Correct equation of Freundrich iostherm is

Options

A. `log ""((x)/(m)) = log K + (1)/(n) log C`
B. `log""((m)/(x))=log K +(1)/(n)log C`
C. `log""((x)/(m)) =log C +(1)/(k) log C`
D. `log""((x)/(m)) = log C +(1)/(n) log K `

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 on a solid surface varies with the concentration of the gas in the surrounding phase. It is an empirical relationship that can be expressed mathematically.

2. **Basic Equation**:
The Freundlich isotherm can be represented by the equation:
\[ \frac{X}{M} = K \cdot C^{\frac{1}{n}} \]
where:
- \(X\) = mass of the gas adsorbed
- \(M\) = mass of the adsorbent
- \(K\) = Freundlich constant
- \(C\) = concentration of the solution
- \(n\) = constant that indicates the degree of non-linearity of the isotherm.

3. **Taking Logarithms**:
To linearize this equation, we take the logarithm of both sides:
\[ \log\left(\frac{X}{M}\right) = \log(K \cdot C^{\frac{1}{n}}) \]

4. **Applying Logarithmic Properties**:
Using the property of logarithms that states \(\log(ab) = \log(a) + \log(b)\), we can expand the right side:
\[ \log\left(\frac{X}{M}\right) = \log K + \log\left(C^{\frac{1}{n}}\right) \]
This can be further simplified using the property \(\log(a^b) = b \cdot \log(a)\):
\[ \log\left(\frac{X}{M}\right) = \log K + \frac{1}{n} \log C \]

5. **Final Form**:
The final equation can be rearranged as:
\[ \log\left(\frac{X}{M}\right) = \log K + \frac{1}{n} \log C \]
This is the required equation for the Freundlich isotherm.

6. **Identifying the Correct Option**:
From the options provided, we identify that this equation corresponds to option 1:
\[ \log\left(\frac{X}{M}\right) = \log K + \frac{1}{n} \log C \]

### Conclusion:
Thus, the correct equation of the Freundlich isotherm is:
\[ \log\left(\frac{X}{M}\right) = \log K + \frac{1}{n} \log C \]
And the answer is option 1.