At `5xx10^(5)` bar pressure, density of diamond and graphite are `3 g//c c` and `2g//c c ` respectively, at certain temperature T. `(1 L. atm=100 J)`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the problem
We need to find the difference between the change in internal energy (ΔU) and the change in enthalpy (ΔH) for the conversion of graphite to diamond under the given conditions.

### Step 2: Calculate the volumes of graphite and diamond
Given that the density of graphite is 2 g/cc and the density of diamond is 3 g/cc, and both have the same molar mass of 12 g/mol, we can calculate the volumes.

1. **Volume of Graphite (V1)**:
\[ V_1 = \frac{\text{mass}}{\text{density}} = \frac{12 \text{ g}}{2 \text{ g/cc}} = 6 \text{ cc} = 6 \text{ ml} \]

2. **Volume of Diamond (V2)**:
\[ V_2 = \frac{\text{mass}}{\text{density}} = \frac{12 \text{ g}}{3 \text{ g/cc}} = 4 \text{ cc} = 4 \text{ ml} \]

### Step 3: Calculate ΔV
Now we calculate the change in volume (ΔV):
\[ \Delta V = V_2 - V_1 = 4 \text{ ml} - 6 \text{ ml} = -2 \text{ ml} \]
Convert ml to liters:
\[ \Delta V = -2 \text{ ml} = -0.002 \text{ L} \]

### Step 4: Calculate PΔV
Given the pressure \( P = 5 \times 10^{-5} \) bar, we need to convert this to atm for our calculations.
1 bar = 0.98692 atm, so:
\[ P = 5 \times 10^{-5} \text{ bar} \times 0.98692 \text{ atm/bar} \approx 4.93 \times 10^{-5} \text{ atm} \]

Now calculate \( P \Delta V \):
\[ P \Delta V = (4.93 \times 10^{-5} \text{ atm}) \times (-0.002 \text{ L}) = -9.86 \times 10^{-8} \text{ L atm} \]

### Step 5: Convert L atm to Joules
Using the conversion \( 1 \text{ L atm} = 100 \text{ J} \):
\[ P \Delta V = -9.86 \times 10^{-8} \text{ L atm} \times 100 \text{ J/L atm} = -9.86 \times 10^{-6} \text{ J} \]

### Step 6: Relate ΔU and ΔH
Using the relation:
\[ \Delta H - \Delta U = P \Delta V \]
We can express ΔU - ΔH as:
\[ \Delta U - \Delta H = -P \Delta V \]
Thus:
\[ \Delta U - \Delta H = -(-9.86 \times 10^{-6} \text{ J}) = 9.86 \times 10^{-6} \text{ J} \]

### Step 7: Final Result
The final answer is:
\[ \Delta U - \Delta H = 9.86 \times 10^{-6} \text{ J} \]