Subtopic: Water activity, sorption and desorption isotherms
Question Statement:
Moisture sorption data of dehydrated milk powder fitted to the linearized Brunauer-Emmett-Teller (BET) equation $\frac{a_w}{(1 - a_w) m} = \frac{1}{m_0 C} + \frac{C - 1}{m_0 C} a_w$ yields a straight-line plot with slope $S = 22.5\text{ g solids/g water}$ and intercept $I = 2.5\text{ g solids/g water}$. The monolayer moisture content ($m_0$) of the milk powder in $\text{g water/g solids}$ is ________ (round off to 2 decimal places).
Answer Key:
0.04
Step-by-Step Solution & Explanation
In the linear form of the BET equation:
$y = I + S x$
Where:
$I = \frac{1}{m_0 C}, \quad S = \frac{C - 1}{m_0 C}$
Summing slope and intercept:
$S + I = \frac{C - 1 + 1}{m_0 C} = \frac{C}{m_0 C} = \frac{1}{m_0}$
$m_0 = \frac{1}{S + I} = \frac{1}{22.5 + 2.5} = \frac{1}{25.0} = 0.04\text{ g water/g solids}$