Alveolar Gas Equation

WHAT IS IT?
The alveolar gas equation (sometimes referred to as the alveolar air equation) calculates the partial pressure of oxygen in the alveoli; written as PA02 (NOTE THE A IS CAPITAL, little a stands for arterial).

DETAILS ON HOW IT IS CALCULATED? 
STEP 1: Barometric pressure (PB) minus partial pressure of water vapor (PH2O)
EXPLANATION:

Dalton's Law

The barometric pressure, PB is the partial pressure of all the gasses in the air added together. Prior to reaching the alveoli, air is warmed and humidified. Water vapor is a gas and therefore has a partial pressure. At normal body temperature, the partial pressure of water vapor (PH2O) is 47 torr. PH2O must be subtracted from PB to determine the total amount of gasses inspired into the lungs.
STEP 2: Multiply this number by the fraction of inspired oxygen (FiO2)
EXPLANATION:
Once the total amount of gasses is determined, we can find out how much of that gas is oxygen. FiO2 is the percentage of air that is made up of oxygen, so if we multiply our total amount of gasses by the percent of oxygen, it will determine the amount of oxygen inspired into the lungs.
STEP 3: Divide the partial pressure of CO2 in the arteries (PaCO2) by the respiratory quotient (RQ) which is 0.8 unless otherwise determined. If multiplication is easier, multiply the PaCO2 by 1.25 to get the exact same answer, either way works.
EXPLANATION:
Once we have the total amount of oxygen inspired into the lungs, we must subtract the amount of oxygen consumed by the lungs. This cannot be measured directly, so we can estimate oxygen consumption in an indirect way. RQ is the ratio between the amount of CO2 produced and the amount of O2 consumed. In general, it is safe to use the normal value of 0.8 for the RQ. We can divide the PaCO2 by the RQ to indirectly estimate the amount of oxygen consumed by the lungs.
STEP 4: Subtract the amount of oxygen consumed by the lungs from the amount of oxygen inspired into the lungs.
Steps 1 and 2 determines how much oxygen is inspired into the lungs, and step 3 determines how much oxygen is consumed by the lungs. By subtracting the consumption of oxygen from the total oxygen available, we get the actual partial pressure of oxygen in the alveoli or PAO2.

THE ACTUAL EQUATION:

PAO2 = (PB - PH2O) FiO2 - PaCO2/RQ                                        

            OR (with constants)                                                  

PAO2 = (PB - 47) FiO2 - PaCO2/0.8                                                

     OR (if multiplication is easier)  
                                                   
PAO2 = (PB - 47) FiO2 - PaCO2 x 1.25                                  

EXPLANATION: Again, PB is barometric pressure, PH2O is partial pressure of water vapor which is a constant of 47, FiO2 is fraction of inspired oxygen or the percentage of oxygen the person is breathing (.21 if breathing regular room air), PaCO2 is the partial pressure of CO2 in the arteries and is obtained from an arterial blood gas, RQ is respiratory quotient which is normally 0.8 (1.25 is a factor that can by used to multiply rather than divide to get the same answer).

SHORTCUT:
I recommend that educators teach the actual equation and explain exactly what it is calculating. Yet, in times when a calculator is not available (during board exams), shortcuts can be used to calculate the answers more easily.  Stanley (2015) provides a shortcut that proves to be quite accurate and easier to calculate.

PAO2 = (O2% x 7) - (PaCO2 + 10)

WHY IS PAO2 IMPORTANT?
PAO2 alone does not tell us a whole lot, but it becomes important when it is compared to PaO2 (remember big A is alveolar and little a is arterial. Because gas reaches equilibrium during diffusion, ideally PAO2 and PaO2 should be the same. Large differences between the two indicates problems with gas exchange.
PAO2 is also needed to determine alveolar oxygen content which is used to determine intrapulmonary shunting.

VIDEOS FOR BETTER UNDERSTANDING:

If cookies prevent videos from opening, click on the links under Khan Academy in the reference section.

References:

Des Jardins, T. (2013). Cardiopulmonary Anatomy & Physiology: Essentials of Respiratory Care.

           Clifton Park, New York: Delmar.

Khan Academy (Producer). (2017). Alveolar gas equation- part 1 [Video file]. Retrieved from https://www.khanacademy.org/science/health-and-medicine/respiratory-system/gas-exchange-jv/v/alveolar-gas-equation-part-1

Khan Academy (Producer). (2017). Alveolar gas equation- part 2 [Video file]. Retrieved from https://www.khanacademy.org/science/health-and-medicine/respiratory-system/gas-exchange-jv/v/alveolar-gas-equation-part-2

Stanley, Dennis R. (2015). Respiratory Therapy Exam Review: Therapist Multiple Choice Exam. Las

           Vegas, Nevada: Lindsey Jones LLC.

Alveolar Gas Equation Practice Questions

1.      A patient is receiving 55% FiO2 on a day when the barometric pressure is 685 mm Hg. A blood gas shows that the PaCO2 is 45 torr. What is the patients PAO2?

2.      A patient comes to the clinic in respiratory distress. The blood gas shows a PaCO2 of 56 torr, while the patient is breathing room air. If the barometric pressure is 702 mmHg, what is the PAO2?

3.      A patient is on a nasal cannula at 2LPM. A blood gas shows a PaCO2 of 42. If the barometric pressure is 740, what would you calculate the PAO2 to be (hint: what is FiO2 estimated at 2LPM).

4.      A 27-year-old young woman came to the emergency room complaining of pleuritic chest pain of several hours duration. Her chest x-ray and physical exam were normal except for splinting with deep inspirations. Arterial blood gas showed pH: 7.45, PaCO2: 31 mm Hg, HCO3-: 21 mEq/L, PaO2: 83 mm Hg (breathing ambient air; PB: 747 mm Hg).  Calculate the PAO2 (Sift through all the unnecessary numbers and information!).

5.      A 60-year-old male with COPD is an air entrainment device set at 42%. The blood gas shows a PaCO2 of 60. If the barometric pressure is 730 mmHg, what is the PAO2?

LINK TO ONLINE CALCULATOR:
This link allows you to plug in values and check your work:
https://www.easycalculation.com/medical/alveolar-gas-equation.php

References:

Alveolar gas equation calculator. (n.d.). Retrieved March 11, 2017, from https://www.easycalculation.com/medical/alveolar-gas-equation.php

Alveolar Gas Equation Practice Answer Key

1.      PAO2= (685-47).55 – 45/0.8  OR [45 x 1.25]

                               350.9      -     56.25 = 294.65

            PAO2 = 294.65

2.      PAO2= (702-47).21 – 56/0.8 OR [56 x 1.25]

       137.55   -     70 = 67.55

            PAO2 = 67.55

3.      PAO2= (740-47).28 – 42/0.8 OR [42 x 1.25]

       194.04    -     52.5  = 141.54

            PAO2 = 141.54

4.      PAO2 = (747-47).21 – 31/0.8 OR [31 x 1.25]

                     147       -     38.75 = 108.25

PAO2 = 108.25

5.      PAO2 = (730-47).42 – 60/0.8 OR [60 x 1.25]

286.86       -      75 = 211.86

            PAO2 = 211.86