The mole fraction of He gas in a saturated solution at `20^(@)C` is `1.25 xx 10^(-6)`. Calculate the pressure of He gas above the solution . (`K_(H)` of He at `20^(@)C = 144.98 ` k bar)

Explanation

To solve the problem of calculating the pressure of helium gas above a saturated solution at 20°C, we will use Henry's Law. Here’s a step-by-step solution:

### Step 1: Understand Henry's Law
Henry's Law states that the partial pressure of a gas above a solution is directly proportional to its mole fraction in the solution. This can be expressed mathematically as:

\[ P = K_H \times x \]

where:
- \( P \) = partial pressure of the gas
- \( K_H \) = Henry's law constant for the gas
- \( x \) = mole fraction of the gas in the solution

### Step 2: Identify Given Values
From the problem, we have:
- Mole fraction of helium gas, \( x = 1.25 \times 10^{-6} \)
- Henry's law constant for helium at 20°C, \( K_H = 144.98 \, \text{kbar} = 144.98 \times 10^3 \, \text{bar} \)

### Step 3: Substitute Values into Henry's Law Equation
Now, we will substitute the values of \( K_H \) and \( x \) into the equation:

\[ P = K_H \times x \]
\[ P = (144.98 \times 10^3 \, \text{bar}) \times (1.25 \times 10^{-6}) \]

### Step 4: Perform the Calculation
Now, we will calculate the pressure \( P \):

\[ P = 144.98 \times 10^3 \times 1.25 \times 10^{-6} \]
\[ P = 144.98 \times 1.25 \times 10^{-3} \]
\[ P = 181.225 \times 10^{-3} \]
\[ P = 0.181225 \, \text{bar} \]

### Step 5: Round the Result
Rounding the result to three significant figures, we get:

\[ P \approx 0.181 \, \text{bar} \]

### Final Answer
The pressure of helium gas above the solution at 20°C is approximately **0.181 bar**.

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