The solubility of common salt is `36.0` g in 100 g of water at `20^(@)` C . If systems I , II and III contains `20.0 , 18.0 "and" 15.0` of the salt added to `50.0` g of water in each case , the vapour pressures would be in the order :

Options

A. `I lt II lt III `
B. `I gt II gt III`
C. `I = II gt III`
D. `I = II lt III`

Answer

To solve the problem, we need to analyze the vapor pressures of three different systems with varying amounts of common salt (sodium chloride) dissolved in water. The solubility of common salt is given as 36.0 g in 100 g of water at 20°C.

### Step-by-Step Solution:

1. **Understanding Saturation**:
The solubility of common salt is 36.0 g in 100 g of water. This means that in 50 g of water, the maximum amount of salt that can dissolve is half of 36.0 g, which is:
\[ \text{Maximum salt in 50 g water} = \frac{36.0 \, \text{g}}{2} = 18.0 \, \text{g} \]

2. **Analyzing the Systems**:
- **System I**: Contains 20.0 g of salt in 50.0 g of water.
- **System II**: Contains 18.0 g of salt in 50.0 g of water.
- **System III**: Contains 15.0 g of salt in 50.0 g of water.

3. **Determining Saturation**:
- **System I** (20.0 g of salt): This exceeds the solubility limit (18.0 g), so it will be a saturated solution with some undissolved salt.
- **System II** (18.0 g of salt): This is exactly at the solubility limit, hence it is also a saturated solution.
- **System III** (15.0 g of salt): This is below the solubility limit, so it is an unsaturated solution.

4. **Effect on Vapor Pressure**:
The presence of salt in water lowers the vapor pressure of the solution due to the colligative properties. The more solute (salt) present, the lower the vapor pressure:
- **System I**: Has the highest amount of salt (20.0 g), leading to the lowest vapor pressure.
- **System II**: Has 18.0 g of salt, leading to a vapor pressure slightly higher than System I.
- **System III**: Has the least amount of salt (15.0 g), leading to the highest vapor pressure among the three systems.

5. **Ordering the Vapor Pressures**:
Based on the analysis, we can order the vapor pressures from highest to lowest:
\[ \text{Vapor Pressure Order: III > II = I} \]

### Final Answer:
The vapor pressures would be in the order: **III > II = I**.