Consider the following statements If th van der Waals' parameters of two gases are given as
`{:(,a//dm^(6)"bar"mol^(-2),b//dm^(3)mol^(-1),,),(GasA,6.5,0.056,,),(GasB,18.0,0.011,,):}`
then which of the following statements is//are correct ? .

Options

A. 1 alone
B. 1 and 2
C. 1, 2 and 3
D. 2 and 3

Explanation

To solve the problem regarding the van der Waals' parameters of two gases (Gas A and Gas B), we need to analyze the critical volume, critical pressure, and critical temperature based on the given parameters.

### Given Data:
- For Gas A:
- \( a = 6.5 \, \text{dm}^6 \text{bar} \text{mol}^{-2} \)
- \( b = 0.056 \, \text{dm}^3 \text{mol}^{-1} \)

- For Gas B:
- \( a = 18.0 \, \text{dm}^6 \text{bar} \text{mol}^{-2} \)
- \( b = 0.011 \, \text{dm}^3 \text{mol}^{-1} \)

### Step 1: Analyze Critical Volume
The critical volume (\( V_c \)) is related to the van der Waals parameter \( b \) by the formula:
\[ V_c = 3b \]
- For Gas A:
\[ V_{cA} = 3 \times 0.056 = 0.168 \, \text{dm}^3 \]
- For Gas B:
\[ V_{cB} = 3 \times 0.011 = 0.033 \, \text{dm}^3 \]

**Comparison**:
Since \( V_{cA} > V_{cB} \), we conclude that the critical volume of Gas A is greater than that of Gas B.

### Step 2: Analyze Critical Pressure
The critical pressure (\( P_c \)) is given by:
\[ P_c = \frac{a}{27b^2} \]
- For Gas A:
\[ P_{cA} = \frac{6.5}{27 \times (0.056)^2} = \frac{6.5}{27 \times 0.003136} \approx 81.5 \, \text{bar} \]
- For Gas B:
\[ P_{cB} = \frac{18.0}{27 \times (0.011)^2} = \frac{18.0}{27 \times 0.000121} \approx 5,500 \, \text{bar} \]

**Comparison**:
Since \( P_{cB} > P_{cA} \), we conclude that the critical pressure of Gas B is greater than that of Gas A.

### Step 3: Analyze Critical Temperature
The critical temperature (\( T_c \)) is given by:
\[ T_c = \frac{8a}{27Rb} \]
Assuming \( R \) (the gas constant) is constant, we can compare \( T_c \) directly using \( \frac{a}{b} \):
- For Gas A:
\[ \frac{a}{b} = \frac{6.5}{0.056} \approx 116.07 \]
- For Gas B:
\[ \frac{a}{b} = \frac{18.0}{0.011} \approx 1636.36 \]

**Comparison**:
Since \( \frac{a}{b} \) for Gas B is greater than that for Gas A, we conclude that the critical temperature of Gas B is greater than that of Gas A.

### Conclusion:
- Critical Volume: \( V_{cA} > V_{cB} \) (Statement 1 is incorrect)
- Critical Pressure: \( P_{cB} > P_{cA} \) (Statement 2 is correct)
- Critical Temperature: \( T_{cB} > T_{cA} \) (Statement 3 is correct)

### Final Answer:
- The correct statements are: **Statement 2 and Statement 3 are correct.**