When a gas is bubbled through water at 298 K, a very dilute solution of gas is obtained . Henry's law constant for the gas is 100 kbar. If gas exerts a pressure of 1 bar, the number of moles of gas dissolved in 1 litre of water is

Options

A. 0.555
B. `55.55xx10^(-5)`
C. `55.55xx10^(-3)`
D. `5.55xx10^(-5)`

Explanation

To solve the problem, we will use Henry's Law, which states that at a constant temperature, the amount of gas that dissolves in a liquid is directly proportional to the partial pressure of that gas above the liquid.

### Step-by-step Solution:

1. **Identify Given Values**:
- Henry's Law constant (K_H) = 100 kbar = 100,000 bar (since 1 kbar = 1000 bar)
- Pressure of the gas (P) = 1 bar
- Temperature = 298 K (not directly needed for calculations)

2. **Apply Henry's Law**:
According to Henry's Law:
\[ P = K_H \cdot C \]
where \( C \) is the concentration of the gas in moles per liter (mol/L).

3. **Rearrange the Formula to Solve for C**:
\[ C = \frac{P}{K_H} \]

4. **Substitute the Values**:
\[ C = \frac{1 \text{ bar}}{100,000 \text{ bar}} = 1 \times 10^{-5} \text{ mol/L} \]

5. **Calculate the Number of Moles of Gas Dissolved**:
Since we are looking for the number of moles of gas dissolved in 1 liter of water, we can directly use the value of \( C \):
\[ \text{Number of moles of gas} = C = 1 \times 10^{-5} \text{ moles} \]

6. **Convert Moles to Millimoles**:
To express this in millimoles:
\[ 1 \times 10^{-5} \text{ moles} = 0.00001 \text{ moles} = 0.01 \text{ millimoles} \]

7. **Final Result**:
The number of moles of gas dissolved in 1 liter of water is:
\[ 0.01 \text{ millimoles} \]

### Summary:
The number of moles of gas dissolved in 1 liter of water is \( 0.01 \) millimoles.

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