When 1 L of `CO_2` is heated with graphite , the volume of the gases collected is 1.5 L. Calculate the number of moles of CO produced at STP

Options

A. `1/(11.2)`
B. `28/22.4`
C. `1/(22.4)`
D. `14/(22.4)`

Answer

To solve the problem, we need to analyze the reaction between carbon dioxide (CO₂) and graphite (C) to produce carbon monoxide (CO). The balanced chemical equation for this reaction is:

\[ \text{CO}_2 + \text{C} \rightarrow 2\text{CO} \]

### Step-by-Step Solution:

1. **Identify the Initial Conditions**:
- We start with 1 L of CO₂.
- The total volume of gases collected after the reaction is 1.5 L.

2. **Determine the Volume of CO Produced**:
- According to the balanced equation, 1 mole of CO₂ produces 2 moles of CO.
- If we denote the volume of CO produced as \( V_{CO} \), then the volume of CO will be \( 2 \times V_{CO₂} \).
- Since the total volume of gases collected is 1.5 L, we can express this as:
\[ V_{CO} + V_{CO₂ \text{ remaining}} = 1.5 \text{ L} \]

3. **Calculate the Remaining Volume of CO₂**:
- Let \( x \) be the volume of CO₂ that remains unreacted.
- From the reaction, we know that:
\[ V_{CO₂ \text{ remaining}} = 1 - x \]
- Substituting this into the total volume equation gives:
\[ V_{CO} + (1 - x) = 1.5 \]

4. **Express the Volume of CO in Terms of x**:
- From the balanced equation, we know that:
\[ V_{CO} = 2(1 - x) \]
- Therefore, substituting this into the total volume equation:
\[ 2(1 - x) + (1 - x) = 1.5 \]
- Simplifying this gives:
\[ 3 - 3x = 1.5 \]
- Rearranging gives:
\[ 3x = 3 - 1.5 = 1.5 \quad \Rightarrow \quad x = 0.5 \]

5. **Calculate the Volume of CO Produced**:
- Now substituting \( x = 0.5 \) back into the equation for CO:
\[ V_{CO} = 2(1 - 0.5) = 2(0.5) = 1 \text{ L} \]

6. **Calculate the Number of Moles of CO at STP**:
- At STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 L.
- Therefore, the number of moles of CO produced is:
\[ \text{Number of moles of CO} = \frac{\text{Volume of CO}}{22.4 \text{ L/mol}} = \frac{1 \text{ L}}{22.4 \text{ L/mol}} \approx 0.04464 \text{ moles} \]

### Final Answer:
The number of moles of CO produced at STP is approximately **0.04464 moles**.