We already learned how to calibrate our TO-15 system, what our concentration units mean, and how to properly read our vacuum gauge while pressurizing samples. We are clearly going out of order here, because I have never covered how to prepare a working standard (necessary for calibrations) from a Stock Standard. Therefore, the following multi-part blog series will demonstrate how to use a static dilution to make a working standard.
Okay… first things first. We need to determine our stock standard concentration, canister volume, stock Standard Injection Volume, and final canister pressure. How we go at deriving all of the aforementioned may vary. For example, we often have a 1 ppmv stock standard and a 6 L canister, so those variables are gimmes. More often than not we also know the final canister concentration we desire. For today’s example we will use 2.0 ppbv.
All that is left to determine is the Stock Standard Injection volume and final canister pressure. For the following example we will say that we want a final canister pressure of 30 psig. Now that we have everything we need, but the stock standard injection volume, the math is as follows:
First we determine the final volume of gas in the canister. We know we start with a fully evacuated canister at -14.7 psig and pressurize the canister to 30 psig. So we recognize that we have added 3 atmospheres (~14.7 psig/atmosphere) to the canister. Therefore, our final gas volume is 3 x 6 L = 18 L.
Remembering that we want 2.0 ppbv from 1 ppmv, the rest of the math looks as follows:
Where we are solving for the stock standard injection volume (x), 18 L is our gas volume from above, 0.002 ppmv is our desired concentration, and 1.00 ppmv is our stock standard concentration. The result of this is 0.036 L = 36 mL.
We now know that if we inject 36 mL of our 1 ppmv stock standard into a 6 L canister and pressurize this canister to 30 psig, the final concentration will be ~1.97 ppbv.
We can take the above math and manipulate it any way we want it. And by that I mean, we can move x (what we are solving for) to the top right if we want to solve for the final desired concentration or to the bottom left to solve for the final gas volume, etc… In my experience, we are generally solving for x on the left-hand side, where we are either solving for the injection volume or final gas volume (which ultimately is extrapolated out to final canister pressure).
Now that I have given you some examples, I will give you the shortcut I use when in the lab. Without further ado I introduce you to the:
Super Standard Calculator – V2.01
Stay tuned for next time when I blog about how to introduce a stock standard into a canister…