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 of calculating the number of moles of CO produced when 1 L of CO₂ is heated with graphite, we can follow these steps:

### Step 1: Understand the Reaction
When carbon dioxide (CO₂) is heated with graphite (carbon), it can produce carbon monoxide (CO) according to the reaction:
\[ \text{CO}_2 + \text{C} \rightarrow 2 \text{CO} \]

### Step 2: Set Up the Initial Conditions
We start with 1 L of CO₂. According to the problem, after the reaction, the total volume of gases collected is 1.5 L.

### Step 3: Define Variables
Let \( x \) be the volume of CO₂ that reacts. Since 1 L of CO₂ is present initially, the volume of CO₂ left after the reaction will be \( 1 - x \) L.

From the stoichiometry of the reaction, for every 1 L of CO₂ that reacts, 2 L of CO is produced. Therefore, the volume of CO produced will be \( 2x \) L.

### Step 4: Write the Volume Equation
The total volume of gases after the reaction is the sum of the remaining CO₂ and the produced CO:
\[ (1 - x) + 2x = 1.5 \]

### Step 5: Simplify the Equation
Now, simplify the equation:
\[ 1 - x + 2x = 1.5 \]
\[ 1 + x = 1.5 \]

### Step 6: Solve for \( x \)
Subtract 1 from both sides:
\[ x = 1.5 - 1 \]
\[ x = 0.5 \, \text{L} \]

### Step 7: Calculate the Volume of CO Produced
Now, we can find the volume of CO produced:
\[ \text{Volume of CO} = 2x = 2 \times 0.5 = 1 \, \text{L} \]

### Step 8: Calculate the Number of Moles of CO at STP
At standard temperature and pressure (STP), 1 mole of gas occupies 22.4 L. Therefore, the number of moles of CO produced can be calculated as:
\[ \text{Number of moles of CO} = \frac{\text{Volume of CO}}{22.4} = \frac{1 \, \text{L}}{22.4 \, \text{L/mol}} \]

### Step 9: Final Calculation
Calculating the number of moles:
\[ \text{Number of moles of CO} = \frac{1}{22.4} \approx 0.04464 \, \text{moles} \]

### Conclusion
The number of moles of CO produced at STP is approximately 0.04464 moles.

---