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

Step 1: Write the definition of water activity.
Water activity is defined as \(a_w = \dfrac{p_w}{p_{ws}}\), the ratio of the partial pressure of water vapour exerted by the food to the saturation vapour pressure of pure water at the same temperature.
The relative humidity of the surrounding air, in equilibrium with the food, is \(RH = \dfrac{p_{air}}{p_{ws}} \times 100\).

Step 2: Use the equilibrium condition given.
The question states \(a_w = RH/100\) for this food-air system at equilibrium.
Since \(p_{ws}\) is the same reference saturation pressure in both ratios, equating \(a_w\) and \(RH/100\) forces \(p_w = p_{air}\).
This is exactly what equilibrium moisture means: no net moisture transfer, so the driving vapour pressures on both sides must match.

Final Answer:
The partial pressure of water vapour of the food equals the partial pressure of water vapour in the surrounding air. \[ \boxed{p_{w,food} = p_{w,air}} \]