Question

What is the density of water vapor in g/m^3 on a hot dry day in the desert when the temperature is 50.0°C and the relative humidity is 6.50%?

Answer 1

`Density = 538 (g)/(m3)`

Step-by-step explanation:

To get the density you need the vapor pressure for the moisture, to get this first you need to find in tables (found in internet, books, apps) the saturation vapor pressure for water at 50°C:

`P_(sat) = 12350 Pa  @ 50°C`

Now, a relative humidity of 6,5% means that the actual vapor pressure is 6,5% that of the saturated air so:

`P_(vapor) = 12350 Pa * 0,065 = 802,75 Pa = 0,792 atm`

According to the ideal gases formula density can be calculated as:

`d = (P*M)/(R*T)`

Where:

Ideal gases constant
`R = 0,082 (atm L)/(mol k)`

Pressure P = 0,792 atm

Temperature T = 50°C = 323 K

molar mass M = 18 g/mol

`d = 0,538 (g)/(L) = 538 (g)/(m3)`