Hello class,

For this discussion, you will give an example of a real-world scenario in which someone would need to make a gas-law calculation.

Here’s an example: 

As many of you probably know, the most common serious condition associated with severe COVID-19 infection is acute respiratory failure due to compromised lung function.  Early in the pandemic, the standard treatment was invasive mechanical ventilation (IMV)  (which includes intubation), which typically has significant negative long-term effects on the patient.  Fortunately, later in the pandemic, an alternate treatment emerged:  High-flow nasal oxygen (HFNO).  With HFNO, intubation is not necessary.  Instead, a tube is inserted into the nose, and the patient’s lungs are flooded with oxygen.  Some patients who were put on HFNO were able to avoid mechanical ventilation altogether.  In addition, because HFNO has less serious side effects than IMV, it can be used on a much wider range of patients.

But this creates an issue for hospitals:  Both IMV and HFNO have high oxygen flow rates.  These can vary, but 60.0 L/min is a typical value.  If the hospital uses HFNO on a wider range of patients than IMV, it will need much larger oxygen reserves.

Suppose the hospital’s oxygen cylinders have a volume of 200.0 L (these are large cylindersabout 1.3 m tall), and they can be filled with oxygen to a pressure of 200.0 atm.  The hospital needs to know the rate at which to reorder cylinders. So how long does it take one patient to use up one cylinder? 

To answer this, we need to know the volume that cylinder’s oxygen would have after it expands to 1 atm pressure.  So we use Boyle’s Law:

V2 = V1 x (P1/P2) = 200.0 L x (200.0 atm/1 atm) = 40,000 L  (the underline allows us to keep track of significant figures).

Now we need to know how long 40,000 L will last:

40,000 L /(60.0 L/min) = 667 min;  667 min x (1 hr/60 min) =11.1 hours.

Thus we can see the enormous resource burden on a hospital from HFNO treatment:  Each addition patient requires more than two of these oxygen cylinders per day.