Dew point and absolute humidity

[Karol]

Homework Statement

Room temperature is 20⁰C and relative humidity is 60%. what is the absolute moisture

Homework Equations

Vapor pressure at 20⁰C=17.5[atm]
PV=nRT
Molecular weight of water=18[gr/mol]

The Attempt at a Solution

The vapor pressure at 20⁰C:
$$\frac{x}{17.5}=0.6\rightarrow x=10.5[atm]$$
$$PV=nRT\rightarrow 10.5\cdot 1=n\cdot 0.08208\cdot 293\rightarrow n=0.437[mol]$$
$$0.437\cdot 18=7.86[\frac{gr}{m^3}]$$
It should be 10[gr/m³]

 

[Chestermiller]

Homework Statement

Room temperature is 20⁰C and relative humidity is 60%. what is the absolute moisture

Homework Equations

Vapor pressure at 20⁰C=17.5[atm]

That should be mm Hg.

PV=nRT
Molecular weight of water=18[gr/mol]

The Attempt at a Solution

The vapor pressure at 20⁰C:
$$\frac{x}{17.5}=0.6\rightarrow x=10.5[atm]$$

Again, that should be mm Hg

$$PV=nRT\rightarrow 10.5\cdot 1=n\cdot 0.08208\cdot 293\rightarrow n=0.437[mol]$$
$$0.437\cdot 18=7.86[\frac{gr}{m^3}]$$

The gas constant value you used here for liters. You also need to use a pressure of 10.5/760 atm.

Chet

 

[Karol]

$$\frac{x}{0.023}=0.6\rightarrow x=0.0138[atm]$$
$$PV=nRT\rightarrow 0.0138\cdot 1[liter]=n\cdot 0.08208\cdot 293\rightarrow n=0.000574[\frac{mol}{liter}]=0.574[\frac{mol}{m^3}]$$
$$0.574\cdot 18=10.3[\frac{gr}{m^3}]$$

 

[Chestermiller]

$$\frac{x}{0.023}=0.6\rightarrow x=0.0138[atm]$$
$$PV=nRT\rightarrow 0.0138\cdot 1[liter]=n\cdot 0.08208\cdot 293\rightarrow n=0.000574[\frac{mol}{liter}]=0.574[\frac{mol}{m^3}]$$
$$0.574\cdot 18=10.3[\frac{gr}{m^3}]$$

Excellent!

Chet

 

[HalfLostAndSearching]

I would like to clarify that the calculation provided is correct, but it is not the absolute moisture. The term "absolute moisture" is not commonly used in scientific literature. The correct term for the amount of water vapor in a given volume of air is "absolute humidity." The calculation provided gives the absolute humidity in units of grams per cubic meter (g/m3). Therefore, the absolute humidity at 20°C and 60% relative humidity is approximately 7.86 g/m3.