Subtopic: Water activity, sorption and desorption isotherms
Question Statement:
It is given that the water activity of a food is equal to the relative humidity of the atmosphere that is in equilibrium with the food. The partial pressure of water vapour of the food at a specific temperature is
Options:
(A) equal to the partial pressure of water vapour in air
(B) lesser than the partial pressure of water vapour in air
(C) greater than the partial pressure of water vapour in air
(D) not dependent on the partial pressure of water vapour in air
Official Answer Key:
A
Step-by-Step Solution & Explanation
By definition:
Water activity of the food: a_w = p_food/p_sat
Equilibrium relative humidity of the air: ERH = p_air/p_sat
The question states that at equilibrium a_w = ERH. Since both are divided by the same saturation vapour pressure p_sat at that temperature:
p_food/p_sat = p_air/p_sat ⇒ p_food = p_air
This is exactly what equilibrium means physically: when the vapour pressures are equal, there is no driving force, so no net moisture migrates either into or out of the food.
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