TO-15 Canister Relative Humidity: Part II (Examples and Calculations)

In my last blog I left you hanging on how to calculate the theoretical relative humidity (% RH) in a canister. So to help us learn, I will use the two following example scenarios under which we may look at canister RH, and how the calculations are done: 1) we know how much water was put in a canister and what pressure and temperature the canister is at – so what is the relative humidity? 2) we know what relative humidity we desire and at what pressure and temperature - so how much water do we need to add to the canister?

Recall from my first blog that relative humidity is defined as the ratio of the partial pressure of water vapor to the saturated vapor pressure of water at a set temperature. Temperature is italicized, as it is important to note that with increasing temperature (for a constant volume of air) saturation vapor pressure increases. The following figure is excellent for understanding the relationship between temperature and RH:

This is the relationship between vapor denisty and temperature:

Now… time for us to visit physics 101 with our two examples:

Example 1: If 200 µL of H2O is injected into an evacuated 6 L canister @ 22.5 °C and then filled to a final pressure of 30 psig… what is the theoretical relative humidity?

• Recall: Saturation Vapor Density = 19.99 g/m³ @ 22.5 °C

• Recall: Density of H₂O = 0.99765874 g/cm³

Calculation steps:

1. Units conversion: 200 µL ÷ 1000 µL/cm³ = 0.200 cm³
2. Mass of water in canister = density of water x volume: 0.99765874 g/cm³ x 0.200 cm³ = 0.20 g
3. Volume of gas in canister = size of canister x # of atmospheres: 6 L ÷ 1000 L/m³ x 3 atmospheres (30” HG to 30 psig) = 0.018 m³
4. Vapor density in canister = mass of water ÷ volume of air (taken from 2 & 3): 0.20 g ÷ 0.018 m³ = 11.11 g/m³
5. % Relative Humidity = vapor density ÷ saturation vapor density x 100: 11.11 g/m³ ÷ 19.99 g/m³ x 100 = 55.77% RH

Example 2: If the desired theoretical relative humidity is 75% in an evacuated 6 L canister @ 22.5 °C filled to a final pressure of 30 psig… what volume of H2O needs to be injected into the canister?

• Recall: Saturation Vapor Density = 19.99 g/m³ @ 22.5 °C

• Recall: Density of H₂O = 0.99765874 g/cm³

Calculation steps:

1. Desired humidity (not relative, hence no %) is desired vapor density = ratio x saturation vapor density: 0.75 x 19.99 g/m³ = 14.99 g/m³
2. Volume of gas in canister = size of canister x # of atmospheres: 6 L ÷ 1000 L/m³ x 3 atmospheres (30” HG to 30 psig) = 0.018 m³
3. Required mass of water in canister = desired vapor density x volume of gas in canister (taken from 1 & 2): 14.99 g/m³ x 0.018 m³ = 0.2699 g
4. Required water injection volume = mass of water x density of water: 0.2699 g x 0.99765874 g/cm³ = 0.2692 cm³
5. Units conversion: 0.2692 cm³ x 1000 µL/cm³ = 269.2 µL

So... considering that the majority of individuals who are interested in canister RH are probably going to be faced with scenario 2, I have gone ahead and put together this sophisticated RH calculator for those that are interested:

Canister RH Calculator - V1.01

Feel free to copy and paste into your own Excel workbook, just please keep in mind that this is strictly for 22.5 °C. In the meantime stay tuned for part III of this series, where we learn how canister RH can affect our results…