What volume of air containing 21% oxygen (by volume) is required to completely burn 1 kg of carbon containing 100% combustible substances?

Answer

To solve the problem of determining the volume of air containing 21% oxygen required to completely burn 1 kg of carbon, we can follow these steps:

### Step 1: Write the combustion reaction of carbon
The combustion of carbon can be represented by the following chemical equation:
\[ \text{C (s)} + \text{O}_2 \text{(g)} \rightarrow \text{CO}_2 \text{(g)} \]

### Step 2: Determine the amount of carbon in grams
Since the problem states that we have 1 kg of carbon, we convert this to grams:
\[ 1 \text{ kg} = 1000 \text{ grams} \]

### Step 3: Calculate the moles of carbon
The molar mass of carbon (C) is 12 g/mol. To find the number of moles of carbon in 1000 grams, we use the formula:
\[ \text{Moles of C} = \frac{\text{mass of C}}{\text{molar mass of C}} = \frac{1000 \text{ g}}{12 \text{ g/mol}} \]
Calculating this gives:
\[ \text{Moles of C} = 83.33 \text{ moles} \]

### Step 4: Determine the moles of oxygen required
From the balanced equation, we see that 1 mole of carbon requires 1 mole of oxygen (O2) for complete combustion. Therefore, the moles of O2 required will also be:
\[ \text{Moles of O}_2 = 83.33 \text{ moles} \]

### Step 5: Calculate the volume of oxygen at STP
At standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 liters. Thus, the volume of oxygen needed can be calculated as follows:
\[ \text{Volume of O}_2 = \text{Moles of O}_2 \times 22.4 \text{ L/mol} \]
Calculating this gives:
\[ \text{Volume of O}_2 = 83.33 \times 22.4 = 1866.592 \text{ liters} \]

### Step 6: Calculate the volume of air required
Since the air contains 21% oxygen by volume, we can set up a proportion to find the total volume of air needed:
\[ \text{Volume of air} = \frac{\text{Volume of O}_2}{\text{Percentage of O}_2} = \frac{1866.592 \text{ L}}{0.21} \]
Calculating this gives:
\[ \text{Volume of air} = 8885.9 \text{ liters} \]

### Final Answer
Thus, the volume of air required to completely burn 1 kg of carbon is approximately:
\[ 8885.9 \text{ liters} \]