GAS LAWSPhysics & Anaesthetic implication

"We live submerged at the bottom of an ocean of air - Torricelli, 1644"

Dr.J.Edward Johnson.M.D., D.C.H.,Asst. ProfessorKanyakumari Govt Medical College & Hospital,Asaripallam, Nagercoil,Tamilnadu, INDIA.

Molecular Theory

Van der Waals forces

Lattice(oscillates)

•All matter is made of tiny particles called atoms. •These atoms are in constant motion Brownian motion (random motion).• Each particle has kinetic energy.• Collisions between particles are perfectly elastic.

Interface

Saturated Vapour Pressure

Pressure

The Gas LawsIntroduction

1. Definitions: Pressure = force/area P = F/A

2. Units: • Pascal (Pa):  1 Pa = 1 Newton/m2 or 1N/m2

The Pascal is the Standard International Unit of pressure The Newton is the Standard International Unit of force

• Atmosphere (atm): one atm  =101325 Pa   • Pounds per sq inch (psi): one atm = 14.7 psi or lbs/in2• Torricelli (torr): one atm = 760 torr

mmHg: 1 mmHg = 1 torr• Millimeters Hg: one atm = 760 mmHg

1 atm = 14.7 psi = 760 mmHg = 101 kPa

In the Torricellian tube, the atmospheric pressure supports, mercury 760 mm tall

Pressure P= f/a

Pressure is inversely proportional to area

20ml

10ml

1 atm

2 atm

Anesthesia Machine ExamplesPressure Relief ValveExpiratory ValvePressure-reducing valve AKA pressure regulator

Oxygen Failure warning device

Pressure P= f/a

Comparison of Variables & Constants in Gas Laws

Variables allowed to change

Variables held constant Resulting relationship Formal designation

Pressure and VolumeNumber of molecules and Temperature

P1V1 = P2V2 Boyle's Law

Volume and Temperature

Number of molecules and Pressure

V1/T1=V2/T2 Charles' Law

Pressure and Temperature

Number of molecules and Volume

P1/T1=P2/T2 Amonton's Law

Number molecules and Volume

Pressure and Temperature V1/n1=V2/n2 Avogadro's Law

Pressure, Volume, & Temperature

Number of molecules P1V1/T1=P2V2/T2 Combined Gas Law

Pressure, Volume, Temperature & Number of molecules

-- P1V1/n1T1=P2V2/n2T2 Ideal Gas Law

Boyle’s Law (Pressure – Volume Law)

The volume of a given amount of gas at a constant temperature varies inversely with the pressure

P1V1 = P2V2

Graph of pressure vs. volume for a gas enclosed in a cylinder at constant temperature (Boyle's law)

Example - CylindersFor example, if we have a cylinder of gas under pressure equivalent to 13,800 kPa (the internal volume or capacity of the cylinder is about 10 liters), how much gas would be available at atmospheric pressure which we will say is about 100 kPa.

13,800 kPa

10 liters

AtmosphereCylinder

P1

V1

100 kPaP2

V2 ?P1V1 = P2V2

13,800 x 10 = 100 x V2

V2 = 13,800 x 10

100

V2 = 1380 lts

Charles’ Law (Temperature-Volume Law)

Gas volume varies directly with temperature at a constant pressure

V1/T1=V2/T2

Remember, always use degrees Kelvin for temperature representation

Amontons' Law of Pressure-Temperature

Gas pressure varies directly with temperature at a constant volume

P1/T1=P2/T2

Gay-Lussac Law Law of combining volumesThe ratio between the volumes of the reactant gases and the products can be expressed in simple whole numbers.

STP- 273.15˚ k(0˚C) - 101kPas(760mmHg)

“Pay TV Can Be Good”

Pressure-Volume-TemperatureRelationships

Pay- T - V -

Can Be Good

Pressure constant-Charles Temperature constant-Boyles Volume constant-GayLussac

Avogadro's LawFor a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant.

Avogadro's Law“Equal volumes of any two gases at the same temperature and pressure contain the same number of molecules.”

V∝ n (at constant T and P)

One mole of any gas contains the same number of molecules (Avogadro's number =6.02×1023)

Gram molecule(mass of gas)

Same number of molecules in one gram molecule

H2 O2

H2O

2H2+O2=2H20

Ideal Gas Law (Universal Gas Law) Under the same condition of temperature and pressure, equal volumes of all gases contain the same number of molecules.

He N2 O2

Calibration of Vaporizers

One mole of Gas

22.4 L At STP

Isoflurane18.45gm

O2 O2 + Isoflurane224 L

Mol.wt of Iso – 184.5184.5 gm of Iso = 1 mol

0.1 mol 2.24 L 2.24 = 1% 224

Calculation of volume of Nitrous Oxide gas

3.4kg

Mol. Wt of N2O - 44

1 mol = 44 gm

44 gm(1mol) occupies = 22.4 L3400 gm occupies = 22.4 x 3400 = 1730 L 44

Combined gas law

The combined gas law is a gas law which combines Charles's law, Boyle's law, and Gay-Lussac's law

Combined gas law

Dalton’s Law of Partial Pressures The total pressure exerted by a mixture of gases is the sum of their individual partial pressures

Ptotal = Pa + Pb + Pc + etc

GASPartial Pressure (mmHg)

Inhaled Alveolar Exhaled

Nitrogen 594.70 570 569

Oxygen 160.00 103 116

CO2 0.30 40 28

H2O vapor

5.00 47 47

TOTAL 760 760 760

PARTIAL PRESSURE of AIR

Dalton’s Law of Partial Pressures

Entanox Cylinders

• What is the partial pressures of O2 and N2O if you are administering a ratio of 70/30?

• N20 70% X 760 mmHg = 532 mmHgO2 30% X 760 mmHg = 228 mmHg

760 mmHg

• Would this differ if you were administering anesthesia at Denver General Hospital?

• N20 70% X 630 mmHg = 441 mmHgO2 30% X 630 mmHg = 189 mmHg

630 mmHg

Dalton’s Law of Partial Pressures

Miami = 14.7 psi Denver = 12.2 psiMiami = 760mmHg Denver = 630mmHg

Adiabatic heating and coolingAdiabatic changes in temperature occur due to changes in pressure of a gas while not adding or subtracting any heat

Cryoprobe – N2O or CO2

Critical TemperatureAs the substance approaches critical temperature, the properties of its gas and liquid phases converge, resulting in only one phase at the critical point

Critical Temp of N2O = 36.5˚CCritical Temp of O2 = -119 ˚C