How do you determine the equilibirium moisture content (me) when we are given t

Question

How do you determine the equilibirium moisture content (me) when we are given the moisture sorption isotherm of a product, GAB equation as:

m = 19.480aw/(1-1.049aw)(1-1.049aw+6.869aw)
where m is moisture content in % and aw is water activity?

I have already plotted a graph for m vs. aw and we are given mi (initial moisture content) = 1.1% dry basis (db) and mc (critical moisture) = 4.50% db

I also need to know how to derive the working isotherm (m = b aw + C)

where b is the slope, m is in gH2O/g and C is the constant.
critical amount of O2 that would cause oxidative rancidity = 1 mL per gram
product stored at 25 C and 70% RH

Explanation / Answer

Have you seen this training place?

http://rpaulsingh.com/learning/virtual/experiments/sorption/

For each temperature you have an isotherm . It is an experimental procedure; put the collected data in a Table and try to fit a parabolic (second degree) equation in Excel (your GAB equation).

Then for any water activity value you can read on the graph or calculate a (material specific) moisture content value (all paired values, m and aw, are at equilibrium).

Or if you have a critical moisture content, then you can find the permissible maximum relative humidity.

Let me know if you need a specific question to solve.

Note: the water activity (aw) is the equilibrium relative humidity (ERH) in the surrounding environment of a food, divided by 100.

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