a resting person requires 14.5 L of O2 per hour to maintain metabolic activities. Such a person breathes in 0.50 L of air at approximately 20 degrees C with each breath. The inhaled air is 20.9%O2 while the exhaled air is 16.3% O2. (a) how many breaths per minute does a resting person need to take to provide the necessary oxygen? (b) How many O2 molecules does a resting person inhale per breath?
To find the number of breaths per minute a resting person needs to take to provide the necessary oxygen, we first need to calculate the amount of oxygen inhaled per minute.
To do this, we need to find the difference in the amount of oxygen between inhaled and exhaled air. Let's calculate it step by step:
1. Calculate the amount of oxygen inhaled per breath:
Inhaled oxygen per breath = 0.50 L * 20.9% = 0.1045 L (rounded to four decimal places)
2. Calculate the amount of oxygen exhaled per breath:
Exhaled oxygen per breath = 0.50 L * 16.3% = 0.0815 L (rounded to four decimal places)
3. Calculate the net amount of oxygen inhaled per breath:
Net inhaled oxygen per breath = Inhaled oxygen per breath - Exhaled oxygen per breath
= 0.1045 L - 0.0815 L
= 0.023 L (rounded to three decimal places)
Now that we know the net amount of oxygen inhaled per breath, we can calculate the number of breaths per minute required to meet the oxygen requirement of 14.5 L/hour:
4. Calculate the number of breaths required per minute:
Oxygen requirement per minute = Oxygen requirement per hour / 60 minutes
= 14.5 L / 60
≈ 0.2417 L/min (rounded to four decimal places)
Number of breaths required per minute = Oxygen requirement per minute / Net inhaled oxygen per breath
= 0.2417 L/min / 0.023 L/breath
≈ 10.51 breaths/min (rounded to two decimal places)
Therefore, a resting person needs to take approximately 10.51 breaths per minute to provide the necessary oxygen.
Next, let's calculate the number of oxygen molecules inhaled per breath:
1. Calculate the number of moles of oxygen inhaled per breath:
Moles of oxygen = Volume of oxygen inhaled per breath / Molar volume of gas at 20°C and 1 atm.
= 0.1045 L / 22.4 L/mol (approximated molar volume)
2. Calculate the number of molecules of oxygen inhaled per breath:
Number of molecules = Moles of oxygen * Avogadro's number
= Moles of oxygen * 6.022 × 10^23
Using the same steps, calculate the number of oxygen molecules inhaled per breath using the exhaled oxygen percentage. After that, subtract the exhaled count from the inhaled count to find the net number of oxygen molecules inhaled per breath.
Finally, you can use the calculated net number of oxygen molecules inhaled per breath to answer part (b) of the question.