A submarine has run into trouble and is stuck at the bottom of the ocean. Several people are on board and must make their way to the surface without any diving gear. The air pressure aboard the submarine is 3.100 atm. The air temperature inside the submarine is 10.01 ¢XC and you can take body temperature (inside the lungs) to be 37.74 ¢XC. The first person to leave takes a breath as deep as possible by exhaling as far as possible (leaving a volume of 1.070 L in their lungs), and then slowly inhaling to increase their lung volume by 4.590 L. His body temperature is also 37.74 ¢XC.

Question

A submarine has run into trouble and is stuck at the bottom of the ocean. Several people are on board and must make their way to the surface without any diving gear. The air pressure aboard the submarine is 3.100 atm. The air temperature inside the submarine is 10.01 ¢XC and you can take body temperature (inside the lungs) to be 37.74 ¢XC. The first person to leave takes a breath as deep as possible by exhaling as far as possible (leaving a volume of 1.070 L in their lungs), and then slowly inhaling to increase their lung volume by 4.590 L. His body temperature is also 37.74 ¢XC.

(i) How many particles of air do their lungs contain after inhaling?
(ii) This person breathes out all the way to the surface in order to maintain a constant lung volume. How many moles of gas remain in the lungs?

Answer 1

for A-1). just use PV = nRT. the question suggests constant pressure. So Charles law applies?

Um... so .

Let = volume of the lung (4.98L)
Let = temperature of the body (309.38K)
Let = temperature of the submarine (291.51K)
Let = be your unknown

Answer 2

To answer the questions, we need to use the ideal gas law equation:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature

First, we need to find the number of moles of air in the person's lungs after inhaling.

(i) To find the number of particles of air in their lungs after inhaling, we need to calculate the number of moles of air. We can use the ideal gas law equation and rearrange it to solve for the number of moles (n).

PV = nRT

We have the following values:
P = 3.100 atm (pressure in the submarine)
V = 1.070 L + 4.590 L (initial lung volume + increased lung volume)
R = 0.0821 L·atm/(mol·K) (ideal gas constant)
T = 37.74 ¢XC + 273.15 ¢K (body temperature in Kelvin)

Let's calculate n:

n = PV / RT

n = (3.100 atm) * (1.070 L + 4.590 L) / (0.0821 L·atm/(mol·K) * (37.74 ¢XC + 273.15 ¢K))

Simplifying the equation:
n = (3.100 atm) * (5.660 L) / (0.0821 L·atm/(mol·K) * (310.89 K))

n = 13.550 moles

Therefore, the person's lungs contain approximately 13.550 moles of air after inhaling.

(ii) To find the number of moles of gas remaining in the lungs when the person breathes out all the way to the surface, we need to consider that the temperature remains constant during the process. Since the volume is also constant, we can directly use the ideal gas law to calculate the number of moles of gas remaining.

Using the same ideal gas law equation:

PV = nRT

We have the following values:
P = 1 atm (pressure at the surface of the ocean)
V = 5.660 L (constant lung volume)
R = 0.0821 L·atm/(mol·K) (ideal gas constant)
T = 37.74 ¢XC + 273.15 ¢K (body temperature in Kelvin)

Let's calculate n:

n = PV / RT

n = (1 atm) * (5.660 L) / (0.0821 L·atm/(mol·K) * (37.74 ¢XC + 273.15 ¢K))

Simplifying the equation:
n = (1 atm) * (5.660 L) / (0.0821 L·atm/(mol·K) * (310.89 K))

n = 0.222 moles

Therefore, approximately 0.222 moles of gas remain in the person's lungs when they breathe out all the way to the surface.

Note: These calculations assume the air behaves ideally and that there are no other factors, such as dissolved gases or changes in atmospheric conditions, affecting the results.