Adsorption constants Langmuir isotherm, determination

A wastewater containing a [C ] = 25 mg/L of phenol is to be treated using PAC to produce an effluent concentration [C] = 0.10 mg/L. The PAC is simply added to the stream and the mixture subsequently settled in the following sedimentation tank. The constants of the Langmuir equation are determined by running a jar test producing the results below. The volume of waste subjected to each test is one liter. If the flow rate Q is 0.11 m /s, calculate the quantity of PAC needed for the operation. What is the adsorption capacity of the PAC Calculate the quantity of PAC needed to treat the influent phenol to the ultimate residual concentration. Use the Langmuir isotherm. 

A Langmuir isotherm for an adsorption experiment shows that X, the amount of solute sorbed per weight sorbate, is 0.085 when the solute concentration in the fluid phase is 0.05. If the Langmuir constant K for the experimental conditions is 1.3, apply the concept of a unit operation to determine the value of X when the solute concentration is 0.1. Plot the Langmuir isotherm for C values of 2,4, 6, 8, and 10. What does the plot tell you about the amount of solute absorbed vs the fluid phase concentration ... 

In Section 4-1, it was shown that isotherm linearity is determined by 6, the fractional coverage of the surface by sample. The maximum value of 0 for isotherm linearity (the linear capacity 0o.i) in turn depends upon adsorbent heterogeneity specifically, the types of adsorbent sites (as defined by their Ki values) and their relative concentrations (iV,). Nowhere have we considered the variation of linear capacity with the extent of sample adsorption, i.e., the dependence of 60.1 on A . For a Langmuir isotherm Eq. (4-1) shows that linear capacity corresponds to 10% surface coverage, regardless of the value of X . Similarly, for a surface which contains several different site types (differing in values), it may easily be shown that if the Kf values of all sites are increased by a constant factor Q, K° is... 

Experimental equilibrium data for the adsorption of methane on Calgon Carbon Corp. PCB activated carbon are listed in Table 18-3. Determine if the Langmuir isotherm, Eq. 118-5a). is a good fit to the data at T = 373 K and if the adsorption equilibrium constant p follows the Arrhenius form, Eq. 

Recall from our previous section on incomplete reaction processes that the ratio of the rate constants for the forward and reverse reaction processes yields the equilibrium constant K for the reaction. Thus, in the case of an incomplete reaction, this equilibrium constant, in concert with the gas-phase CO concentration, would determine the equilibrium surface coverage of CO. This equation is known as the Langmuir isotherm and it is one of a number of physical models that is Irequently encomitered when describing gas-solid adsorption processes. 

For dilute solutions the heats of successive adsorptions are often proportional to the amounts of adsorption (a necessary condition for conformity with Langmuir s equation). The equilibrium constants can be determined directly from the heat isotherms, as suggested by T. Allen and R. M. Patel [10], writing the relationship... 

Figures 13.18-13.22 display results of Langmuir analyses of adsorption isotherm data from steel-steel and steel-starch friction and hexadecane-water interfacial-tension measurements. As can be seen in figs. 13.18-13.22, in all cases plots of [veg oil] vs. 9 gave a straight line with an intercept close to 1. From linear regression analyses of the data, the exact values of the intercepts and slopes are obtained. From the slope, the equilibrium constant Kq is determined and used to calculate the free energy of adsorption using eq. (13.10).

One application of adsorption on surfaces is to measure the ability of activated charcoal to adsorb acid. (Activated charcoal, a form of treated carbon, is very porous and is used to adsorb impurities from water. Its use in aquariums typifies this behavior.) In a lab experiment, a student mixes a given amount of powdered charcoal into a series of acetic acid solutions. The acetic acid solutions have different initial concentrations. Some of the acid is adsorbed onto the charcoal. By taking aliquots after equilibrium is established, the student determines the change in acid concentration. Plot a Langmuir isotherm for the experimental data and determine the equilibrium constant for the adsorption. The experimental data are as follows ... 

Determine the constant K in the Langmuir isotherm from the following adsorption data. The adsorbed volume of gas per surface refer to 298 K and 1 atm condition. Assume a cubic lattice with lattice constant a = 2.5 A and that the gas is adsorped as a monolayer with one molecule/unit cell (with area a ). 

---