Consider the van der Waals constants, a and b, for the following gases.
`{:("Gas","Ar","Ne","Kr","Xe"),(a//"(""atm dm"^(3)"mol"^(-2)")",1.3,0.2,5.1,4.1),(b//"("10^(-2)"dm"^(6)"mol"^(-1)")",3.2,1.7,1.0,5.0):}`
Which gas is expected to have the highest critical temperature?

Options

A. Ar
B. Ne
C. Kr
D. Xe

Explanation

To determine which gas among Argon (Ar), Neon (Ne), Krypton (Kr), and Xenon (Xe) is expected to have the highest critical temperature, we can use the van der Waals equation and the relationship between the van der Waals constants \(a\) and \(b\) and the critical temperature \(T_c\).

### Step-by-Step Solution:

1. **Understand the Critical Temperature Formula**:
The critical temperature \(T_c\) can be calculated using the formula:
\[ T_c = \frac{8a}{27Rb} \]
where \(R\) is the universal gas constant.

2. **Calculate the \( \frac{a}{b} \) Ratio for Each Gas**:
Since the critical temperature is directly proportional to \( \frac{a}{b} \), we will calculate this ratio for each gas.

- For Argon (Ar):
\[ \frac{a}{b} = \frac{1.3}{3.2} \approx 0.40625 \]

- For Neon (Ne):
\[ \frac{a}{b} = \frac{0.2}{1.7} \approx 0.11765 \]

- For Krypton (Kr):
\[ \frac{a}{b} = \frac{5.1}{1.0} = 5.1 \]

- For Xenon (Xe):
\[ \frac{a}{b} = \frac{4.1}{5.0} = 0.82 \]

3. **Compare the \( \frac{a}{b} \) Ratios**:
Now we will compare the calculated \( \frac{a}{b} \) values:
- Argon: \(0.40625\)
- Neon: \(0.11765\)
- Krypton: \(5.1\)
- Xenon: \(0.82\)

4. **Identify the Highest Value**:
The highest \( \frac{a}{b} \) ratio is for Krypton (5.1).

5. **Conclusion**:
Since Krypton has the highest \( \frac{a}{b} \) ratio, it is expected to have the highest critical temperature among the given gases.

### Final Answer:
**Krypton (Kr)** is expected to have the highest critical temperature.