Correct equation of Freundlich isotherm is

Options

A. `log (m/x)=logk+1/m log c `
B. `log(x/m)= logC +1/n log k `
C. `log (x/m)=logk+ 1/n log c `
D. `log (x/m)= log k + 1/k log c `

Explanation

To solve the question regarding the correct equation of the Freundlich isotherm, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Freundlich Isotherm**:
The Freundlich isotherm describes how the amount of gas adsorbed onto a solid surface varies with the pressure (or concentration) of the gas. It is typically represented by the equation:
\[ \frac{x}{m} = k c^{\frac{1}{n}} \]
where:
- \( x \) = mass of gas adsorbed
- \( m \) = mass of adsorbent
- \( k \) = Freundlich isotherm constant
- \( c \) = concentration of the gas

2. **Taking the Logarithm of Both Sides**:
To linearize the Freundlich isotherm equation, we take the logarithm of both sides:
\[ \log\left(\frac{x}{m}\right) = \log(k) + \frac{1}{n} \log(c) \]

3. **Rearranging the Equation**:
The equation can be rearranged to show the relationship clearly:
\[ \log\left(\frac{x}{m}\right) = \log(k) + \frac{1}{n} \log(c) \]
This can also be expressed as:
\[ \log\left(\frac{x}{m}\right) + \log(k) = \frac{1}{n} \log(c) \]

4. **Identifying the Correct Option**:
From the rearranged equation, we can see that the correct form of the Freundlich isotherm is:
\[ \log\left(\frac{x}{m}\right) = \log(k) + \frac{1}{n} \log(c) \]
Therefore, the correct option among the given choices is the one that matches this equation.

### Conclusion:
The correct equation of the Freundlich isotherm is:
\[ \log\left(\frac{x}{m}\right) = \log(k) + \frac{1}{n} \log(c) \]
Thus, the third option from the provided choices is correct.