Two reactions are given below :
`C_("(graphite)")+O_(2(g))rarrCO_(2(g)),DeltaH=-393.7kJ`
`C_("(diamond)")rarrC_("(graphite)"),DeltaH=-2.1kJ`
What quantity of diamond will give 800 kJ of heat on burning ?

Options

A. a.24.25 g
B. b.15.24 g
C. c.2 g
D. d.12.12 g

Explanation

To solve the problem, we need to determine how much diamond (in grams) will produce 800 kJ of heat when burned. We will use the provided thermodynamic equations and their enthalpy changes.

### Step-by-Step Solution:

1. **Write the combustion reaction for diamond:**
The combustion of diamond can be represented as:
\[ C_{(diamond)} + O_2(g) \rightarrow CO_2(g) \]
We need to find the enthalpy change (ΔH) for this reaction.

2. **Use the provided reactions:**
We have two reactions:
- \( C_{(graphite)} + O_2(g) \rightarrow CO_2(g), \Delta H = -393.7 \, \text{kJ} \)
- \( C_{(diamond)} \rightarrow C_{(graphite)}, \Delta H = -2.1 \, \text{kJ} \)

3. **Combine the reactions:**
To find the ΔH for the combustion of diamond, we can add the two reactions:
- First, we reverse the second reaction to represent the conversion of graphite back to diamond:
\[ C_{(graphite)} \rightarrow C_{(diamond)}, \Delta H = +2.1 \, \text{kJ} \]
- Now, adding the two reactions:
\[ C_{(diamond)} + O_2(g) \rightarrow CO_2(g) \quad \text{(from combustion)} \]
\[ C_{(graphite)} \rightarrow C_{(diamond)} \quad \text{(reversed)} \]
The overall reaction becomes:
\[ C_{(diamond)} + O_2(g) \rightarrow CO_2(g) \]
The ΔH for this combined reaction is:
\[ \Delta H = -393.7 \, \text{kJ} + 2.1 \, \text{kJ} = -391.6 \, \text{kJ} \]

4. **Determine the amount of diamond needed for 800 kJ:**
We know that burning 12 g of carbon (as graphite) releases 393.7 kJ. We need to find out how much diamond will release 800 kJ.
Using the relationship:
\[ \frac{12 \, \text{g}}{391.6 \, \text{kJ}} = \frac{x \, \text{g}}{800 \, \text{kJ}} \]
Cross-multiplying gives:
\[ x = \frac{12 \, \text{g} \times 800 \, \text{kJ}}{391.6 \, \text{kJ}} \]

5. **Calculate the value of x:**
\[ x = \frac{9600}{391.6} \approx 24.5 \, \text{g} \]

### Final Answer:
The quantity of diamond that will give 800 kJ of heat on burning is approximately **24.5 grams**.