The Freundlich adsorption isotherm equation is expressed as:
\[ q_e = K_f C_e^{1/n} \]
where:
- \( q_e \) is the amount of adsorbate per unit mass of adsorbent at equilibrium,
- \( C_e \) is the equilibrium concentration of the adsorbate in the solution,
- \( K_f \) and \( n \) are constants specific to the system.
To linearize this equation using natural logarithms, we can perform the following steps:
- Take the natural logarithm of both sides:
\[ \ln(q_e) = \ln(K_f C_e^{1/n}) \]
- Use the property of logarithms to separate the terms on the right side:
\[ \ln(q_e) = \ln(K_f) + \frac{1}{n} \ln(C_e) \]
- Rearrange the equation:
\[ \ln(q_e) = \ln(K_f) + \frac{1}{n} \ln(C_e) \]
- Identify the linear terms: This equation is now in the form of \( y = mx + b \), where:
- \( y = \ln(q_e) \)
- \( x = \ln(C_e) \)
- \( m = \frac{1}{n} \) (the slope)
- \( b = \ln(K_f) \) (the y-intercept)
Thus, the Freundlich isotherm can be represented as a linear graph by plotting \( \ln(q_e) \) against \( \ln(C_e) \). The slope of this line will be equal to \( \frac{1}{n} \), and the y-intercept will be \( \ln(K_f) \). This linearization of the Freundlich isotherm allows for easier determination of the parameters \( K_f \) and \( n \) through linear regression analysis of experimental data.
1 answer