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Question 8.12: A heliox breathing mixture of oxygen and helium is prepared ...

A heliox breathing mixture of oxygen and helium is prepared for a patient with chronic obstructive pulmonary disease (COPD). The gas mixture has a total pressure of 7.00 atm. If the partial pressure of the oxygen in the tank is 1140 mmHg, what is the partial pressure, in atmospheres, of the helium in the breathing mixture?

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ANALYZE THE PROBLEM Given Need Connect
P_{total} = 7.00  atm     P_{O_{2}} = 1140  mmHg partial pressure of He Dalton’s law

STEP 1  Write the equation for the sum of the partial pressures. 

P_{total} = P_{O_{2}} + P_{He}       Dalton’s law

STEP 2  Rearrange the equation to solve for the unknown pressure.To solve for the partial pressure of helium (P_{He}), we rearrange the equation to give the following:

P_{He} = P_{total}  –  P_{O_{2}}

Convert units to match.

P_{O_{2}}=1140  \cancel{mmHg} \times \frac{1  atm}{760  \cancel{mmHg}} =1.50  atm

STEP 3   Substitute known pressures into the equation, and calculate the unknown pressure.

P_{He} = P_{total}  –  P_{O_{2}}

 

P_{He} = 7.00  atm  –  1.50  atm = 5.50  atm

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