Henry's law constant of oxygen is `1.4 xx 10^(-3)` mol `"lit"^(-1) "atm"^(-1)` at 298 K. How much of oxygen is dissolved in 100 mL at 298 K when the partial pressure of oxygen is 0.5 atm?

Options

A. 1.4g
B. 3.2g
C. 25.4mg
D. 2.24mg

Explanation

To solve the problem, we will use Henry's Law, which states that the solubility (C) of a gas in a liquid is directly proportional to the partial pressure (P) of that gas above the liquid. The relationship can be expressed mathematically as:

\[ C = K_H \cdot P \]

Where:
- \( C \) = concentration of the gas in mol/L
- \( K_H \) = Henry's law constant (given as \( 1.4 \times 10^{-3} \) mol/L·atm)
- \( P \) = partial pressure of the gas (given as 0.5 atm)

### Step-by-Step Solution:

1. **Identify the values given:**
- Henry's law constant (\( K_H \)) = \( 1.4 \times 10^{-3} \) mol/L·atm
- Partial pressure of oxygen (\( P \)) = 0.5 atm

2. **Calculate the solubility of oxygen using Henry's Law:**
\[ C = K_H \cdot P \]
Substituting the values:
\[ C = (1.4 \times 10^{-3} \, \text{mol/L·atm}) \cdot (0.5 \, \text{atm}) \]
\[ C = 0.7 \times 10^{-3} \, \text{mol/L} \]

3. **Convert the concentration from mol/L to moles in 100 mL:**
Since 100 mL is equal to 0.1 L, we can find the number of moles of oxygen dissolved in 100 mL:
\[ \text{Moles of } O_2 = C \cdot \text{Volume} \]
\[ \text{Moles of } O_2 = (0.7 \times 10^{-3} \, \text{mol/L}) \cdot (0.1 \, \text{L}) \]
\[ \text{Moles of } O_2 = 0.7 \times 10^{-4} \, \text{mol} \]

4. **Calculate the mass of oxygen dissolved:**
To find the mass, we need the molar mass of oxygen (\( O_2 \)), which is approximately 32 g/mol.
\[ \text{Mass} = \text{Moles} \times \text{Molar Mass} \]
\[ \text{Mass} = (0.7 \times 10^{-4} \, \text{mol}) \cdot (32 \, \text{g/mol}) \]
\[ \text{Mass} = 2.24 \times 10^{-3} \, \text{g} \]

5. **Convert grams to milligrams:**
Since 1 g = 1000 mg:
\[ \text{Mass in mg} = 2.24 \times 10^{-3} \, \text{g} \times 1000 \, \text{mg/g} \]
\[ \text{Mass in mg} = 2.24 \, \text{mg} \]

### Final Answer:
The amount of oxygen dissolved in 100 mL at 298 K when the partial pressure of oxygen is 0.5 atm is **2.24 mg**.