Which equation will explain the nature of PV versus P curve for `CO_(2)` gas at moderately low pressure?

Options

A. `PV = RT + Pb`
B. `PV = RT + a//V`
C. `PV = RT – a//V`
D. PV = RT - aV

Explanation

To determine the equation that explains the nature of the PV versus P curve for CO₂ gas at moderately low pressure, we can follow these steps:

### Step 1: Understand the Real Gas Equation
The real gas equation is given by:
\[ P + \frac{AN^2}{V^2}(V - NB) = nRT \]
where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = universal gas constant
- \( T \) = temperature
- \( A \) and \( B \) = constants specific to the gas

### Step 2: Analyze Conditions at Moderately Low Pressure
At moderately low pressure, the volume \( V \) becomes sufficiently large. This allows us to neglect the term \( \frac{AN^2}{V^2} \) because it becomes very small compared to the other terms.

### Step 3: Simplify the Equation
Since \( V \) is large, we can simplify the equation by neglecting the \( \frac{AN^2}{V^2} \) term:
\[ P + \frac{AN^2}{V^2} \cdot V \approx nRT \]
This simplifies to:
\[ P \approx nRT \]

### Step 4: Further Simplification
Next, we can also neglect the \( NB \) term because at low pressure, the volume \( V \) is large enough that \( V - NB \) can be approximated as \( V \). Thus, we can rewrite the equation as:
\[ P + \frac{AN^2}{V^2} \cdot V = nRT \]

### Step 5: Rearranging the Equation
Now, if we take \( n = 1 \) mole, the equation simplifies to:
\[ PV + \frac{A}{V} = RT \]
Rearranging gives us:
\[ PV = RT - \frac{A}{V} \]

### Conclusion
This final equation \( PV = RT - \frac{A}{V} \) describes the relationship between pressure \( P \), volume \( V \), and temperature \( T \) for CO₂ gas at moderately low pressure. This indicates that as pressure increases, the volume effect becomes significant due to the term \( -\frac{A}{V} \).

### Final Answer
The equation that explains the nature of the PV versus P curve for CO₂ gas at moderately low pressure is:
\[ PV = RT - \frac{A}{V} \]

---