Question

The partial pressure of water at 298 K is 23 mbar in our atmosphere. A thirsty explorer wants to condense water vapour in the air to drink. What is the minimum volume of air he needs to work with to obtain 1 L of water through this process? Remember that the density of water is 1 g/mL.

Answer 1

In this problem, we observe that the amount of water required is 1 litre.

Now, since the number of moles is proportional to the partial pressure in the system i.e.

n p

or, n₁/n₂ = p₁/p₂

And the number of moles is also proportional to the volume of gas i.e.

n V

or, n₁/n₂ = V₁/V₂

we have,

V₁/V₂ = p₁/p₂

or, V₁/V_total = p₁/p_total

Hence, we need to calculate the value of V_total, as we have the value of V₁ = 1 litre, p1 = 0.23 bar, p_total = 1.013 bar (atmospheric pressure = 1.013 x 10⁵ Pa = 1.013 bar)

Hence V_total = 1.013 / 0.23 = 4.404 litre. This will be the total volume of air required and the required answer.