STATE OF MATTER
Matter can exist in three different forms in nature—solid, liquid or gas; although plasma, a fourth state of matter has also been identified under the extremes of temperature and pressure. Matter is either an element made from similar atoms, e.g. iron or compound made from two or more types of atoms, e.g. water (H2O) in nature. An element is a basic unit of matter, which retains the same properties on subdivisions by chemical or mechanical means. Oxygen and other gases, such as hydrogen, helium, chlorine and nitrogen are elements in nature. Atoms of different elements may form molecules or compounds. Hydrogen can exist in atomic or molecular form, whereas nitrogen and oxygen occurs in molecular form (N2 and O2).
Molecule and Compound
All substances consist of exceedingly small particles called molecules. There are about 1019 molecules in 1 ml of air under the normal conditions of temperature (T) and pressure (P). A molecule possesses the distinctive properties of the parent element or compound. A molecule is found to consist of two or more atoms of same kind or of different kinds. The number of molecules comprising a macroscopic quantity of a gas is enormous typically around 1023 molecules. The number of molecules and their velocity determine many properties of gases.
A compound is composed of two or more elements united chemically to form a substance different from the individual elements forming that compound. For example, carbon dioxide is a compound of carbon and oxygen. On subdivisions, the compound loses its properties and may resume those of the constituent elements. Both elements and compounds exist as molecules as the smallest component.
All the molecules of matter are in a state of incessant motion. This is known as Brownian movement and forms the basis of the kinetic theory of matter. This motion results from temperature—the higher the temperature, the larger the velocity of the molecules. At absolute zero temperature, the velocity of a classical molecule goes to zero. Molecules of a gas have great mobility and travel longer distances before colliding with other molecules. It is because of this mobility that a gas has no fixed shape and mixes readily with other gases.
PHYSICAL PROPERTIES OF GASES
The air we normally breathe is a mixture of gases of which oxygen and nitrogen constitute the main bulk.
Breathing of additional or supplemental gases is required in abnormal situations. The physical properties of these gases influence the mechanics of normal breathing, as well as the therapeutic strategies. Equal volumes of gases at the same temperature and pressure contain equal number of molecules (Avogadro's Hypothesis).
Volume is the space occupied by a gas. The volume of a cuboid-shaped vessel is determined by the multiplication of internal length, width and height of the vessel. It is expressed in cubic centimeters (cc), cubic feet or liters (L), etc. (1 L ≡ 1000 cc or ml).
A 10 cm cube has the volume equaling 1 L. Volume of a container of uniform cross-sectional area A and height is given by V = A h. The gas shall occupy the available volume irrespective of the amount (mass) of gas. For example, if a small vessel containing oxygen is emptied in a larger vessel, the entire volume of the larger vessel will be occupied by the same amount of gas.
Mass and Weight
Mass is the bulk or the total mass of number of molecules of the gas. In the above mentioned example, the mass of the gas in two cylinders shall remain the same, although the volume has changed. The number of molecules per unit of volume in the two vessels has changed, i.e. lesser number of molecules per unit volume in the larger vessel.
Weight is often used synonymously with mass. Weight is determined by the pull of gravity on mass (i.e. m × g). Since, the force of gravity on the earth is nearly constant, mass is equivalent to weight on the surface of the earth. In fact, weight is scaled to indicate mass and therefore both represent the same thing.
Density is expressed as the weight in the grams of one liter of a gas. Since the weight of 22.4 liters of a gas is that of a gram molecule of that gas, one liter of gas shall weigh molecular weight/22.4 gm. When expressed this way, the density will be measured in gm/liter. It is also measured in gm/cc, which will equal 1/1000 in value to that in gm/liter.
The density of a gas is also expressed as relative to the density of air. Density of air shall vary depending upon its composition. For all practical purposes, it comprises of 1 volume of oxygen (about 20%) and 4 volumes of nitrogen (about 80%). At NTP, the density of air is (32 × 1/5 + 28 × 4/5)/22.4 = 1.3 gm/L. Therefore, the density of oxygen relative to that of air is 1.1. When expressed this way, it becomes unimportant, if the density of individual gases was calculated in gm/liter or gm/cc.
The gas molecules are always in a state of motion and constantly bombard the walls of the container. The force applied to (or acting upon) a unit area of the wall is called the gas pressure. The closer the molecules, the greater the number, which strikes each unit area and therefore the greater the pressure applied. Also, larger the velocity (or temperature), larger is the impact on the walls, leading to greater pressure.
Gas pressure is generally considered as that of a stationary gas when the pressure exerted is the same at any point in a gas container. The pressure is usually expressed in the millimeters of mercury (mm Hg) or Centimeters of water (cm H2O) or pounds per square inch (psi). One millimeters of mercury means force on a unit area (1 cm2) on which 1 mm of height of Hg is placed. The volume of height h cm on unit area is A × h = h cm3 and in mass is hd where d is the density of the liquid. The force on unit area due to this is hdg, which is also the pressure p. Thus, p due to a height h of a liquid of density d, p = hdg. The pressure due to 1 mm Hg can be calculated by putting h = 0.1 cm, d = 13.6 gm/cc and g = 980 cm/S2.
Atmospheric air is pulled to the earth by gravity and generates a force upon the surface of the earth, resulting in atmospheric pressure. Atmospheric pressure is the sum of pressures of all gases (e.g. N2, O2 and CO2) present in air. It is measured with the help of a glass tube filled with either mercury or water (manometer). The height of the column of mercury (or water) multiplied by its density is a measure of the atmospheric pressure. Standard pressure is measured at sea level and expressed in mm Hg (torr) or cm H2O.
It is important to convert atmospheric pressure (≡ 76 cm of Hg) in CGS units. This is approximately 106 CGS units.
It is relevant here to mention that the lungs are subject to atmospheric pressure all the time. Since, the alveoli are in direct communication with the atmosphere through the tracheobronchial tree, the alveolar pressure is the same as the atmospheric pressure. The changes in alveolar pressure during inspiratory and expiratory phases of respiration are relative to the atmospheric pressure. During inspiration when the alveolar pressure is −10 cm H2O, it implies the presence of atmospheric pressure—10 cm H2O (i.e. 1030 – 10 cm H2O). Similarly, when positive pressure is administered to a patient through a ventilator, the ventilator gauge pressure of 10 or 20 cm H2O refers to a total pressure of 1040 or 1050 cm H2O (i.e. atmospheric pressure + gauge pressure).
In a mixture of gases in a container, each gas exerts the same pressure, which it would if it alone occupied the container. There is no interference from the presence of other gas(es). The pressure exerted by each individual gas is called the partial pressure. The total pressure exerted by the mixture of gases is equal to the sum of the partial pressures of all the gases contained in the mixture (Dalton's law). The partial pressure is determined by the fraction of the concentration of the gas in the mixture.
The atmospheric air has a total pressure of 760 mm Hg when dry at sea level. The partial pressures of N2 (79%) and O2(21%) therefore, are as follows:
Temperature and Heat
Temperature is the thermal state of a substance, which determines whether the substance will give or receive heat from another substance in contact. It is an indication of the level of molecular activity. Heat is the thermal energy of a substance, which can be given to or abstracted from it. Temperature is the measurement of heat.
Calorie is the unit of heat. It is defined as the quantity of heat required to raise the temperature of 1 gm of water by 1°C. As an example, if one calorie is required to raise the temperature of 1 gm of water by 1°C, 1000 calories will be required for 1000 gm of water. The caloric value of food is expressed by a larger heat unit, i.e. the kilocalorie (cal or kcal), which is equivalent to 1000 cal.
To raise the temperature to a given range, similar weights of different substances require different quantities of heat. The number of calories required to raise the temperature of 1 gm of that substance by 1°C is the specific heat of that substance.
The specific heat depends on the state of the matter— solid, liquid or gas. Specific heat of water is 1 (It follows from the definition of 1 calorie).
For gases, such as O2 and air, it is 0.0603 cal per cc, it is quite high when expressed per gm.
We can calculate the total quantity of heat required to raise the temperature of a given volume by multiplying the volume with specific heat and temperature rise, i.e. volume (cc) × specific heat (cal per cc) × temperature rise(°C).
THE GAS LAWS
There is a definite relationship between the gas properties described above. These relationships are described in different laws to understand the behavior of gases. These laws are valid for ideal gases only, where the assumption that the gas particles are very small and do not interact with each other is valid.
Pressure (P) of a gas is inversely proportional to its volume (V) provided the absolute temperature (T) of the mass of gas is kept constant. In other words, the product of pressure and volume remains constant. It follows immediately from the ideal gas equation,
The application of this law in respiratory physiology is best exemplified in the use of body plethysmography to measure total lung capacity. It is also employed in many mechanical ventilators whereby the gas is driven into patient's lungs or into the cylinder of the ventilator by the upstroke and downstroke movements of the piston.
When pressure and mass of a gas are kept constant, the volume of the gas will vary directly with its absolute temperature. Again from gas equation,
It is because of this reason that volumes measured with the help of lung function equipments (at room temperature) are a little lower than those at body temperature (37°C) and need to be corrected for the same. If the temperature of a container of a gas is lowered, the volume shrinks. Therefore, more gas can be stored in the same cylinder at a lower temperature.
Temperature and pressure of a gas are directly proportional when the volume and mass are kept constant.
It implies an increase in pressure if the temperature is increased. For this reason safety valves are provided with devices using high pressure gases to vent high pressures in case there is an accidental heating.
The General Gas Law
Assume N ideal noninteracting molecules of a gas each of mass m are contained in a cube of volume V. They are in motion if the temperature is above 0°K (0°K = −273°C). If the temperature is T in Kelvin, the kinetic energy from each molecule is of the order of kT, where K is called Boltzmann constant (K = 1.38 × 10–16 CGS units). Because of this kinetic motion, the molecules of the gas keep bombarding the walls of the cube and exert pressure. The pressure increase results in extra energy (obtainable from force × distance or p x volume relation). In this way it is quite evident that one can equate the energy because of pressure PV as resulting from kinetic energy of N molecules, PV = NkT.
If N is expressed in No (Avogadro No.), PV = η NokT, where η = N/No. This is the famous gas equation valid for all ideal gases. is the number of moles of the gas, Nok is also called gas constant R. R ≃ 6 × 1023 × 1.38 × 10–16 erg/deg K
The gas equation can be used to determine how the given initial state (P1, V1, T1) relates to (P2, V2, T2), some final state by using P1V1(T1= P2V2/T2).
It may be stated here that under the conditions of lower temperature and high pressure the gas changes its state to liquid. This is because the gas molecules get attracted to each other (van der Waals forces) rather than being repelled. The higher pressure condenses the molecules and the lower temperature reduces their activity.
The temperature at which the gas turns into liquid is the “critical temperature” of that gas. For oxygen, it is −116°C. A pressure of 50 atmospheres is required to liquefy oxygen at −116°C. To keep the oxygen in a liquid form at 1 atmosphere in a flask open to the atmosphere, the temperature is lowered to below −183°C. This principle forms the basis of the availability of oxygen in the liquid form for storage and ambulatory use.
The amount of gas that enters into physical solution in a liquid is directly proportional to the partial pressure of the gas. For example, the greater the partial pressure of oxygen in the alveoli, the greater the solubility in plasma.
The rate of diffusion (D) of a gas is inversely proportional to the square root of its density (d).
Therefore, a light gas (such as helium) will diffuse at a faster rate than a heavier gas (such as oxygen).
Flow of a gas through a partially obstructed tube can be described by Bernoulli's principle, i.e. the pressure required to produce flow is the difference in velocity at two points and the density of the gas (Fig. 1.1).
GAS SOLUTION AND TENSION
The amount of gas dissolved in a liquid is directly proportional to the pressure of the gas (Henry's law). It also varies with the temperature—lesser amount is dissolved at the same pressure if temperature is increased. A state of equilibrium is reached when no further gas dissolves in the liquid. This is a state of full saturation with the gas at a given temperature and pressure. The gas in solution is said to exert the same “tension” as the partial pressure of the gas over the liquid in equilibrium with it. For example, when the partial pressure of oxygen in alveoli is 100 mm Hg, the tension of O2 in alveolar capillaries is 100 mm Hg. At this pressure, 0.3 cc of oxygen at NTP dissolves in 100 cc of water. The weight of oxygen dissolved in 100 cc water is:
The amount of oxygen dissolved in plasma or water is the same (0.004 gm/100 ml). This is quite sufficient to supply all the oxygen necessary for the metabolism of the body.
Vapor is defined as the gaseous state of a substance, which at room temperature and pressure is a liquid. On the other hand a gas at room temperature exists only in the gaseous state. Like any other gas, the molecules of a vapor are continuously in violent motion and bombard the walls of the container. The force exerted on each unit area is called the pressure of the vapor (Vapor pressure).
A vapor in a mixture of gases obeys the same laws as the gases. The partial pressure of the vapor in a mixture bears the same proportion to the total pressure as the volume, i.e. it depends on the percent (or fractional) concentration in the mixture. For example, the concentration of about 16% of water vapors in air at NTP, which is sufficient to saturate air with water vapors exerts a pressure of 16% of 760 mm Hg (47 mm Hg).
The presence of water vapors in air or oxygen is referred to as humidity. It is largely through the process of evaporation that the molecules of water (or any other liquid) evaporate into the overlying air (or any other gas in a container).
The molecules leave the liquid substance when their kinetic energy exceeds the surface tension of the liquid. If a liquid is kept in a closed container for long, a state of equilibrium is reached when the number of molecules returning to the liquid (condensation) is exactly equal to the number leaving it (evaporation). This is called the saturation-point. This is further dependent upon temperature; if the temperature increases, the number of molecules leaving the liquid also increase and the saturation point is raised, i.e. there is a greater amount of vapors in the same amount of gas. Reverse happens with a fall in temperature.
The air we breathe is normally humid due to the presence of water vapor. The actual amount of water vapor present in air is expressed as “relative humidity”, which is defined as the ratio of the amount of water vapor present in a given volume with the amount of water vapor, which the air (or the gas) is capable of holding at the given temperature, in the same volume.
The humidity of air varies with the atmospheric conditions. Once inhaled in the lungs, air gets fully saturated. The amount of water vapor required to saturate the alveolar air at body temperature and pressure is the body humidity.
The presence of water vapor in the inhaled air exerts its own partial pressure, and lowers the pressures of constituent gases of air—oxygen and nitrogen. Therefore, PN2 or PO2 is calculated as a proportion of the atmospheric pressure minus water vapor pressure, i.e. Patm – PH2O.
When fully saturated, PH2O of atmospheric air is equal to 47 mm Hg. Therefore, PO2= (Patm – PH2O) × 21% = (760 – 47) × 0.21 = 150 mm Hg. The rest, i.e. 760 – (150 + 47) would be approximately the PN2.
EXPRESSION OF GAS VOLUMES AND PRESSURES
In view of the effects of temperature, pressure and humidity on all gases, these are expressed with reference to those conditions. Some of the common expressions are:
- Standard (or normal) temperature and pressure (STP) or NTP Temperature 0°C; Pressure 760 mm Hg.
- STPD: D indicates “dry” = complete absence of water vapor.
- Ambient temperature and pressure—dry or saturated (ATPD or ATPS). Ambient implies the room conditions.
- Body temperature and pressure saturated (BTPS): Body temperature (usually 37°C), ambient pressure and water vapor pressure (47 mm Hg).
Normally, gas volume measurements are made in the ambient conditions. Conversion is required to express the volume at BTPS or STPD. STPD is used for the uniformity of expression. This is done by multiplying with conversion factors. Tables of conversion factors from ATPS to STPD, STPD to BTPS, or BTPS to ATPS are available in most laboratories. Such corrections are also required to express volume of a gas (such as O2) produced in the laboratory. The volume is expressed at STPD, which is different than that produced at ATPS.
FLOW OF GASES
Flow is the movement of particles of a liquid or a gas from higher to lower pressure. It is expressed in the terms of volume per unit time, e.g. liters per minute or per second (L/min or L/sec). The movement of air into the lungs during inspiration and out into the atmosphere during expiration is accomplished by the flow of air through tracheobronchial tree. Similarly, oxygen flows from a container cylinder to the lungs or a ventilator through connecting tubes as long as there is a pressure difference.
The flow is described as laminar, if it is smooth and gas particles move along lines parallel to the walls of the tube. But it is turbulent if the lines of flow are irregular, broken up and disorderly (Fig. 1.2). Whether the flow is laminar or turbulent, it has to meet a certain resistance while moving from one to the other end of the tube. The laminar flow is described Hagen-Poiseuille equation, i.e. V = Πγ4ΔΡ)/(8ηl).
Resistance is defined by the pressure difference under given conditions, between the entry and the exit points of a tube. The resistance is dependent on the tube length (l)and diameter. It is also directly proportional to the velocity of flow (∇) or rate in case of laminar flow. The flow is also viscosity (η) dependent and density-independent. When the flow is turbulent, the resistance rises for steeply. The laminar flow through a straight tube of uniform size is inversely proportional to the length (l) of the tube and directly to the fourth power of radius (r).
When the flow exceeds a “critical flow rate”, the laminar flow is replaced by the turbulent flow throughout the length of the tube. Turbulent flow is less efficient since the Δ Α varies directly with V2. Turbulent flow is density dependent and viscosity-independent. The critical flow varies directly with the internal diameter of the tube — the larger the diameter, the greater the flow. At a flow below the critical rate, local turbulence may occur as a result of irregularities in the pathways of the gas. During oxygen administration this may occur due to the constriction of kinking of the tubes.
Turbulence in a flowing system can also be predicted by Reynold's number. It is the ratio between inertial (density dependent, viscosity independent) and viscous (viscosity dependent, density independent) forces— a dimensionless number.
In case of pipes,
Flow is “laminar” when the number is less than 2,000 and “turbulent” when it is more than 3,000. Turbulent flow is dominated by inertial forces producing random eddies and flow fluctuations. Between 2,000 and 3,000, the flow is transitional, i.e. neither fully laminar nor fully turbulent.
Flow Through Orifices
An orifice is a narrow opening of a tube. Unlike a tube, the diameter of the fluid pathway of the orifice exceeds the length. The greater the diameter compared to the length, the more does the opening approach the “ideal” orifice. The flow through an orifice depends on the diameter (or the cross-section area) of the orifice and the difference in pressures on either side of the orifice.
The intrinsic property of a liquid that influences its flow, which we earlier termed as resistance is called viscosity. It is attributed to the internal friction between different layers, which move at different speeds. While the laminar flow largely depends on viscosity, it is the density, which determines the flow when turbulent. The coefficient of viscosity is equal to the force per unit area necessary to maintain the unit difference of velocity between two parallel planes.
The flow through an orifice is at least partially turbulent. The lower the density, i.e. the lighter the gas, the greater is its volume flow for any given pressure difference on the either side of the orifice.
The molecules in a fluid (liquid or gas) unlike in a solid, move freely in all directions. The time taken by a molecule to travel a given distance depends upon its closeness to other molecules, and the intermolecular spaces. The gas molecules do not necessarily collide with the neighboring molecules when they move around or across a membrane.
Diffusion across a membrane is determined by the difference in concentrations between the two neighboring layers of the solution. The rate of diffusion is proportional to the gradient of concentration, i.e. the change of concentration per unit length in the direction of diffusion (Fick's law).
Diffusion also depends on molecular movement. The rates of diffusion of gases at similar partial pressures through a porous membrane are inversely proportional to the square roots of their molecular weights (Graham's law). The molecular weight of oxygen and CO2 being 32 and 44 respectively, the diffusion ratio will be 1.2.
It implies that oxygen diffuses 20% faster than CO2 through a dry, porous membrane. It is because of the solubility of CO2 in water of the moist alveolar membrane that the CO2 diffusion is higher than O2.
Solubility: Another factor, which determines diffusion across a wet film is the solubility of the gas. The rate of diffusion is directly proportional to the solubility of the gas in the fluid.
Permeability: A membrane is permeable, if it allows the particular molecules to pass through, i.e. across the membrane. Permeability of different membranes to the molecules of different substances (solid, liquid or gases) is variable.
Osmosis: Osmosis is the migration of molecules of a solvent across a membrane. The pressure, which stops the transfer of molecules is called the osmotic pressure of the solution. The osmotic pressure of a solution depends only on the number of dissolved particles per liter and not on the nature of the substances, which is dissolved.
The diffusion mechanisms also depend upon the pressures, volume and filtration. In respiratory system, the diffusion of gases and fluids across the alveolar membrane are critically important for normal gas-exchange functions of the lung and in the maintenance of a fluid balance.