By plotting log x/m on y-axis and log P on x-axis we s hould get

Options

A. (a)
B. (b)
C. (c)
D. (d)

Answer

To solve the question, we need to analyze the relationship between the variables involved in the Freundlich isotherm equation and derive the nature of the graph when plotting log(x/m) against log(P).

### Step-by-Step Solution:

1. **Understand the Freundlich Isotherm Equation**:
The Freundlich isotherm can be expressed as:
\[ \frac{x}{m} = k \cdot P^{\frac{1}{n}} \]
where:
- \( x \) = mass of adsorbate
- \( m \) = mass of adsorbent
- \( P \) = pressure of the gas
- \( k \) and \( n \) = constants (with \( n > 1 \))

2. **Take the Logarithm of Both Sides**:
We can take the logarithm of both sides of the equation:
\[ \log\left(\frac{x}{m}\right) = \log(k) + \frac{1}{n} \log(P) \]

3. **Rearranging the Equation**:
Rearranging the equation gives us:
\[ \log\left(\frac{x}{m}\right) = \log(k) + \frac{1}{n} \log(P) \]
This can be rewritten in the form of a linear equation:
\[ y = mx + c \]
where:
- \( y = \log\left(\frac{x}{m}\right) \)
- \( x = \log(P) \)
- \( m = \frac{1}{n} \) (slope)
- \( c = \log(k) \) (y-intercept)

4. **Identify the Nature of the Graph**:
The equation \( y = \frac{1}{n} x + \log(k) \) indicates that when we plot \( \log\left(\frac{x}{m}\right) \) on the y-axis and \( \log(P) \) on the x-axis, we will get a straight line. The slope of this line will be \( \frac{1}{n} \), and the y-intercept will be \( \log(k) \).

### Conclusion:
By plotting \( \log\left(\frac{x}{m}\right) \) on the y-axis and \( \log(P) \) on the x-axis, we should get a straight line graph, confirming the linear relationship derived from the Freundlich isotherm equation.