The equation for the standard atmosphere between sea level and 11 km above the e

Question

The equation for the standard atmosphere between sea level and 11 km above the earth's surface can be given by: P_atm = 760(1 - 0.022558z)^5.2SS9, where P_atm is the barometric pressure in millimeters of mercury, and is the altitude above mean sea level in kilometers. A given person has 15 g Hgb per 100 mL blood and a partial pressure of alveolar CO2 of 33 mmHg. Based on the hemoglobin saturation curve shown below, how much hemoglobin a comparable person would need to have the same amount of oxygen in his/her blood at 14,000 ft above mean sea level. Assume the person at the higher altitude has a partial pressure of alveolar carbon dioxide of 15 mmHg.

Explanation / Answer

(i)

Atmospheric pressure :

Given formulae,

Patm = 760 ( 1 -0.022558*11)5.2359 = 170.72 mm of Hg

The person will have an oxygen content of his/her blood of:

1.34 (15 / 100 ) = 20.1 mL O2 100 mL blood

To find the oxygen content of the blood in the high-altitude native solve for the hgb content that will give the same total oxygen content at 85 percent saturation:

20.1/ 100 = 1.34 ( X /100 )*0.85

x = 0.201/ 0.01139 = 17.64 gm Hgb/ 100 mL blood

So , the person will need 17.64 gm Hgb/ 100 mL blood hemoglobin.

WE know that,

1 ft = 0.0003048

Hence,

14000 ft = 4.2672 KM

Given formulae,

Patm = 760 ( 1 -0.022558*z)5.2359

= 760 ( 1 -0.022558*4.2672 )5.2359

   = 447.366 mm Hg

Therefore,

Pco2 = (0.21 ( 447.366 - 47) - 50 ) /1.2

= 28.39 mm Hg

The partial pressure of carbon dioxide in the arterial blood is 28.39 mmHg.

     

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