During the normal breathing cycle, a great deal of air remains in the lungs, cal

Question

During the normal breathing cycle, a great deal of air remains in the lungs, called the residual volume. The residual and tidal volumes are important to consider in Problems 7A.12–7A.14.

7A.12 (M) Assume that an allergen is in an aerosol form (1.0 g/(L air)) and can be inspired and expired at the same rate as normal air. After a sufficiently long exposure time, the equilibrium concentration of allergen in the lungs is 1.0 g/(L air). Write equations describing the loss of allergen from the lung for a normal lung, assuming no further exposure. How long will it take to decrease the allergen concentration in the alveoli to less than 1.0% of its inspired concentration (i.e., less than 0.010 g/(L air))? Develop a graph of the concentration of allergen in the lung as a function of time. Use an integral mass balance to check your answer.

Explanation / Answer

The average tidal volume is 500ml in one respiratory cycle , and in one min 12 such cycles occur that is called the respiratory rate.

so in 1 min he'll breath 12×500ml = 6000ml of air with the allergen

Now the concentration of allergen in air is 1gm/L so in 6000ml or 6L it'll be 6gms of allergen which enters into his lungs at equilibrium the concentration remains 1gm/L that's the allergen accumulated in the lungs .

Now the person is exposed to normal environment , so according to Le chartliers principle the equilibrium will shift in the direction to oppse the change so now the change is shift in environment from allergic to normal the environment doesn't have allergen so the allergen will be lost from the lungs

1% of 6gm is = 0.06 gms

6000ml = 6gms

x = 0.06 gms

60ml of air

per min or 60 sec = 6000ml of air

x sec = 60 ml

= 0.6 sec will be required to loose 1%

The graph will show for every 0.6 sec there will be 0.010 g /L

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