much potassium superoxide (KO₂) is consumed when a person exhales a certain amount of carbon dioxide (CO₂) over a period of time.

### Step 1: Write the balanced chemical equation
The reaction between potassium superoxide (KO₂), carbon dioxide (CO₂), and water (H₂O) produces potassium bicarbonate (KHCO₃) and oxygen (O₂). The balanced equation is:

\[ 4 \, KO_2 + 2 \, CO_2 + 2 \, H_2O \rightarrow 4 \, KHCO_3 + O_2 \]

### Step 2: Calculate the total amount of CO₂ exhaled in 5 minutes
Given that a person exhales 0.667 g of CO₂ per minute, the total amount of CO₂ exhaled in 5 minutes can be calculated as follows:

\[ \text{Total CO}_2 = 0.667 \, \text{g/min} \times 5 \, \text{min} = 3.335 \, \text{g} \]

### Step 3: Calculate the number of moles of CO₂ exhaled
To find the number of moles of CO₂, we use the molar mass of CO₂, which is approximately 44 g/mol. The number of moles can be calculated using the formula:

\[ \text{Moles of CO}_2 = \frac{\text{mass of CO}_2}{\text{molar mass of CO}_2} = \frac{3.335 \, \text{g}}{44 \, \text{g/mol}} \approx 0.0758 \, \text{moles} \]

### Step 4: Determine the moles of KO₂ consumed
From the balanced equation, we see that 2 moles of CO₂ react with 4 moles of KO₂. Therefore, the stoichiometric ratio is:

\[ \frac{4 \, \text{moles KO}_2}{2 \, \text{moles CO}_2} = 2 \, \text{moles KO}_2 \text{ per mole CO}_2 \]

Thus, the moles of KO₂ consumed can be calculated as follows:

\[ \text{Moles of KO}_2 = 2 \times \text{Moles of CO}_2 = 2 \times 0.0758 \approx 0.1516 \, \text{moles} \]

### Step 5: Calculate the mass of KO₂ consumed
Now, we need to find the mass of KO₂ consumed. The molar mass of KO₂ is approximately 71 g/mol. The mass can be calculated using:

\[ \text{Mass of KO}_2 = \text{Moles of KO}_2 \times \text{Molar mass of KO}_2 = 0.1516 \, \text{moles} \times 71 \, \text{g/mol} \approx 10.75 \, \text{g} \]

### Final Answer
The mass of KO₂ consumed in 5 minutes is approximately **10.75 grams**.

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