The lowest concentration of oxygen that can support aquatic life is about `1.3xx10^(-4)mol//L` . The partial pressure of oxygen is `0.21 atm` at sea level.
What is the lowest partial pressure of oxygen that can support life ?
`k_(H)(O_(2))=11.3xx10^(-3)mol//L.atm`

Options

A. `0.02 atm`
B. `0.10 atm`
C. `1.0 atm`
D. `10 atm`

Explanation

To find the lowest partial pressure of oxygen that can support aquatic life, we can use Henry's Law, which states that the concentration of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid. The formula we will use is:

\[ P = \frac{S}{k_H} \]

Where:
- \( P \) is the partial pressure of the gas,
- \( S \) is the concentration of the gas in the liquid,
- \( k_H \) is the Henry's law constant for the gas.

### Step 1: Identify the given values
- The lowest concentration of oxygen that can support aquatic life, \( S = 1.3 \times 10^{-4} \, \text{mol/L} \)
- The Henry's law constant for oxygen, \( k_H = 11.3 \times 10^{-3} \, \text{mol/L.atm} \)

### Step 2: Substitute the values into the formula
Using the formula \( P = \frac{S}{k_H} \):

\[ P = \frac{1.3 \times 10^{-4} \, \text{mol/L}}{11.3 \times 10^{-3} \, \text{mol/L.atm}} \]

### Step 3: Perform the calculation
Calculating the above expression:

\[ P = \frac{1.3 \times 10^{-4}}{11.3 \times 10^{-3}} \]

\[ P = \frac{1.3}{11.3} \times 10^{-4 + 3} \]

\[ P = \frac{1.3}{11.3} \times 10^{-1} \]

Calculating \( \frac{1.3}{11.3} \):

\[ \frac{1.3}{11.3} \approx 0.115 \]

Now, multiplying by \( 10^{-1} \):

\[ P \approx 0.115 \times 0.1 \]

\[ P \approx 0.0115 \, \text{atm} \]

### Step 4: Final result
Thus, the lowest partial pressure of oxygen that can support aquatic life is approximately:

\[ P \approx 0.0115 \, \text{atm} \]