For the solution of the gases `w,x,y and z` in water at `298 K` the Henry's law constant `(K_(H))` are `0.5,2,35` and `40 k bar`,respectively. The correct plot for the given data is :

Options

A.
B.
C.
D.

Answer

To solve the problem, we need to analyze the Henry's law constants for the gases W, X, Y, and Z and determine the correct plot based on their values. Here’s a step-by-step solution:

### Step 1: Understand Henry's Law
Henry's law states that the partial pressure of a gas in a solution is directly proportional to its mole fraction in that solution. The equation can be expressed as:
\[ P = K_H \cdot X \]
where:
- \( P \) = partial pressure of the gas
- \( K_H \) = Henry's law constant
- \( X \) = mole fraction of the gas

### Step 2: Identify the Given Data
The Henry's law constants for the gases are:
- \( K_H \) for W = 0.5 kbar
- \( K_H \) for X = 2 kbar
- \( K_H \) for Y = 35 kbar
- \( K_H \) for Z = 40 kbar

### Step 3: Determine the Relationship
From the equation \( P = K_H \cdot X \), we can rearrange it to express the mole fraction of water:
\[ P = K_H \cdot (1 - X_{water}) \]
This indicates that as the mole fraction of water increases, the partial pressure of the gas decreases, resulting in a downward slope in the plot.

### Step 4: Analyze the Slope and Intercepts
- The slope of the plot will be negative because of the inverse relationship between the mole fraction of water and the partial pressure of the gas.
- The y-intercept of the plot will be equal to the Henry's law constant \( K_H \) for each gas.

### Step 5: Compare the Values
The values of \( K_H \) indicate the y-intercepts:
- For W (0.5 kbar), the y-intercept is low.
- For X (2 kbar), the y-intercept is slightly higher.
- For Y (35 kbar), the y-intercept is much higher.
- For Z (40 kbar), the y-intercept is the highest.

### Step 6: Determine the Correct Plot
We need to find a plot that:
1. Has a downward slope (indicating a negative relationship).
2. Shows the correct order of y-intercepts based on the values of \( K_H \):
- W < X < Y < Z

### Step 7: Evaluate the Options
- The correct plot will show W closest to the origin, followed by X, then Y, and finally Z, all in a downward sloping manner.

### Conclusion
Based on the analysis, the correct plot corresponds to the first option, which accurately reflects the values of \( K_H \) and the negative slope as per Henry's law.