At 760 torr pressure and `20^(@)C` tempreature , 1 L of water dissolves 0.04 gm of pure oxygen or 0.02 gm of pure nitrogen. Assuming that dry air is compound of 20% oxygen and 80% nitrogen (by volume), the masses (in g/L) of oxygen and nitrogen dissolved by 1 L of water at `20^(@)C` exposed to air at a total pressur of 706 torr are respectively :

Options

A. 0.008, 0.016
B. 0.016, 0.008
C. 0.16, 0.08
D. 0.04, 0.02

Answer

To solve the problem, we need to determine the masses of oxygen and nitrogen that can be dissolved in 1 L of water at a total pressure of 706 torr, given that at 760 torr, 1 L of water can dissolve 0.04 g of oxygen and 0.02 g of nitrogen.

### Step-by-Step Solution:

1. **Understand the relationship between pressure and solubility**: According to Henry's Law, the solubility of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid.

2. **Calculate the partial pressures of oxygen and nitrogen in dry air**:
- Dry air consists of 20% oxygen and 80% nitrogen by volume.
- The partial pressure of oxygen (P_O2) at 706 torr is:
\[ P_{O2} = 0.20 \times 706 \text{ torr} = 141.2 \text{ torr} \]
- The partial pressure of nitrogen (P_N2) at 706 torr is:
\[ P_{N2} = 0.80 \times 706 \text{ torr} = 564.8 \text{ torr} \]

3. **Determine the solubility of oxygen at 706 torr**:
- At 760 torr, 1 L of water dissolves 0.04 g of oxygen.
- Using Henry's Law, the mass of oxygen dissolved at 706 torr can be calculated as:
\[ \text{Mass of } O_2 = \left(\frac{0.04 \text{ g}}{760 \text{ torr}}\right) \times 141.2 \text{ torr} = 0.0074 \text{ g} \]

4. **Determine the solubility of nitrogen at 706 torr**:
- At 760 torr, 1 L of water dissolves 0.02 g of nitrogen.
- Using Henry's Law, the mass of nitrogen dissolved at 706 torr can be calculated as:
\[ \text{Mass of } N_2 = \left(\frac{0.02 \text{ g}}{760 \text{ torr}}\right) \times 564.8 \text{ torr} = 0.0149 \text{ g} \]

5. **Final results**:
- The mass of oxygen dissolved in 1 L of water at 706 torr is approximately 0.0074 g.
- The mass of nitrogen dissolved in 1 L of water at 706 torr is approximately 0.0149 g.

### Summary of Results:
- Mass of oxygen dissolved: **0.0074 g/L**
- Mass of nitrogen dissolved: **0.0149 g/L**