Calculate difference between `DeltaH` and `DeltaU` when 1 mole of grey tin `(` density `=5.75g//cm^(3))` changes to white tin `(` density `=7.31g//cm^(3))` at 10 bar . ( at `298 K, DeltaH=+2.1 kJ,` at `wt=119` of `Sn)`

Options

A. `-8.8J`
B. `-4.4J`
C. `-2.2J`
D. `4.4J`

Explanation

To calculate the difference between ΔH (enthalpy change) and ΔU (internal energy change) when 1 mole of grey tin changes to white tin at a specific pressure and temperature, we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**:
The relationship between ΔH and ΔU is given by the equation:
\[ \Delta H = \Delta U + \Delta(PV) \]
Therefore, we can express the difference as:
\[ \Delta H - \Delta U = \Delta(PV) \]

2. **Convert Pressure to Standard Units**:
The pressure is given as 10 bar. To convert this to pascals (Pa), we use the conversion:
\[ 1 \text{ bar} = 10^5 \text{ Pa} \]
Thus,
\[ P = 10 \text{ bar} = 10 \times 10^5 \text{ Pa} = 10^6 \text{ Pa} \]

3. **Calculate the Volume Change (ΔV)**:
We need to find the volumes of grey tin (V1) and white tin (V2) using the densities provided.

- **Density of Grey Tin**: \( \rho_1 = 5.75 \text{ g/cm}^3 \)
- **Density of White Tin**: \( \rho_2 = 7.31 \text{ g/cm}^3 \)
- **Mass of Tin**: \( m = 119 \text{ g} \)

The volume can be calculated using the formula:
\[ V = \frac{m}{\rho} \]

- For grey tin (V1):
\[ V_1 = \frac{119 \text{ g}}{5.75 \text{ g/cm}^3} = 20.69565 \text{ cm}^3 \]

- For white tin (V2):
\[ V_2 = \frac{119 \text{ g}}{7.31 \text{ g/cm}^3} = 16.27379 \text{ cm}^3 \]

4. **Convert Volumes to m³**:
Since 1 cm³ = \( 10^{-6} \) m³, we convert the volumes:
- \( V_1 = 20.69565 \times 10^{-6} \text{ m}^3 \)
- \( V_2 = 16.27379 \times 10^{-6} \text{ m}^3 \)

5. **Calculate ΔV**:
\[ \Delta V = V_2 - V_1 = (16.27379 - 20.69565) \times 10^{-6} \text{ m}^3 = -4.42186 \times 10^{-6} \text{ m}^3 \]

6. **Calculate Δ(PV)**:
Now, we can calculate Δ(PV):
\[ \Delta(PV) = P \Delta V = 10^6 \text{ Pa} \times (-4.42186 \times 10^{-6} \text{ m}^3) = -4.42186 \text{ J} \]

7. **Final Calculation of ΔH - ΔU**:
\[ \Delta H - \Delta U = -4.42186 \text{ J} \approx -4.4 \text{ J} \]

### Conclusion:
The difference between ΔH and ΔU when 1 mole of grey tin changes to white tin at 10 bar is approximately \(-4.4 \text{ J}\).