Henry's constant for argon is 40 K bar is water determine molal concentration of argon in water when it is stored above water at 10 bar pressure.

Explanation

To determine the molal concentration of argon in water when it is stored above water at a pressure of 10 bar, we can follow these steps:

### Step 1: Use Henry's Law
According to Henry's Law, the partial pressure of a gas above a liquid is proportional to the mole fraction of that gas in the liquid. The formula is given by:
\[ P = k_H \cdot x \]
Where:
- \( P \) = partial pressure of the gas (in bar)
- \( k_H \) = Henry's constant (in K bar)
- \( x \) = mole fraction of the gas in the solution

### Step 2: Rearranging the Formula
We can rearrange the formula to find the mole fraction \( x \):
\[ x = \frac{P}{k_H} \]

### Step 3: Substitute the Values
Given:
- \( P = 10 \) bar
- \( k_H = 40 \) K bar (which is equivalent to 40,000 bar)

Substituting the values into the equation:
\[ x = \frac{10}{40,000} \]
\[ x = 2.5 \times 10^{-4} \]

### Step 4: Calculate the Number of Moles of Argon
To find the molal concentration, we need to calculate the number of moles of argon in 1 liter of water. We know that 1 liter of water contains approximately 55.5 moles of water.

Using the mole fraction formula:
\[ x = \frac{n_{argon}}{n_{argon} + n_{water}} \]
Since the number of moles of argon is much smaller than the number of moles of water, we can approximate:
\[ x \approx \frac{n_{argon}}{n_{water}} \]

Rearranging gives us:
\[ n_{argon} = x \cdot n_{water} \]

Substituting the values:
\[ n_{argon} = 2.5 \times 10^{-4} \cdot 55.5 \]
\[ n_{argon} = 1.39 \times 10^{-2} \text{ moles} \]

### Step 5: Calculate the Molal Concentration
Molal concentration is defined as the number of moles of solute (argon) per kilogram of solvent (water). Since we have 1 liter of water, which weighs approximately 1 kg, the molal concentration is:
\[ \text{Molal concentration} = \frac{n_{argon}}{1 \text{ kg of water}} \]
\[ \text{Molal concentration} = 1.39 \times 10^{-2} \text{ mol/kg} \]

### Final Answer
The molal concentration of argon in water is approximately \( 1.39 \times 10^{-2} \) mol/kg.

---