Question

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

• 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

Hint:

Write water activity and relative humidity as ratios to the same saturation pressure, then compare.

Answer 1

The Correct Option is A

Equilibrium moisture content problems always reduce to comparing vapour pressures on the two sides of an interface.

1. equal to the partial pressure of water vapour in air: at equilibrium there is no net moisture movement between food and air, which only happens when the two vapour pressures match; this fits the given condition $a_w = RH$.
2. lesser than the partial pressure of water vapour in air: this would drive moisture from air into the food, so the system would not yet be at equilibrium.
3. greater than the partial pressure of water vapour in air: this would drive moisture out of the food, again not an equilibrium state.
4. not dependent on the partial pressure of water vapour in air: contradicts the very definition of equilibrium between two moist phases.

Since $a_w$ equals $RH$ here, the two partial pressures must be equal, so option A is correct.