To determine the conditions under which any gas shows maximum deviation from ideal gas behavior, we can follow these steps:
### Step 1: Understand Ideal Gas Behavior
The ideal gas behavior is described by the equation:
\[ PV = nRT \]
where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature.
### Step 2: Understand Real Gas Behavior
Real gases deviate from ideal behavior, and this deviation can be expressed using the compressibility factor \( Z \):
\[ Z = \frac{PV}{nRT} \]
For an ideal gas, \( Z = 1 \). For real gases, \( Z \) can be greater or less than 1 depending on the conditions.
### Step 3: Identify the Factors Affecting Deviation
The deviation from ideal behavior is influenced by:
- **Pressure**: At high pressures, gas molecules are forced closer together, leading to interactions that deviate from ideal behavior.
- **Temperature**: At low temperatures, gas molecules have lower kinetic energy, which can enhance intermolecular attractions and lead to deviations.
### Step 4: Analyze Conditions for Maximum Deviation
From the Van der Waals equation, which accounts for intermolecular forces and the volume occupied by gas molecules, we can conclude:
- At **high pressure**, the volume of the gas decreases significantly, leading to increased interactions between molecules.
- At **low temperature**, the kinetic energy of the gas molecules decreases, allowing these interactions to have a more pronounced effect.
### Step 5: Conclusion
Thus, the maximum deviation from ideal gas behavior occurs at:
- **High pressure**
- **Low temperature**
### Final Answer:
Any gas shows maximum deviation from ideal gas behavior at **high pressure and low temperature**.
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