BME 403: Respiratory Section

How to Convert BTPS to STPD

A typical problem that I strongly suspect might show up on an exam involves the conversion of a gas measured under BTPS conditions into STPD conditions.

For example, check out the Respiratory Exam from 1995 , and see just how many questions involve this type of conversion.

Here's a typical sample problem:

1 liter of gas at BTPS is collected. How much volume will the gas occupy at STPD?

Here's how to solve it:

Remember that, according to the Ideal Gas Law ,

PV/T = a constant

for a given bundle of gas.

In our problem, we've got THE SAME gas at the end as we started out with; the only things that have changed are the temperature, pressure, and amount of water vapor.

So, we can set up the following equality:

P1 * V1 / T1  =  P2 * V2 / T2               (1)

Where P, V, and T are pressure, volume, and temperature, and where the subscript 1 denotes initial (BTPS) conditions and subscript 2 denotes final (STPD) conditions. In other words:

P1 = gas pressure at the beginning (in this case, 760 mm Hg)

P2 = gas pressure at the end (in this case, STPD standard pressure: 760 mm HG)

V1 = initial volume (in this case, 1 liter)

V2 = final volume (which we want to solve for)

T1 = initial temperature (in this case, BTPS standard temperature, 37 degrees C or 310 K)

T2 = final temperature (in this case, STPD standard temperature, 0 degrees C or 273 K)

Rearrange equation (1) above to get:


V2 = T2 * P1 * V1 / (P2 * T1)                    (2)

Remember that our initial gas is under BTPS conditions, which means that part of the 760 mmHg of pressure in our initial gas is being exerted by the partial pressure of water . The value P1 refers only to the Partial Pressure of our initial gas. So, to find P1, we must subtract the water vapor pressure from our total gas pressure.


P1 = Ptotal - Pwater

P1 = 760 mmHG - 47 mmHG

P1 = 713 mmHG

Note that we do not have to repeat this step for our final conditions to find P2 since in STPD, the water vapor pressure is 0 mmHg.

Plug P1 and the above values into equation (2), and you'll get the following:


273 K * 713 mmHG * 1 Liter / ( 760 mmHg * 310 K)
(3)

Please notice that in equation (3) I do not use degrees C. When you are using the ideal gas law, please use the Kelvin scale (K), or you will be a very sad camper when you find that your gas has a negative volume below the freezing point of water.

At this point, solving for V2 gives you 0.826 liters of gas.

Practice this problem, and try to solve problem #6 from the 1995 Respiratory Section Exam , to try to get the hang of this kind of conversion.

Hopefully by now you've noticed that this method will allow you to convert BTPS volumes into STPD, or vice-versa. You can also use it for converting gas at ANY temperature, pressure, and humidity to BTPS, STPD, or whatever.

Questions? Please e-mail me.

How to Convert BTPS to STPD

1 liter of gas at BTPS is collected. How much volume will the gas occupy at STPD?

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