One litre of a mixture of CO and `CO_2` is passed through red-hot charcoal. The volume now becomes 1.6 litre. Find the composition of the mixture by volume.

Options

A. 0.35
B. 0.4
C. 0.5
D. 0.6

Answer

To solve the problem, we need to determine the composition of a mixture of carbon monoxide (CO) and carbon dioxide (CO₂) that is passed through red-hot charcoal, resulting in a change in volume. Here’s a step-by-step solution:

### Step 1: Define Variables
Let:
- \( x \) = volume of CO₂ in the initial mixture (in liters)
- Therefore, the volume of CO in the initial mixture = \( 1 - x \) liters (since the total volume is 1 liter)

### Step 2: Write the Reaction
When CO₂ is passed through red-hot charcoal, it reacts to form CO:
\[ \text{CO}_2 + \text{C} \rightarrow 2 \text{CO} \]
This means that for every 1 liter of CO₂ that reacts, it produces 2 liters of CO.

### Step 3: Calculate the Final Volume
After the reaction, the volume of CO produced from the CO₂ is:
- From \( x \) liters of CO₂, we get \( 2x \) liters of CO.

Now, the total volume after the reaction will be the remaining CO (from the initial mixture) plus the CO produced from CO₂:
- Remaining CO = \( 1 - x \) liters (initial CO)
- CO produced from CO₂ = \( 2x \) liters

Thus, the total volume after the reaction is:
\[ \text{Total Volume} = (1 - x) + 2x = 1 + x \]

### Step 4: Set Up the Equation
According to the problem, the total volume after the reaction is 1.6 liters:
\[ 1 + x = 1.6 \]

### Step 5: Solve for \( x \)
Now, we can solve for \( x \):
\[ x = 1.6 - 1 \]
\[ x = 0.6 \text{ liters} \]

### Step 6: Find the Volume of CO
Now that we have the volume of CO₂, we can find the volume of CO:
\[ \text{Volume of CO} = 1 - x = 1 - 0.6 = 0.4 \text{ liters} \]

### Conclusion
The composition of the mixture by volume is:
- Volume of CO₂ = 0.6 liters
- Volume of CO = 0.4 liters