Ideal Gas Law

Pressure, volume, temperature, and amount of gas

Macroscopic physical properties of gases.

Ideal gas

A hypothetical construct that real gases approximate under certain conditions.

Ideal gas law

Relates gas quantities for gases and is quite accurate for low pressures and moderate temperatures.

1783

Year when the first hydrogen filled balloon flight, manned hydrogen filled balloon flight and hot air balloon flight occurred

Guillaume Amontons

A French physicist who was the first to empirically establish the relationship between the pressure and temperature of a gas.

Joseph Louis Gay-Lussac

A French physicist who determined the relationship between the pressure and temperature of a gas even more precisely.

Amonton’s law or Gay-Lussac’s law

The law that states that the pressure for a given amount of gas is directly proportional to its temperature on the kelvin scale when the volume is held constant

P1/T1 = P2/T2

Mathematical representation of the Amonton’s law

Absolute zero

0 on the Kelvin scale, which is the lowest possible temperature

Jacques Alexandre César Charles

French Scientist and a ballon flight pioneer who was the first to find out the relationship between the volume and temperature of the given amount of gas at the constant pressure.

Charles’ law

Law which states that the volume of a given amount of gas is directly proportional to its temperature on the Kelvin scale when the pressure is held constant.

V1/T1 = V2/T2

Mathematical representation of the Charles’ law

Robert Boyle

An English chemist and a natural philosopher to observe the inversely proportional relationship of the gas’ volume to the pressure it applies.

Boyle’s law

The law that states that the given amount of gas at a constant temperature, its pressure and volume are inversely proportional.

P = 1/V or P1V1 = P2V2

Mathematical representation of the Boyle’s law

Intercostal muscles

The muscles that are between the ribs

Amedeo Avogadro

An Italian scientist to state that the equal volumes of all gases, measured under the same conditions of temperature and pressure, contain the number of molecules, in 1811

Avogadro’s law

A law that says that for a confined gas, the volume and the number of moles are directly proportional if the pressure and temperature both remain constant.

V1/n1 = V2/n2

Mathematical representation of the Avogadro’s law

PV = nRT

Mathematical representation of the ideal gas law

R

The symbol that represents the ideal gas constant or the universal gas constant

0.08206 L atm mol^-1 K^-1 and 8.314 kPa L mol^-1 K^-1

Two values of the ideal gas constant

Ideal behavior

When a real gas behaves like an ideal gas, following the gas laws accurately. Happens best at low pressure and high temperature.

Kinetic molecular theory

A model that explains gas laws by assuming gas particles move randomly, and don’t attract each other, and collide elastically.

Limitations of Ideal Gas Law

At high pressures and low temperatures, real gases deviate from ideal behavior because particles have volume and attract each other.

Van de Waals equation

A modified gas law for real gases that adjusts the Ideal gas law by including particle volume and intermolecular forces.

(P + (a/V^2)) (V - b) = nRT

Van de Waals equation formula

Correction for intermolecular attractions (a)

The a/V^2 term adds to pressure to correct for attractive forces that reduce collisions with the container walls.

Correction for Particle Volume (b)

The (V - b) term subtracts excluded volume because gas particles themselves take up the space

Breathing and Boyle’s Law

Breathing works by Boyle’s Law: when Lung volume increases, pressure drops and air flows in (inhalation). When lung volume decreases, pressure rises and air flows out (exhalation)

Syringe and Boyle’s law

In an airtight syringe at a constant temperature, pushing the plunger decreases the volume and increases the pressure;

Pulling it out increases the volume and decreases the pressure.

Propellant

A pressurized gas or liquified gas used in aerosol products like hair sprayers to expel the product in a fine, controlled mist

Isobutane

(C₄H₁₀) A very common hydrocarbon propellant that is used in hairsprays due to its efficiency, rapid evaporation, and lower environmental impact compared to the older propellants.

Combined gas law

A gas law that links pressure, volume, and temperature for a fixed amount of gas.

Showing how gas changed when more than one condition changes.

(P1V1)/T1 = (P2V2)/T2

Mathematical representation of the combined gas law

Atmosphere absolutes (ATA)

The pressure measurement unit utilized by the diving community

Pressure increase with the Ocean Depth

Pressure increases as divers go deeper. At the surface 1 ATA;

Every 33 feet of salt water add 1 ATA.

The total pressure on the diver

The sum of the atmospheric pressure and the water pressure above the diver.

Air Pocket Compression/Expansion

On descent: Air pockets (ears, lungs) compress

On ascent: Air pockets expand, risking the eardrum rupture or lung injury.

Equalization (Descent)

Divers add air to body spaces (ears, masks, sinuses) to balance the increasing pressure.

Equalization (Ascent)

Diver releases air from the body to prevent over expansion and injury.

Buoyancy

The upward force exerted by the fluid that opposes the weight of an object immersed in it.

Buoyancy Compensator Device (BCD)

The devices used by divers that holds air in order to control the buoyancy.

BCD and Boyle’s Law

Ascending: Air expands in the BCD (lower pressure) → buoyancy increases → risk of uncontrolled ascent.

Descending: Air compresses in the BCD (higher pressure) → buoyancy decreases → risk of uncontrolled descent

Air consumption with depth

Deeper = more compressed air in tanks. At 33 ft (2 ATA), air volume halves, so the air diver uses air twice as fast as at the surface.

Standard temperature and pressure

Full form of STP

273.15 K and 1 atm (101.325 kPa)

What’s the STP

22.4 L

What is the Standard molar volume of the 1 mole gas at STP