Gas Laws

Endothermic Reactions

-An endothermic reaction requires more energy than it produces. -It consumes heat rather than produces heat. -With endothermic reactions, solubility of liquids/solids (not gases*) is increased with increased temperature. -The solubility of gases in liquid is decreased with increased temperature because the gas wants to escape the liquid. These gas molecules have no desire to "be soluble" in the liquid.

Blood Gas Partition Coefficient (BGPC) = Ostwald Solubility Coefficient

-Anesthetic agents with low BGPC, such as N2O, are taken up by the blood less avidly than more soluble agents like halothane (HALO). As a consequence, the alveolar concentration of N2O rises faster than that of HALO, and induction is faster. -The relative solubilities of an anesthetic in air, blood and tissues are expressed as partition coefficients. -The agent follows a series of partial pressure gradients to reach its target, the brain: -Agent delivered -> inhaled/inspired into alveolar space -> into arterial bloodstream -> into brain & tissue. -Each coefficient [λ] is the ratio of the concentrations of the anesthetic gas in each of two phases at equilibrium. -Equilibrium is defined as equal partial pressures in the two phases. -λ is defined as the ratio of the conc. of gas dissolved in solution to the conc. of gas in the gas phase at equilibrium at 37 degrees C. -The higher the blood:gas partition coefficient (also called Ostwald Solubility Coefficient), the longer it takes to induce anesthesia and the longer it takes to emerge from anesthesia. DES (BGPC ≈ 0.42) : "quick on - quick off" ISO (BGPC ≈ 1.43) : "slow on - slow off"

Critical Temperature

-As we increase the temperature of a gas, liquefaction becomes more and more difficult because higher and higher pressures are required to overcome the increased kinetic energy of the molecules. -In fact, for every substance, there is some temperature above which the gas can no longer be liquefied, regardless of pressure. -This temperature is the critical temperature (Tc), the highest temperature at which a substance can exist as a liquid. -Above the critical temperature, the molecules have too much kinetic energy for the intermolecular attractive forces to hold them together in a separate liquid phase. -The critical temperature of N2O is 39.5 oC; thus, N2O can be compressed and stored as a liquid at room temperature. -The critical temperature of O2 is ‐119 oC. -O2 cannot be liquefied at room temperature, no matter how much pressure is applied.

Avogadro's Law: The Volume-Mole Relationship

-Avogadro's Law states that "equal volumes of gases at the same temperature and pressure contain the same number of molecules regardless of their chemical nature and physical properties". -This number (Avogadro's number) is 6.022 x 1023. -It is the number of molecules of any gas present in a volume of 22.4L and is the same for the lightest gas (hydrogen) as for a heavy gas such as carbon dioxide or Bromine. -The volume of a gas is directly proportional to the number of gas molecules, as long as temperature and pressure are held constant. -One mole of an ideal gas occupies 22.4 L at STP (standard temperature & pressure).

Avogadro's Number

-Avogadro's number is one of the fundamental constants of chemistry. -It permits calculation of the amount of pure substance (mole), the basis of stoichiometric relationships. -It also makes possible determination of how much heavier a simple molecule of one gas is than that of another, as a result the relative molecular weights of gases can be ascertained by comparing the weights of equal volumes. -Helium is a noble gas and is not sharing its electrons. A mole of helium would be 4 g MW (molecular weight), and contain 6.022 x 1023 atoms. Same with Ne (MW 20.0g) Oxygen O2 -Oxygen shares its electrons with another oxygen atom; a mole of oxygen contain 6.022 x 1023 molecules. Its molecular weight of a mole of oxygen (O2) would be 32 g (2x 16.0 g MW of oxygen). Methane CH4 -A mole of methane (CH4) contains 6.022 x 1023 molecules and its MW is 16.0 g (4 x 1g (H)+ 12.0 g (C)).

Concentration and Second Gas Effects

-Before administering inhalation agents, atmospheric N2 is in equilibrium with the body N2. -When N2O and sevoflurane is turned on simultaneously, N2O diffuses into the blood from the alveoli in much greater amounts than N2 diffuses from the blood into the alveoli (N2O is 34x more soluble in blood than is N2). -Consequently, because N2O is diffusing out of the alveoli at a greater rate than N2 is diffusing into the alveoli, the alveoli "shrink". -The concentration of both the second gas (sevoflurane) and N2O remain elevated. -Because concentration of the second gas (SEVO) is sustained, the rate of diffusion of the second gas (SEVO) remains elevated. -The uptake of a volatile agent is increased when it is administered simultaneously with N2O. This is the second gas effect, which is explained by Fick's law of diffusion.

Application of Fick's Law

-Concentration effect The higher the concentration of anesthetic agent delivered, the faster anesthesia is achieved. This is also referred to as overpressuring (see also Henry's law). As with any drug, the larger the initial dose administered, the faster the onset of action. -Second gas effect The second gas effect is a phenomenon in which two anesthetics of varying onset speeds are administered together. A high concentration of a fast anesthetic (N2O) is administered with a slower anesthetic gas. The slower gas achieves anesthetic levels more quickly than if it had been given alone. -Diffusion hypoxia (dilutional hypoxia after N2O delivery is discontinued)

Define critical temperature.

-Critical temperature above which a gas cannot be liquified, now matter how much pressure is applied.

Dalton's Law of Partial Pressures

-Dalton's law states the total pressure of a gaseous mixture is the sum of the partial pressure of each of the component gases. -Ptotal =∑Pi=P1 +P2 +......+Pn -Ptotal = total pressure -Pi = partial pressure of each component gas

Diffusion in Anesthesia

-Diffusion is a passive process of transport. A single substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. -N2O diffuses into air‐filled cavities; therefore, the delivery of N2O is contraindicated in patients with pneumothorax or where air‐ filled cavity expansion is undesirable. -N2O‐expansion of ETT cuffs may cause tracheal mucosal damage.

Diffusion

-Diffusion is the process of net movement of one type of molecule through space as a result of random motion intended to minimize a concentration gradient. -Kinetic energy allows molecules to move freely in a fluid, and therefore mixtures of fluids tend to evenly distribute. -Molecules with smaller mass will diffuse faster.

Application of Boyle's Law

-During inspiration when patient is spontaneously breathing, the intrapulmonary pressure decreases and volume increases. -During expiration, intrapulmonary pressure increases and volume decreases. -Measurement of FRC by body plethysmography. -Imagine you bring a balloon from San Diego (sea level) to higher elevation such as Denver. Boyle's Gas Law: In Denver is the atmospheric pressure less than in San Diego, therefore, the balloon's volume Increases

Solubility of Solids and Liquids

-Example: pour sugar (solid solute) in cold water (solvent) and warm it up -Solubility of solids in liquids is proportionately related to temperature. -As temperature increases, the kinetic energy of a salt increases and ions are dissolve well in liquid. Example: pour honey (liquid solute) into cold milk (solvent) and warm it up -Solubility of liquid (solute) in liquid (solvent) is also proportionately related to temperature. -As temperature increases, the kinetic energy of a liquid solute increases and their molecules (honey) are dissolve well in the liquid solvent (warm milk).

Fick's Law

-Fick's law for diffusion of a gas across a tissue plane is an encompassing law that accounts for -Partial pressure gradient (P1‐ P2 = ∆P) -Membrane area -Solubility of gas in membrane -Membrane thickness. -Square root of the molecular weight.

Henry's Law

-Henry's Law states "at constant temperature, the amount of gas dissolved in a liquid is directly proportional to the partial pressure of that gas at equilibrium above the gas‐liquid interface." -The formula is: C = kpgas -C is the solubility of a gas at a fixed temperature in a particular solvent (mlgas/L) -k is Henry's law constant (M/atm) -pgas is the partial pressure of a gas (often measured in atm) -Increasing the partial pressure of a gas above a liquid will increase the amount of gas that dissolves in the liquid. -Increased delivery of oxygen (FiO2) to patients to improve arterial oxygenation (PaO2) and overpressuring (high concentration) anesthetics reflect the direct relationship of pressure and solubility described by Henry's Law.

Solubility of Gases

-However, gases dissolve differently in liquids with increased temperature -Gas solubility in liquids is inversely related to temperature. -As temperature increases, less gas is able to dissolve into -An increased temperature represents greater kinetic energy. Greater kinetic energy allows dissolved gas molecules to escape and prevents further dissolving. -Lower temperature slows the kinetic energy of gas molecules, allowing them to dissolve into liquids. -A clinical example of temperature affecting solubility is seen with the slower emergence of hypothermic patients receiving general anesthesia with volatile agent (DES, ISO, or SEVO). The hypothermic patient retains anesthetic gases in the blood due to increased solubility related to (the lower body) temperature. Gas solubility in a liquid is directly proportional to pressure -> Henry's Law

How much O2 is dissolved if the FIO2 is 40?

-If the inspired O2 is given, estimate the PaO2 by multiplying the inspired concentration by 5 (for healthy lungs). -Multiply by 3 for moderate lung dysfunction and multiply by 2 for severe lung dysfunction. -40 x 5 (healthy lungs) = 200 mmHg, the estimated PaO2 amount dissolved = 200 mmHg x 0.003 = 0.6 ml O2/ 100ml blood. -40 x 3 (mod. lungs) = 120 mmHg, the estimated PaO2 amount dissolved = 120 mmHg x 0.003 = 0.36 ml O2/ 100ml blood. -40 x 2 (sick lungs) = 80 mmHg, the estimated PaO2 amount dissolved = 80 mmHg x 0.003 = 0.24 ml O2/ 100ml blood.

What is the difference between Oncotic and Hydrostatic Pressure?

-In the capillaries hydrostatic pressure increases filtration by pushing fluid and solute OUT of the capillaries, while capillary oncotic pressure (also known as colloid osmotic pressure) pulls fluid into the capillaries and/or prevents fluid from leaving.

What is the definition of "fluid"?

-In the scientific usage of the word, a fluid is any material that has the ability to flow. -Thus, both liquids and gases are considered fluids. -Basic forces, like those that result from gravity or pressure differences, cause fluids to flow. -When fluids are placed in a container, they assume the shape of the container, unlike solids that keep their shape.

Critical Pressure

-Liquefaction of gases becomes more difficult as the temperature increases, because the kinetic energies of the particles that make up the gas also increase. -The critical temperature of a substance is the temperature at and above which vapor of the substance cannot be liquefied, no matter how much pressure is applied.

Liquefaction of Gases

-Liquefaction of gases is the process by which a gas is converted to a liquid. -For example, oxygen normally occurs as a gas. However, by applying sufficient amounts of pressure and by reducing the temperature by a sufficient amount, oxygen can be converted to a liquid. -Liquefaction of a gas occurs when its molecules are pushed closer together.

Medical Air

-Medical air cylinders contain compressed atmospheric air which is made up of 21% Oxygen and 79% Nitrogen. -A full "E" cylinder of medical air contains about 625 liters of medical air under a pressure of 1,900 psig. -The gauge pressure on a medical air cylinder will decrease in a manner proportional to the amount of gas in the cylinder

Valley Material Need to Know

-Most capillary walls are permeable to small solutes (Na+, Cl‐, etc.), so small solutes do not exert an osmotic effect. -Ions (Na+, Cl‐, etc.) do not penetrate lipid bilayers but diffuse via channels. -The capillaries of the brain have a blood‐brain barrier and are exceptions. -Albumin (molecular weight MW = 69,000 g/mol) is a substance in the blood that does not penetrate the capillary wall. -Albumin provides the osmotic pressure in the blood. -Note also that albumin is the major determinant of intravascular volume. -The process by which the fetus receives O2 and drugs (local anesthetics, general anesthetics) is simple diffusion across the placental barrier. -Diffusion of a gas from alveoli to blood (or from blood to alveoli) requires a difference in partial pressure (∆P). -The main factors determining diffusion rate across membranes for non‐gases is the concentration gradient (for non‐ionized substances) or electrochemical gradient (for ions), lipid solubility, and size. -Agents that poorly penetrate the blood‐brain barrier or placental barrier are: -Lipid‐insoluble (such as ionized substances) and/or large molecules (with high molecular weight) -Recognize that ions (e.g., Na+) do not penetrate lipid bilayers.

What is the partial pressure of nitrogen at 1 atm?

-Nitrogen is 79% of the atm. -0.79 x 760 mmHg = 600 mmHg

Nitrous Oxide

-Nitrous oxide (N2O; laughing gas) is colorless and essentially odorless. -Although non‐explosive and nonflammable, nitrous oxide is as capable as oxygen of supporting combustion. -Since N2O is below its critical temperature (+39.5oC ) at room temperature, it exists as a vapor in equilibrium with its liquid phase and is dependent upon the pressure applied to it. -As vapor is drawn off, N2O moves from the liquid to the vapor phase, maintaining the equilibrium between the phases, and the vapor pressure within the cylinder. -A full "E" cylinder of nitrous oxide contains about 1,590 liters. Nitrous oxide cylinders are filled to a gauge pressure of 745‐750 psig. -Because nitrous oxide cylinders are filled with liquid nitrous oxide, the gauge pressure will not change as the gas is used until the liquid is to ~ 3⁄4 depleted. -Without weighing the cylinder, it is difficult to estimate the volume of nitrous oxide remaining in a partially used cylinder. -The anesthetist should be aware that once the nitrous oxide cylinder pressure begins to decrease, the cylinder is nearing depletion (less than 25% remaining).

Exothermic Reactions

-Occasionally, the process may be exothermic, meaning energy is released in excess of the energy required to break the bonds of the solute.

Osmosis

-Osmosis is the movement of water across a semi‐permeable membrane to equilibrate a concentration gradient. -Semi‐permeable membranes are permeable to water only and not to solute.

Overpressurizing

-Overpressuring" is the process of significantly increasing a volatile anesthetic concentration (partial pressure) delivered to a patient to increase the alveolar concentration, and therefore the amount dissolved in the blood, to speed uptake. -Henry's law states that the amount of a gas that dissolves in a liquid is proportional to the partial pressure of the gas in the gas phase. -The main applications of Henry's law in anesthesia pertains to calculating how much O2 dissolves in blood and how much CO2 dissolves in blood. -Solubility coefficient of O2 (aO2) and CO2 (aCO2) in blood: aO2 = 0.003 ml /100 ml blood/ mmHg of O2 aCO2 = 0.067 ml/ 100 ml blood/ mmHg of CO2

Oxygen

-Oxygen has a boiling point of ‐183 oC and a critical temperature of ‐119 oC, which means that at room temperature it is above its critical temperature and always exists as a gas, obeying the gas laws. -The importance of this is that Boyle's law can be applied to oxygen, which means that the reading on the pressure gauge of an oxygen cylinder gives a true indication of the volume remaining. However, inaccuracies may arise in this respect if large alterations in ambient temperature occur. -Oxygen cylinders are filled to a gauge pressure of 1900‐ 2200 pounds per square inch (psig) [~2000 psig]. -A full "E" cylinder contains about 660 liters of oxygen. The gauge pressure on an oxygen cylinder will decrease in a manner proportional to the amount of gas in the cylinder. -Thus, a gauge pressure of 1000 psi on a "E" cylinder of oxygen indicates that it contains about 330 liters.

Permeable vs. Semi-permeable Membrane

-Permeable membrane generally allows uniform distribution of all molecules -Semi‐permeable or selectively permeable membrane like a cell membrane allows some molecules to pass through but not others.

Gay-Lussac's Ideal Gas Law: The Temperature-Pressure Relationship

-Pressure (P) is directly proportional to absolute temperature (K) if the volume (V) is constant. -When temperature of a gas in a container at constant volume increases, pressure increases.

Boyle's Gas Law

-Pressure (P) is inversely proportional to volume (V) at constant temperature (T). -If the volume of a gas is halved, the pressure has doubled. -Squeezing the Ambu bag decreases the volume and increases the pressure. -Releasing the Ambu bag increases the volume and decreases the pressure.

N2O is stored as a liquid in cylinders as you know. what does the gauge pressure of 745 PSI actually represent?

-Since nitrous is stored as a liquid, the cylinder pressure of 745 psi means the vapor pressure of liquid nitrous oxide at room temperature.

Solubility

-Solubility is the maximum amount of one substance (solute) that is able to dissolve into another (solvent). -Factors that may affect solubility of solutes in solvents are the intermolecular interactions between the substances, temperature, and pressure* -Pressure exerts little to no influence on solubility of solids and liquids. But gas solubility in a liquid is directly proportional to pressure and will be discussed later by Henry's Law. -Solids and liquids: "Like dissolves like" - solubility is enhanced by intermolecular interactions between substances that have similar electron configurations. -Example: H2O and salts (NaCL) have similar polarity.

Capillary Hydrostatic Pressure vs. Oncotic/Osmotic Pressure

-The force of hydrostatic pressure means that as blood moves along the capillary, fluid moves out through its pores and into the interstitial space. Hydrostatic pressure is highest at the arteriolar end of the capillary and lowest at the venular end. -Oncotic pressure, or colloid osmotic pressure, is a form of osmotic pressure exerted by proteins, notably albumin, in a blood vessel's plasma (blood/liquid) that usually tends to pull water into the circulatory system. -It is the opposing force to hydrostatic pressure.

Application of Charles' Gas Law

-The inflatable cuff of an LMA expands when placed into an autoclave for sterilization.

Charles' Ideal Gas Law: The Volume-temperature Relationship

-The law says that at constant pressure (P), the volume (V) of a fixed number of particles of gas is directly proportional to the absolute (Kelvin) temperature. -Raising the temperature of a gas causes the gas to fill a greater volume as long as pressure remains constant. -Gases expand at a constant rate as temperature increases, and the rate of expansion is similar for all. -Volume can be measured in any unit (cm3, ml, gallons, etc.) whereas temperature is measured in Kelvin (remember - no °degree sign). -Recall that the Kelvin scale starts at absolute zero, the coldest possible temperature. The increment of 1 Kelvin is equal the increment of 1 oC.

State Gay-Lussac's Law

-The pressure of a given mass of an ideal gas is proportional to the absolute temperature, provided that the volume remains constant. -As temperature increases, pressure increases. -Cylinders have constant volume.

A full cylinder of compressed gas is moved to the loading dock (100 degrees F) form an air conditioned truck. What happens to the pressure inside the cylinder?

-The pressure of the gas in the cylinder will increase. -For the gas at constant volume (gases in cylinders are at constant volume), pressure is directly proportional to the absolute temperature.

Endothermic verses Exothermic Reactions

-The term endothermic process describes a process or reaction in which the system absorbs energy from its surroundings; usually, but not always, in the form of heat. -Energy is required to break the chemical bonds of substances that are dissolving. -Most often this is an endothermic reactions, which means it requires more energy than it produces. -It consumes heat rather than produces heat.

State Boyle's Law

-The volume of a given mass of an ideal gas is inversely proportional to the pressure, provided that the temperature remains constant. -If the pressure doubles, the volume will decrease by 1/2

State Charles' Law

-The volume of a given mass of an ideal gas is proportional to the absolute temperature, provided that the pressure remains constant. -As temperature increases, volume increases (so long as pressure remains constant). -Volume (V) is directly proportional to the absolute temperature (K) at constant pressure (P). -When temperature decreases, volume of a gas decreases.

Graham's Law

-Thomas Graham determined that the rate of effusion of a gas (gas diffusion through an orifice) is inversely proportional to the square root of its molecular weight: -Graham's Law determines the faster diffusion of smaller molecules compared to larger molecules.

Diffusion Hypoxia

-When N2O is turned on, the quantity of N2O diffusing from alveoli to blood vastly exceeds the amount of N2 diffusing from the blood to alveoli (compared with N2O, the blood carries much less N2). -When N2O is turned off, the quantity of N2O diffusing from blood to alveoli is much greater than the amount of N2 diffusing from the alveoli to blood; the blood has limited capacity to hold N2 (poor solubility). -Alveoli expand and gases such as CO2 and O2 are diluted. -If the patient was breathing room at this time, the O2 partial pressure would fall to levels that cause temporary hypoxia. This phenomenon is called dilutional hypoxia or diffusion hypoxia and is explained by Fick's law of diffusion. -Administration of 100% oxygen for several minutes when anesthesia is terminated entirely avoids this potential problem.

Application of Gay-Lussac's Law

-When a full gas cylinder is moved from a cold environment (the loading dock at winter time where the temperature is 0 oC) to a warmer environment (OR at 20oC), the pressure in the cylinder increases. -Conversely, when a full gas cylinder is moved from a warmer environment (same loading dock in the summer time at 45 oC ) to a colder environment (OR at 20oC), the pressure in the cylinder decreases. -Remember, the cylinder has a constant volume.

Concentration Effects

-With the patient breathing room air, atmospheric N2 is equilibrated with body N2 (the amount of N2 entering the blood from the alveoli equals the amount of N2 entering the alveoli from the blood.) -When N2O is turned on, N2O diffuses into the blood in much greater quantities than N2 leaves the blood because N2O is much more blood‐soluble (34x) than N2. -Because N2O leaves the alveoli, the alveoli shrink in size so the alveolar concentration of N2O remains high. -The sustained high N2O concentration in the alveoli permits a more rapid uptake of N2O by the blood (the diffusion gradient remains elevated). -This is the concentration effect, which is explained by Fick's law of diffusion.

If you have 500 mL of oxygen at the pressure of 1520 mmHg (two atmospheres), what volume would be present at 760 mmHg (one atmosphere) if temperature did not change? What low applies?

1000 mL -Halving the pressure to 760 mmHg while maintaining temperature constant doubles the volume. -Boyle's Law applies.

What volume will 2 moles of gas occupy at standard temperature (0 degrees C) and pressure (1 atm)? What law applies?

44.8 liters. -One mole of gas at standard temperature and standard pressure occupies a volume of 22.4 liters, so 2 moles will occupy 44.8 liters.

Whose law explains the operation of a bellows ventilator?

Boyle's Law

A patient is sitting in a chair and breathing spontaneously. Whose gas law applies?

Boyle's Law. -At constant pressure, the volume of a gas in the lungs varies inversely with intrapulmonary pressure. -When intrapulmonary pressure becomes negative (decreases), intrapulmonary volume increases.

Whose law explains what happens when applying pressure to a rebreathing bag?

Boyle's Law. -Putting pressure on a bag (squeezing it) causes the volume to decrease.

What is Dalton's Law?

Dalton's law of partial pressure states that the total pressure of a group of gases is equal to the sum of their individual partial pressures.

As a cylinder of compressed gas empties, the pressure in the cylinder falls. What law applies?

Ideal Gas Law -The cylinder has constant volume. -The number of moles (n) of gas decreases as the gas exits the cylinder, so pressure (p) decreases.

How do you calculate the partial pressure of a gas mixture if you know its percent concentration?

PP=% concentration/100 x total pressure

Ideal Gas Law

PV=nRT -P is pressure measured in atmospheres (atm) -V is volume measured in Liters -n is moles of gas present -R is a constant that converts the units. -T is temperature measured in Kelvin. -Simple algebra can be used to solve for any of these values. -As the name implies, the ideal gas law exactly describes the behavior of an ideal gas under all conditions. Unfortunately, we encounter only real gases -ideal gases don't exist. -Fortunately, though, as long as the pressure on the gas is not too high and the temperature is not too low, real gases approximate ideal behavior.