A gas described by van der Waals equation

Options

A. behaves similar to an ideal gas in the limit of large molar volumes
B. behaves similar to an ideal gas in limit of large pressures
C. is characterized by van der Waals coefficients that are dependent on the identity of the gas but are independent of the temperature
D. has the pressure that is lower than the pressure exerted by the same gas behaving ideally

Explanation

To solve the question regarding the gas described by the van der Waals equation, we will analyze each of the given options step by step.

### Step 1: Understand the van der Waals equation
The van der Waals equation is given by:
\[ \left( P + \frac{a n^2}{V^2} \right) (V - nB) = nRT \]
where:
- \( P \) = pressure of the gas
- \( V \) = volume of the gas
- \( n \) = number of moles of the gas
- \( R \) = universal gas constant
- \( T \) = temperature
- \( a \) = van der Waals constant related to the attraction between gas molecules
- \( b \) = volume occupied by one mole of the gas molecules

### Step 2: Analyze Option 1
**Statement:** It behaves similar to an ideal gas in the limit of a large molar volume.

**Analysis:**
When the volume \( V \) is very large, the terms involving \( a \) and \( b \) become negligible. Thus, the equation simplifies to:
\[ PV = nRT \]
This indicates that the gas behaves ideally. Therefore, **Option 1 is correct.**

### Step 3: Analyze Option 2
**Statement:** It behaves similar to an ideal gas in the limit of a large pressure.

**Analysis:**
At high pressure, the volume occupied by the gas molecules becomes significant, and the attraction between particles cannot be neglected. The equation does not simplify to the ideal gas law. Thus, **Option 2 is incorrect.**

### Step 4: Analyze Option 3
**Statement:** Characterized by van der Waals coefficients that are dependent on the identity of a gas but are independent of the temperature.

**Analysis:**
The coefficients \( a \) and \( b \) are indeed dependent on the identity of the gas and do not change with temperature. Therefore, **Option 3 is correct.**

### Step 5: Analyze Option 4
**Statement:** The pressure is lower than the pressure exerted by the same gas behaving ideally.

**Analysis:**
In the van der Waals equation, the term \( a \) accounts for the attractive forces between molecules, which reduces the pressure compared to that predicted by the ideal gas law. Therefore, **Option 4 is correct.**

### Conclusion
The correct options are:
- Option 1: Correct
- Option 2: Incorrect
- Option 3: Correct
- Option 4: Correct

Thus, the gas described by the van der Waals equation behaves like an ideal gas under certain conditions and has characteristics defined by its coefficients.