Question

Suppose that the volume of the lungs is V, the amount of breathed in and out is W, the initial concentration of chemical is c0, and the ambient concentration of chemical is γ. Given that V=2L, W=0.5L, c0=1mmol/L, γ=5mmol/L, find the following:

Step 1: The amount of chemical in the lungs before breathing is equal to

Step 2: The amount of chemical breathed out is equal to

Step 3: The amount of chemical in the lungs after breathing out is equal to

Step 4: The amount of chemical breathed in is equal to

Step 5: The amount of chemical in the lungs after breathing in is equal to

Step 6: The concentration of chemical in the lungs after breathing in is equal to

Answer 1

step 1

amount of chemical = concentration*volume

c0 = 1 mmol/L and volume,V = 2L

hence, amount of chemical = 1 mmol/L * 2 L = 2 mmol

Step 2

amount of chemical breathed out = Volume breathed out * c0

volume breathed out ,W = 0.5 L

so, amount of chemical breathed out = 0.5 L * 1 mmol/L = 0.5 mmol

Step 3

amount of chemical in the lungs after breathing out = (2-0.5) * c0

= 1.5 L * 1 mmol/L = 1.5 mmol

Step 4

The amount of chemical breathed in =  γ* W

= 5 mmol/L * 0.5 = 2.5 mmol

Step 5

The amount of chemical in the lungs after breathing in = initial amount - amount breathed out + amount breathed in

= 2 mmol - 0.5 mmol + 2.5 mmol

= 4 mmol

Step 6

The concentration of chemical in the lungs after breathing in = total amount/ volume

= 4 mmol / 2 L

= 2 mmol/L