To calculate the capacity of equilibrium adsorption (
-
Material Balance Equation:
-
Initial Conditions:
- Volume of wastewater = 10 L
- Initial concentration of TOC (
) = 20 mg/L - Amount of activated carbon used = 1 g
-
Final Water Volume: Since we are disposing of 10 L of wastewater, we focus on the concentration in the final volume of 10 L.
-
Equilibrium Concentration (
): According to the material balance from our equation:Since we are dealing with 1 g of activated carbon and modifying the original concentration based on
, we can multiply by the number of grams of carbon to find the equation in terms of total mass adsorbed to the carbon. -
Instead of focusing on total mg/L in the 10 L volume, we can express everything in terms of 1 L, leading to:
For 1 g of activated carbon, we need to understand the mass transfer relationship involving the adsorption capacity. -
Total TOC in 10 L:
This is the total mass of TOC that exists before adsorption.
Now, we need to understand that in the presence of
-
Assuming no other breakdown or reaction, we can consider: At equilibrium and with the given relationships in the material balance for 1 L of water:
For 1 g of activated carbon:
Substituting
into this balance will yield a straightforward equation to use:- For every 1 g of activated carbon (or 1000 mg), the equation results into adsorption related to the mass of carbon and its active sites.
To determine
-
Substitute various
back to see if stays zero; because simply reduces the TOC. -
For equilibrium:
Equating with the total throughput flowing through.
Rearranging for computation:
-
Solve from:
-
can be seen simply as: With empirical observations, let's just push through for: Assume TOC goes down to the limits of:
Iterate: targeting a which yields the maximum capacity cleared up. -
Test for practical conservations. (Final estimation ultimately rounds normally yielding to exact specifics.)
Hence solving iteratively finally leads up, yielding:
Thus conclude stability at equilibrium:
Conclusion: Based on material balance, calculation shows