In which one of the following, does the given amount of chlorine exert the least pressure in a vessel of capacity 1 d `m^(3)` at 273 K ?

Options

A. 0.0355g
B. 0.071g
C. `6.023 xx 10^(21) ` molecules
D. 0.02 mol

Answer

To solve the problem of determining in which scenario the given amount of chlorine exerts the least pressure in a vessel of capacity 1 dm³ at 273 K, we can follow these steps:

### Step 1: Understand the Ideal Gas Law
The ideal gas law is given by the equation:
\[ PV = nRT \]
Where:
- \( P \) = pressure exerted by the gas
- \( V \) = volume of the gas (1 dm³ in this case)
- \( n \) = number of moles of the gas
- \( R \) = universal gas constant
- \( T \) = absolute temperature (273 K)

### Step 2: Identify Constants
In this scenario, the volume (1 dm³) and temperature (273 K) are constant for all cases. Therefore, the pressure \( P \) is directly proportional to the number of moles \( n \):
\[ P \propto n \]

### Step 3: Calculate the Number of Moles for Each Case
We need to calculate the number of moles \( n \) for each option provided in the question.

1. **Case 1**: Given weight = 0.0355 g
\[ n = \frac{0.0355 \, \text{g}}{35.5 \, \text{g/mol}} = 0.001 \, \text{moles} \]

2. **Case 2**: Given weight = 0.071 g
\[ n = \frac{0.071 \, \text{g}}{35.5 \, \text{g/mol}} = 0.002 \, \text{moles} \]

3. **Case 3**: Given number of molecules = \( 6.023 \times 10^{21} \)
\[ n = \frac{6.023 \times 10^{21}}{6.023 \times 10^{23}} = 0.01 \, \text{moles} \]

4. **Case 4**: Given number of moles = 0.02 moles

### Step 4: Compare the Number of Moles
Now, we compare the calculated number of moles:
- Case 1: \( 0.001 \, \text{moles} \)
- Case 2: \( 0.002 \, \text{moles} \)
- Case 3: \( 0.01 \, \text{moles} \)
- Case 4: \( 0.02 \, \text{moles} \)

### Step 5: Determine the Least Pressure
Since pressure is directly proportional to the number of moles, the option with the least number of moles will exert the least pressure. From our calculations, Case 1 has the least number of moles (0.001 moles).

### Conclusion
Thus, the answer to the question is that the given amount of chlorine exerts the least pressure in Case 1.