“Under the Sea”
An Ideal Gas Law Problem
Introduction:
You are on vacation in the Bahamas with some of your best friends, and you all decide to
go SCUBA diving. Upon arrival, you and your friends begin suiting up and listening
intently to the SCUBA instructor. The instructor warns the group not to go too deep into
the ocean and not to rush to the surface of the ocean. This could cause the lungs to
collapse or explode. He emphasizes that if you do find yourself rushing to the surface,
you must exhale at a steady rate before reaching the surface. Excitedly, you and your
friends jump into the ocean, and begin exploring. You find yourself deeper than you
imagined, and stuck on a patch of coral reef. Yanking at the equipment, you accidentally
cause your air tank to fall off. You hold your breath and begin to swim to the surface.
What volume of air do you have to release out of your lungs to safely reach the surface
not allowing your instructor’s warning to hold true?
Information Available:
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Depth
Initial Temperature
Final Temperature
Initial Pressure (1 atm)
Gender of Diver
Mass of Diver
Mass of Air Tank
Volume of Air Tank
Volume Inhaled
Information Available in the Library:
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Ideal Gas Law
Boyle’s Law
Charles’ Law
Gay-Lussac’s Law
Avogadro’s Law
Pressure in Ocean Equation (P = Ph + ρgh)
Density of Salt Water (1.025 g/mL)
Density of Water (1.00 g/mL)
Density of Nitrogen (1.2506 g/L)
Density of Oxygen (1.419 g/L)
Universal Gas Constant (R)
Gravitational Constant
Percentage of Each Gas in Tank; Combination of these gases is known as Nitrox
Library-“Under the Sea”
Definitions:
Ideal Gas: An ideal gas is defined as one in which all collisions between atoms or
molecules are perfectly elastic and in which there are no intermolecular attractive
forces.
Ideal Gas Law: This law expresses the relationship between pressure, volume and
temperature of ideal gases.
Boyle’s Law: Boyle's Law (also known as the Boyle Mariotte law) is one of the gas
laws. It relates the volume and pressure of an ideal gas held at a constant
temperature.
Charles’ Law: Charles’s Law is one of the gas laws. It relates the volume and
temperature of an ideal gas held at a constant pressure.
Gay-Lussac’s Law: Gay-Lussac’s Law indicates that for a fixed amount of gas (fixed
number of moles) at a fixed volume, the pressure is proportional to the temperature.
Avagadro’s Law: Avogadro's Law states that under conditions of constant pressure
and temperature, there is a direct relationship between the volume and number of
moles for an ideal gas.
Equations:
Ideal Gas Law Equation
 PV = nRT
o P = Pressure in Atmospheres
o V = Volume in Liters
o n = Number of Moles of Gas
o R= Universal Gas Constant
o T = Temperature in Kelvins
Boyle’s Law Equation
 P1V1 = P2V2
o P = Pressure in Atmospheres
o V = Volume in Liters
o Moles and Temperature remain constant
Charles’ Law Equation
V1 V2
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T1 T2
o V = Volume in Liters
o T = Temperature in Kelvins
o Moles and Pressure remain constant
Gay-Lussac’s Law Equation
P1 P2
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T1 T2
o P = Pressure in Atmospheres
o T = Temperature in Kelvins
o Volume and Moles remain constant
Avagadro’s Law Equation
V1 V2
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n1 n2
o V = Volumes in Liters
o n = Moles
o Pressure and Temperature remain constant
Pressure in Ocean Equation
 (P = Ph + ρgh)
o Ph = Pressure at specific depth
o ρ = Constant
o g = Gravitational Constant
o h = Depth
Constants:
Universal Gas Law Constant (R)
 0.08206 L*atm/K
Gravitational Constant
 9.81 m/s
Densities:
Density of Salt Water
 1.025 g/mL
Density of Water
 1.00 g/mL
Density of Nitrogen
 1.2506 g/L
Density of Oxygen
 1.419 g/L
Percentages of Each of the Gases in the Air Tank
Nitrogen
 60%
Oxygen
 40%
Volume Human Lungs can Hold -- 4-6 Liters