Which of the following curves represents the Henry's law ?

Options

A.
B.
C.
D.

Answer

To determine which curve represents Henry's law, we can follow these steps:

### Step 1: Understand Henry's Law
Henry's law states that the pressure (P) of a gas is directly proportional to its molality (M). This can be expressed mathematically as:
\[ P = k_h \cdot M \]
where \( k_h \) is Henry's constant.

### Step 2: Rearranging the Equation
To analyze the relationship further, we can take the logarithm of both sides of the equation:
\[ \log P = \log k_h + \log M \]

### Step 3: Identify the Form of the Equation
The equation \( \log P = \log k_h + \log M \) resembles the equation of a straight line:
\[ y = mx + c \]
where:
- \( y \) is \( \log P \)
- \( x \) is \( \log M \)
- \( m \) (slope) is 1
- \( c \) (y-intercept) is \( \log k_h \)

### Step 4: Characteristics of the Graph
From the above analysis, we can conclude that:
- The graph will be a straight line.
- The slope of the line will be positive (since the relationship is direct).
- The y-intercept will be \( \log k_h \), which is a constant.

### Step 5: Analyze the Given Options
Now, we need to evaluate the provided curves based on the characteristics we derived:
1. **Option A**: A straight line with a positive slope - This could represent Henry's law.
2. **Option B**: A straight line with a negative slope - This does not represent Henry's law.
3. **Option C**: A straight line with zero intercept - This does not represent Henry's law.
4. **Option D**: A curve that is not a straight line - This does not represent Henry's law.

### Step 6: Conclusion
Based on the analysis, the correct answer is **Option A**, as it is the only option that represents a straight line with a positive slope.

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