Calculate change in internal energy if `Delta H= - 92.2 kJ, P = 40` atm and `Delta V = - 11`.

Options

A. a. `- 42 kJ`
B. b. `-88 kJ`
C. c. `+88 kJ`
D. d. `+42 kJ`

Explanation

To calculate the change in internal energy (ΔU) given the change in enthalpy (ΔH), pressure (P), and change in volume (ΔV), we can use the following relationship:

\[ \Delta H = \Delta U + P \Delta V \]

From this equation, we can rearrange it to solve for ΔU:

\[ \Delta U = \Delta H - P \Delta V \]

### Step-by-Step Solution:

1. **Identify the given values:**
- ΔH = -92.2 kJ
- P = 40 atm
- ΔV = -1 L (Note: The problem states ΔV as -11, but the transcript indicates it is -1 L.)

2. **Convert ΔH to the same units as PΔV:**
- Since P is in atm and ΔV is in liters, we need to convert ΔH from kJ to joules for consistency.
- 1 kJ = 1000 J, thus:
\[ \Delta H = -92.2 \text{ kJ} = -92200 \text{ J} \]

3. **Calculate PΔV:**
- PΔV = (40 atm) × (-1 L)
- We need to convert atm·L to joules. The conversion factor is:
\[ 1 \text{ atm·L} = 101.325 \text{ J} \]
- Therefore:
\[ P \Delta V = 40 \text{ atm} \times (-1 \text{ L}) = -40 \text{ atm·L} = -40 \times 101.325 \text{ J} = -4053 \text{ J} \]

4. **Substitute the values into the ΔU equation:**
\[ \Delta U = \Delta H - P \Delta V \]
\[ \Delta U = -92200 \text{ J} - (-4053 \text{ J}) = -92200 \text{ J} + 4053 \text{ J} \]
\[ \Delta U = -88147 \text{ J} \]

5. **Convert ΔU back to kJ:**
\[ \Delta U = -88.147 \text{ kJ} \approx -88.15 \text{ kJ} \]

6. **Final Answer:**
\[ \Delta U \approx -88 \text{ kJ} \]

### Summary:
The change in internal energy (ΔU) is approximately -88 kJ.