For Freundlich adsorption isotherm, a plot of log(x / m)(y-axis) and logp ( x-axis) gives a stra

step 1 Hello everyone. So our question is upload of log x by m on y -axis and gives a straight line wit

For Freundlich adsorption isotherm, a plot of log(x /...

For Freundlich adsorption isotherm, a plot of $\log (x / \mathrm{m})(y$-axis) and $\log p$ ( $x$-axis) gives a straight line. The intercept and slope for the line is $0.4771$ and 2, respectively. The mass of gas, adsorbed per gram of adsorbent if the initial pressure is $0.04 \mathrm{~atm}$, is $\times 10^{-4} \mathrm{~g}$.

Key Concepts

Adsorption Capacity Calculation

Using the constants derived from the Freundlich isotherm, the adsorbed amount of gas on the adsorbent can be calculated for any given pressure. This involves substituting the initial pressure into the Freundlich equation to obtain the adsorption capacity. This calculation is essential in applications such as gas storage, pollutant removal, and catalysis, where performance depends on the efficiency of the adsorbent.

Isotherm Constants Determination

The parameters in the Freundlich adsorption isotherm, namely the adsorption capacity constant and the adsorption intensity (or heterogeneity factor), can be derived from the linearized form of the equation. The intercept of the line in the logarithmic plot gives the logarithm of the capacity constant, while the slope provides information about the adsorption intensity. These constants are critical for predicting adsorption behavior under various conditions.

Freundlich Adsorption Isotherm

The Freundlich adsorption isotherm is an empirical model used to describe how solutes interact with heterogeneous surfaces. It expresses the relationship between the amount of gas adsorbed per unit mass of adsorbent and the pressure of the gas through a power-law relationship. This model is particularly useful in cases where adsorption does not occur on a uniform surface, allowing for varying adsorption affinities across different sites.

Logarithmic Transformation and Linearization

In many adsorption processes, the relationship between adsorbed amount and pressure follows a non-linear power law. By taking the logarithm of both sides, the Freundlich isotherm can be transformed into a linear equation. This linearization simplifies the determination of model parameters by converting the original power-law relationship into a straight line, where the intercept and slope correspond to the logarithm of a constant and the exponent, respectively.

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