The heat of combustion of carbon to `CO_(2)`is`-395.5kJ//mol`.The heat released upon the formation of`35.2g` of`CO_(2)`from carbon and oxygen gas is

Options

A. `-630kJ`
B. `-3.15kJ`
C. `-315kJ`
D. `+315kJ`

Answer

To solve the problem of calculating the heat released upon the formation of 35.2 g of CO₂ from carbon and oxygen gas, we can follow these steps:

### Step 1: Understand the Reaction
The combustion of carbon (C) in the presence of oxygen (O₂) produces carbon dioxide (CO₂). The balanced chemical equation for this reaction is:
\[ \text{C (s)} + \text{O}_2 \text{(g)} \rightarrow \text{CO}_2 \text{(g)} \]

### Step 2: Identify the Heat of Combustion
The heat of combustion of carbon to CO₂ is given as -395.5 kJ/mol. This means that when 1 mole of carbon combusts, it releases 395.5 kJ of energy.

### Step 3: Calculate the Molar Mass of CO₂
The molar mass of CO₂ can be calculated as follows:
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol
- Therefore, the molar mass of CO₂ = 12 + (16 × 2) = 44 g/mol

### Step 4: Calculate the Number of Moles of CO₂
To find the number of moles of CO₂ in 35.2 g, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
\[ \text{Number of moles of CO}_2 = \frac{35.2 \text{ g}}{44 \text{ g/mol}} \]

### Step 5: Calculate the Heat Released
Now, we can calculate the heat released for the formation of 35.2 g of CO₂:
- The heat released for 1 mole of CO₂ is -395.5 kJ.
- For the number of moles calculated in Step 4, the heat released can be calculated as:
\[ \text{Heat released} = \text{Number of moles} \times \text{Heat of combustion} \]
\[ \text{Heat released} = \left(\frac{35.2}{44}\right) \times (-395.5) \]

### Step 6: Final Calculation
Now, we can perform the calculation:
1. Calculate the number of moles:
\[ \text{Number of moles of CO}_2 = \frac{35.2}{44} \approx 0.8 \text{ moles} \]
2. Calculate the heat released:
\[ \text{Heat released} = 0.8 \times (-395.5) \approx -316.4 \text{ kJ} \]

### Conclusion
The heat released upon the formation of 35.2 g of CO₂ is approximately -316.4 kJ. Since the options provided may round this value, the closest answer is -315 kJ.

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