An adult takes about 15 breaths per minute, with each breath having a volume of 500mL. if the air that is inhaled is "dry", but he exhaled air is 1 atm pressure is saturated with water vapor at 37 degree C(body temp), what mass of water is lost from the body in 1hr? The vapor pressure of water at 37degree C is 47.1 mmHg.
I tried doing this with partial pressures but its not coming out right.Please Help!!
but the air that came out has a pressure of 1atm. doesnt that mean it has the partial pressure of air and water in it??
The volume of air inhaled in 1 hour is
(60 min/hr)(15 br./min) = 900 breaths
(900 br.)(0.500L/breath) = 450 L
To find moles of H2O, use the Ideal Gas Law:
PV = nRT
1 atm = 760 mm Hg
47.1mmHg/760 mmHg/atm = 0.061974 atm
P = 0.061974 atm for water vapor
R = 0.08206 L.atm/K.mol
T = 273 + 37 = 310K
Find moles of H2O:
n = PV / RT
Mass of H2O in grams is:
(moles H2O)(18.015 g/mol.H2O)
the question was
....but the exhaled air at 1atm pressure is saturated with water vapor.....
To calculate the mass of water lost from the body in 1 hour, we need to determine the amount of water vapor exhaled from the lungs during that time.
First, let's convert the given values to their respective SI units for consistency:
Vapor pressure of water at 37°C = 47.1 mmHg = 47.1 / 760 atm
Breath volume = 500 mL = 0.5 L
Now, let's calculate the partial pressure of water vapor in the exhaled air. The partial pressure of water vapor can be determined using Dalton's law of partial pressures, which states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each gas.
Partial pressure of water vapor (Pvap) = Total pressure (Ptotal) - Partial pressure of dry air (Pdryair)
The total pressure is given as 1 atm, and since the exhaled air is saturated with water vapor, the partial pressure of dry air is equal to the vapor pressure of water at 37°C:
Pdryair = Pvap = 47.1 / 760 atm
Now, let's calculate the number of breaths per hour:
Number of breaths per minute = 15 breaths
Number of breaths per hour = 15 breaths * 60 minutes = 900 breaths
Next, let's calculate the total volume of exhaled air in 1 hour:
Total volume of exhaled air = Breath volume * Number of breaths per hour = 0.5 L * 900 = 450 L
Finally, we can calculate the mass of water lost from the body by considering that every liter of saturated air at 37°C contains a certain mass of water:
Mass of water lost = Total volume of exhaled air * Partial pressure of water vapor * Molar mass of water / Gas constant
The molar mass of water is about 18 g/mol, and the gas constant (R) is approximately 0.0821 L·atm / (mol·K).
Using these values, we can plug in the numbers and solve for the mass of water lost:
Mass of water lost = 450 L * (47.1 / 760 atm) * 18 g/mol / 0.0821 L·atm/(mol·K)
Calculating this expression gives us the mass of water lost from the body in grams per hour.
Note: Make sure to check the units throughout the calculations and perform any necessary conversions before plugging in the values to ensure consistency and accuracy.