The heat of transition `(Delta H_(t))` of graphite into diamond would be, where
C (graphite) `+O_(2)(g)to CO_(2)(g) , Delta H =` x kJ
C (diamond) `+O_(2)(g)to CO_(2)(g) , Delta H =` y kJ

Options

A. `x_(1) + x_(2)`
B. `x_(2) - x_(1)`
C. `x_(1) - x_(2)`
D. `x_(1)x_(2)`

Answer

To find the heat of transition (ΔH_t) of graphite into diamond, we will use the given combustion reactions of both graphite and diamond. Here are the steps to derive the solution:

### Step 1: Write the Combustion Reactions
We have two combustion reactions:
1. For graphite:
\[ C_{(graphite)} + O_2(g) \rightarrow CO_2(g) \quad \Delta H = x \text{ kJ} \]
2. For diamond:
\[ C_{(diamond)} + O_2(g) \rightarrow CO_2(g) \quad \Delta H = y \text{ kJ} \]

### Step 2: Identify the Enthalpy Changes
Let:
- ΔH_1 = x (for graphite)
- ΔH_2 = y (for diamond)

### Step 3: Reverse the Reaction for Diamond
To find the heat of transition from graphite to diamond, we need to reverse the combustion reaction for diamond:
\[ CO_2(g) \rightarrow C_{(diamond)} + O_2(g) \quad \Delta H = -y \text{ kJ} \]

### Step 4: Combine the Reactions
Now we can combine the two reactions:
1. Graphite combustion:
\[ C_{(graphite)} + O_2(g) \rightarrow CO_2(g) \quad \Delta H = x \]
2. Reversed diamond combustion:
\[ CO_2(g) \rightarrow C_{(diamond)} + O_2(g) \quad \Delta H = -y \]

### Step 5: Write the Overall Reaction
Adding these two reactions gives:
\[ C_{(graphite)} + O_2(g) + CO_2(g) \rightarrow CO_2(g) + C_{(diamond)} + O_2(g) \]
The O_2 and CO_2 on both sides cancel out, leading to:
\[ C_{(graphite)} \rightarrow C_{(diamond)} \]

### Step 6: Calculate the Enthalpy of Transition
The overall enthalpy change (ΔH_t) for the transition from graphite to diamond is:
\[ \Delta H_t = x - y \]

### Final Answer
Thus, the heat of transition (ΔH_t) of graphite into diamond is:
\[ \Delta H_t = x - y \text{ kJ} \]

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