When `12.0g` of carbon (graphite)reacted with oxygen to form `CO` and `CO_(2)` at `25^(@)C` and constant pressure, `252 kJ` of heat was released and no carbon remained. If `Delta H_(f)^(0)(CO,g)= -110.5 kJ mol^(-1)` and `Delta H_(f)^(0)(CO_(2),g)= -393.5 kJ mol^(-1)`,calculate the mass of oxygen consumed.

Explanation

To solve the problem, we need to calculate the mass of oxygen consumed when 12.0 g of carbon (graphite) reacts with oxygen to form carbon monoxide (CO) and carbon dioxide (CO₂). We know the enthalpy changes for the formation of these compounds and the total heat released during the reaction.

### Step-by-Step Solution:

1. **Calculate Moles of Carbon:**
\[ \text{Moles of Carbon} = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{12.0 \, \text{g}}{12.0 \, \text{g/mol}} = 1 \, \text{mol} \]

2. **Write the Reactions and Their Enthalpy Changes:**
- For the formation of CO:
\[ \text{C (s)} + \frac{1}{2} \text{O}_2 (g) \rightarrow \text{CO} (g) \quad \Delta H_f^0 = -110.5 \, \text{kJ/mol} \]
- For the formation of CO₂:
\[ \text{C (s)} + \text{O}_2 (g) \rightarrow \text{CO}_2 (g) \quad \Delta H_f^0 = -393.5 \, \text{kJ/mol} \]

3. **Let x be the moles of carbon converted to CO:**
- Then, the moles of carbon converted to CO₂ will be \(1 - x\).

4. **Calculate the Total Heat Released:**
The total heat released can be expressed as:
\[ \text{Total Heat} = x \cdot (-110.5) + (1 - x) \cdot (-393.5) \]
Given that the total heat released is \( -252 \, \text{kJ} \):
\[ -252 = x \cdot (-110.5) + (1 - x) \cdot (-393.5) \]

5. **Expand and Rearrange the Equation:**
\[ -252 = -110.5x - 393.5 + 393.5x \]
\[ -252 + 393.5 = (393.5 - 110.5)x \]
\[ 141.5 = 283x \]
\[ x = \frac{141.5}{283} \approx 0.5 \, \text{mol} \]

6. **Calculate Moles of Carbon Converted to CO₂:**
\[ 1 - x = 1 - 0.5 = 0.5 \, \text{mol} \]

7. **Calculate Moles of Oxygen Consumed:**
- For the formation of CO, \(x\) moles of carbon consume \(\frac{x}{2}\) moles of oxygen.
- For the formation of CO₂, \(1 - x\) moles of carbon consume \(1 - x\) moles of oxygen.
\[ \text{Total moles of O}_2 = \frac{x}{2} + (1 - x) = \frac{0.5}{2} + 0.5 = 0.25 + 0.5 = 0.75 \, \text{mol} \]

8. **Calculate the Mass of Oxygen Consumed:**
\[ \text{Mass of O}_2 = \text{Moles} \times \text{Molar Mass} = 0.75 \, \text{mol} \times 32 \, \text{g/mol} = 24 \, \text{g} \]

### Final Answer:
The mass of oxygen consumed is **24 g**.