Physical Pharmacy I - The Gaseous State Lecture Notes PDF

PHySIcAL PHARMAcy I The Gaseous State BEHAVIOR OF GASES  Contents In this lecture you will learn: What is Gas and what are the properties of G ases ?▶ Gas Laws and ideal gas equation?▶ ?▶ How to calculate M. wt of gas using ideal gas equation Ideal and Real Gas : what are the difference...

PHySIcAL PHARMAcy I The Gaseous State BEHAVIOR OF GASES  Contents In this lecture you will learn: What is Gas and what are the properties of G ases ?▶ Gas Laws and ideal gas equation?▶ ?▶ How to calculate M. wt of gas using ideal gas equation Ideal and Real Gas : what are the differences ?▶ Van der Waals modified gas equation (for real gases)?▶ Liquefaction of Gases what does it mean and how to achieve it? ? Aerosols as an example for gas liquefaction What is Gas ? Gas is one of the fundamental states of matter. A pure gas may be made up of Individual atoms) (inert gases) Elemental molecules (made from one type of atom, e.g N2 gas., Compound molecules made from a variety of atoms. ‫ﺗﻨﻮع‬ Properties of Gases Compared to other states of matter:: Gases have negligible intermolecular forces between its particles, and gas particles move at high velocity and are separated by large distances..‫ وﺗﺘﺤﺮك ﺟﺰﯾﺌﺎت اﻟﻐﺎز ﺑﺴﺮﻋﺔ ﻋﺎﻟﯿﺔ وﯾﺘﻢ ﻓﺼﻠﮭﺎ ﺑﻤﺴﺎﻓﺎت ﻛﺒﯿﺮة‬،‫ﻟﻠﻐﺎزات ﻗﻮى ﺑﯿﻦ اﻟﺠﺰﯾﺌﺎت ﻻ ﺗﺬﻛﺮ ﺑﯿﻦ ﺟﺰﯾﺌﺎﺗﮭﺎ‬ Gases show the most uniform behavior irrespective of the nature of the gas and have the following properties: :‫ﺗﻈﮭﺮ اﻟﻐﺎزات اﻟﺴﻠﻮك اﻷﻛﺜﺮ اﺗﺴﺎﻗﺎ ﺑﻐﺾ اﻟﻨﻈﺮ ﻋﻦ طﺒﯿﻌﺔ اﻟﻐﺎز وﻟﮭﺎ اﻟﺨﺼﺎﺋﺺ اﻟﺘﺎﻟﯿﺔ‬  Units of pressure: since pressure is force /area so: dyne/cm2 , Or: Variables describing a gas 1 atm = 760 torr = 760 mmHg = 1 x 105Pa = 14.69 psi = 101.325 kPa 1L=1000ml=1000cm3 zero °C = 273 Kelvin, so: degree in K = °C+ 273 An overview on Gas Laws 1. The volume of a given mass of a gas is inversely proportional to its pressure with temperature remaining constant. Mathematically, if V is the volume of a gas at pressure P, and if temperature is kept constant, then: or In other words, if at constant temperature, V1 is the volume of gas at pressure P1 and on changing the pressure to P2 , the volume changes to V2, then Examples A sample of gas in a cylinder has a volume of 720 ml under pressure of 0.375 atm. What will be the volume occupied by gas under 1 atm when the temperature remains constant ? 0.375 x 720 = 1 x V2 V2 = 270 ml 150 x 100 = 200 x V2 V2 = 75 ml 2. The volume of a given mass of a gas is directly proportional with temperature at constant pressure ‫ﯾﺘﻨﺎﺳﺐ ﺣﺠﻢ ﻛﺘﻠﺔ ﻣﻌﯿﻨﺔ ﻣﻦ اﻟﻐﺎز‬ ‫طﺮدﯾﺎ ﻣﻊ درﺟﺔ اﻟﺤﺮارة ﻋﻨﺪ ﺿﻐﻂ‬ ‫ﺛﺎﺑﺖ‬ Or: Temperature must be in Kelvin units Example A mass of gas has a volume of 150 ml at 25 C0. What will be the volume of gas at 45 C0 if pressure was held constant? V1= 150 ml, T1 = 25 C = 25 + 273 = 298 Kelvin V2 = ? T2 = 45 C = 45 + 273 = 318 Kelvin Exercise V2= 160 ML 3. The pressure of a given mass of a gas is directly proportional with temperature at constant volume Temperature must be in Kelvin units 4. Avogadro’s Law The volume of a gas is directly proportional to the number of moles present in the gas if temperature and pressure are kept constant. Under similar conditions of temperature and pressure, equal volumes of all gases contain the same number of molecules. Or: 1 mole (n) of the substance (gas, liquid, or solid) contains the same number of molecules regardless of the substance identity. This number is known as Avogadro’s number and is equal to (6.023 x 1023 ). Example 𝟐.𝟓 𝑳 𝑽𝟐 = 𝟎.𝟏𝟓 𝒎𝒐𝒍 𝟎.𝟓𝟓 𝒎𝒐𝒍 𝟐.𝟓 𝑳∗𝟎.𝟓𝟓 𝒎𝒐𝒍 V2 = 𝟎.𝟏𝟓 𝒎𝒐𝒍 V2= 9.16 L  The Combined Gas Law Equation (the Ideal Gas Equation) The previously mentioned laws and related equations may be combined to give a general equation, called the gas equation (or more correctly, ideal gas equation: since real gases do not follow this equation) Mathematically, ideal gas equation is given by: Under one set of conditions, although P, V and T change, the ratio PV/T is constant and can be represented as: R is constant vale ; the gas constant This equation is correct for 1 mole of gas: for n moles it becomes n = wt (gm)/M.wt (molar) Example P = 1 atm = 760 mmHg : so : 780 mmHg = 1.026 atm n = 1 mole V = ? R = 0.082 L.atm/mole.K T = 25 + 273 = 298 Kelvin 1.026 x V = 1 x 0.082 x 298 V= 23.8 L Exercises  The Combined Gas Law Equation (the Ideal Gas Equation) Ideal gas law for 2 set of condition is; 1∗20 1∗40 1∗20 2∗10 = =0.2 = =0.2 1∗100𝐾 1∗200𝐾 1∗100 1∗100 where the subscripts 1 and 2 represent initial and final conditions, respectively. 1∗20 1∗40 1∗100 =2∗100=0.2 In this form of the gas constant R dose not appear When working with this equation you may use any units which are convenient for P and V, but T must be in Kelvin Example P1 = 1 atm, P2 = 8.77 x 10-3 atm T1 = 24 + 273 = 297, T2 = - 44.7 + 273 = 228.3 V1 = 2.5 L , V2 = ?? − 3 1∗2.5 8.77∗10 ∗𝑉2 = 297 228.3 V2= 219.6 L How do you calculate molecular weight of a gas? To find the molecular mass of a gas, we can assume it behaves ideally and use the ideal gas law We can modify this law in by replacing the number of moles of gas (n) by its equivalent g/M, in which g is the mass (m) and M is molecular weight of the gas: Thus, to find the molecular weight of a gas, we can measure its volume, mass, pressure and temperature. Example: I Answer: P = 1 atm Wt = 0.5 gm V = 100 mL = 0.1 L R = 0.082 L.atm/mole. K T = 120 + 273 = 393 Kelvin Numerical values of the R in various units The gas constant (R) appears in the equation of ideal gas law as well as many other equations in many fields. Therefore, its value and units varies depending on the equation used as follows: Used in gas laws Used in thermodynamics Numerical values of the R in various units Standard temperature and pressure (STP) As the volume of a given mass of gas differs with temperature and pressure, the STP conditions are used as a reference point to compare gases. It refers to the nominal conditions in the atmosphere at sea level. Standard molar volume (also called, molar volume) is the volume of 1 mole of gas at STP. For ideal gas : V = nRT /P V = (1)(0.082)(273)/(1) V = 22.40 L.. :. The main assumptions in the ideal gas law derivation :era ))TMK( yroeht ralucelom citenik sa nwonk( The gas molecules are very small, hard spheres with no intermolecular interactions between the molecules (i.e., force of attraction between gas molecules is zero) The particles take up no space (have no molecular volume: the volume occupied by the molecules is negligible in comparison to the total volume of the gas) The particles are in state of random, constant rapid motion and collisions between the molecules are perfectly elastic (i.e., there is no energy loss when molecules collide with one another or with the walls of the vessel), and the force of collision will depend only on the particle mass and velocity. The average kinetic energy of a molecule is directly proportional to the absolute temperature of gas. All gases at the same temperature have the same average kinetic energy. Van der Waals realized that two of the assumptions of the kinetic molecular theory were questionable !!  Real Gases In reality, all gases are real gases and show deviation from ideal behavior. Real gases obey the gas laws to a fair degree of approximation only at low pressures and high temperatures In reality, there is a small force of attraction between gas molecules that tends to hold the molecules together. This force of attraction has two consequences: gases condense to form liquids at low temperatures (liquefaction of gases: to be (1) explained later) the pressure of a real gas is sometimes smaller than expected for an ideal gas (to be (2) explained later)  ‫أھﻤﺎل‬ Particles in their movement will hit the wall with a force which depends only on the If the gas is compressed or particle mass and velocity. cooled, it will liquify. The gas can be compressed or cooled without being liquified DEVIATIONS OF REAL GASES FROM GAS LAWS (Deviations from ideal behavior) Real gases deviate significantlyfrom ideal gas behavior at low temperatures or high pressures ‫ﻏﺎزات ﺣﻘﯿﻘﯿﺔ‬ ‫ﯾﻨﺤﺮف ﺑﺸﻜﻞ ﻛﺒﯿﺮ‬ ‫ﻣﻦ ﺳﻠﻮك اﻟﻐﺎز اﻟﻤﺜﺎﻟﻲ ﻓﻲ درﺟﺎت اﻟﺤﺮارة اﻟﻤﻨﺨﻔﻀﺔ أو اﻟﻀﻐﻮط اﻟﻌﺎﻟﯿﺔ‬ Effect of low temperature Fore real gases: The assumption that there is no force of attraction between gas particles cannot be true. ‫ﻻ ﯾﻤﻜﻦ أن ﯾﻜﻮن اﻻﻓﺘﺮاض ﺑﺄﻧﮫ ﻻ‬ ‫ﺗﻮﺟﺪ ﻗﻮة ﺟﺬب ﺑﯿﻦ ﺟﺰﯾﺌﺎت اﻟﻐﺎز‬ (see assumption 1 in the kinetic molecular theory) ‫ ﻓﻲ‬1 ‫ )اﻧﻈﺮ اﻻﻓﺘﺮاض‬.‫ﺻﺤﯿﺤﺎ‬ (‫اﻟﻨﻈﺮﯾﺔ اﻟﺠﺰﯾﺌﯿﺔ اﻟﺤﺮﻛﯿﺔ‬ As temperature decreases, the average kinetic energy of the gas particles decreases. A larger proportion of gas molecules therefore have insufficient kinetic energy to overcome attractive intermolecular forces from neighboring atoms. The attraction forces between the particles will pull the particles which hit the wall of the container back toward the center of the container, this will slow down the particles and means that gas molecules become “stickier” to each other, and collide with the walls of the container with less frequency and force, decreasing pressure of real gas below that of ideal values. In conclusion, at low temperatures: The pressure of a real gas is sometimes smaller than expected for an ideal gas (P real < P ideal)  DEVIATIONS OF REAL GASES FROM GAS LAWS (Deviations from ideal behavior) Real gases deviate significantly from ideal gas behavior at low temperatures or high pressures Effect of high pressure For ideal gases we know that It means that increasing the pressure reduces the volume of gas But: The assumption that gas particles occupy no volume is not true (see assumption 2 in the kinetic molecular theory) Real gas particles occupy a fraction of the total volume of the gas and this fraction is not negligible as compared to total volume of the gas. Therefore “Real gases” are not as compressible at high pressures as an “ideal gas”. In conclusion, at high pressure The volume of a Real gases is therefore larger than expected for Ideal gases which is predicted from the ideal gas equation. (V real > V ideal) VAN DER WAALS’ EQUATION (REDUCED EQUATION OF STATE) (EQUATION OF STATE FOR REAL GASES) Since real gas are composed of gas particles which attract each other, and are therefore influenced by the number of these particles, Van der Waals deduced a modified gas equation by making volume and pressure corrections to the gas equation The units for van der Waals’ constants a and b depend on the units in which P and V are expressed. The gases such as CO2, NH3 and HCl, which can be easily liquefied, have high values of van der Waals’ constant a and b and show maximum departure from the ideal gas equation.  PHASE CHANGES : The understanding of the phase diagram is important since the liquefaction of gases involves the physical conversion of matter. Phase diagram: an overview Every matter exists in a different physical state at different temperature and pressure conditions. A phase diagram is a type of chart used to show conditions (pressure, temperature, volume, etc.) at which thermodynamically distinct phases (such as solid, liquid or gaseous states) occur and coexist at equilibrium. A typical phase diagram has pressure on the y-axis and temperature on the x-axis. As we cross the lines or curves on the phase diagram, a phase change occurs. The diagram is divided into three areas, which represent the solid, liquid, and gaseous states of the substance. - Liquefaction is the transformation of a gaseous substance into a liquid condition. To liquefy a gas, the molecules must be brought closer together..‫ ﯾﺠﺐ ﺗﻘﺮﯾﺐ اﻟﺠﺰﯾﺌﺎت ﻣﻦ ﺑﻌﻀﮭﺎ اﻟﺒﻌﺾ‬،‫ ﻟﺘﺴﯿﯿﻞ اﻟﻐﺎز‬.‫اﻟﺘﺴﯿﯿﻞ ھﻮ ﺗﺤﻮﯾﻞ ﻣﺎدة ﻏﺎزﯾﺔ إﻟﻰ ﺣﺎﻟﺔ ﺳﺎﺋﻠﺔ‬ Conditions Necessary for Liquefaction of Gases ‫اﻟﺸﺮوط اﻟﻼزﻣﺔ ﻟﺘﺴﯿﯿﻞ اﻟﻐﺎزات‬ The following are two conditions that must be met in order for gases to be liquefied: Low temperature: temperature of gas must be below certain temperature so as to be liquified High pressure: the gas must be under certain pressure, above which it can be liquified ‫ ﯾﺠﺐ أن ﺗﻜﻮن درﺟﺔ ﺣﺮارة اﻟﻐﺎز أﻗﻞ ﻣﻦ درﺟﺔ ﺣﺮارة ﻣﻌﯿﻨﺔ ﺣﺘﻰ ﯾﺘﻢ ﺗﺴﯿﯿﻠﮭﺎ‬:‫درﺟﺔ ﺣﺮارة ﻣﻨﺨﻔﻀﺔ‬ ‫ ﺣﯿﺚ ﯾﻤﻜﻦ ﺗﺴﯿﯿﻠﮫ‬،‫ ﯾﺠﺐ أن ﯾﻜﻮن اﻟﻐﺎز ﺗﺤﺖ ﺿﻐﻂ ﻣﻌﯿﻦ‬:‫اﻟﻀﻐﻂ اﻟﻌﺎﻟﻲ‬  When gases are cooled, they lose their kinetic energy and velocity ‫ ﻓﺈﻧﮭﺎ ﺗﻔﻘﺪ طﺎﻗﺘﮭﺎ اﻟﺤﺮﻛﯿﺔ وﺳﺮﻋﺘﮭﺎ‬،‫ﻋﻨﺪﻣﺎ ﯾﺘﻢ ﺗﺒﺮﯾﺪ اﻟﻐﺎزات‬ a. Effect of temperature: Critical Temperature Tc).‫ ﻓﺈن ﻛﻞ ﻏﺎز ﻟﮫ درﺟﺔ ﺣﺮارة ﻣﺤﺪدة ﻻ ﯾﻤﻜﻦ أن ﯾﺴﯿﻞ ﻓﻮﻗﮭﺎ‬،‫ﺑﻐﺾ اﻟﻨﻈﺮ ﻋﻦ ﻣﺪى ارﺗﻔﺎع اﻟﻀﻐﻂ اﻟﻤﻄﺒﻖ‬ No matter how high the. pressure applied, each gas has a specific temperature above which it cannot liquefy. This temperature is referred to as the gas’s critical temperature. It is possible to define it as follows: : :‫ ﻣﻦ اﻟﻤﻤﻜﻦ ﺗﻌﺮﯾﻔﮫ ﻋﻠﻰ اﻟﻨﺤﻮ اﻟﺘﺎﻟﻲ‬.‫ﯾﺸﺎر إﻟﻰ درﺟﺔ اﻟﺤﺮارة ھﺬه ﺑﺎﺳﻢ درﺟﺔ اﻟﺤﺮارة اﻟﺤﺮﺟﺔ ﻟﻠﻐﺎز‬ ‫درﺟﺔ اﻟﺤﺮارة اﻟﺤﺮﺟﺔ ﻟﻠﻐﺎز‬ ‫ھﻲ درﺟﺔ اﻟﺤﺮارة اﻟﺘﻲ‬ The critical temperature of a gas is the temperature above which it is ‫ﯾﺴﺘﺤﯿﻞ ﺗﺴﯿﯿﻠﮭﺎ ﺑﺄي ﻗﺪر ﻣﻦ‬.‫اﻟﻀﻐﻂ‬ impossible to liquefy it with any amount of pressure. A gas must be cooled below its Critical Temperature before it can be liquified. For example, Carbon dioxide has a critical temperature of 30.98 o C. This means that we need to cool it below 30.98 o C in order to.‫ﯾﺠﺐ ﺗﺒﺮﯾﺪ اﻟﻐﺎز إﻟﻰ ﻣﺎ دون درﺟﺔ ﺣﺮارﺗﮫ اﻟﺤﺮﺟﺔ ﻗﺒﻞ أن ﯾﺘﻢ ﺗﺴﯿﯿﻠﮫ‬ liquify it. ‫ ھﺬا ﯾﻌﻨﻲ أﻧﻨﺎ ﺑﺤﺎﺟﺔ إﻟﻰ ﺗﺒﺮﯾﺪه‬.‫ درﺟﺔ ﻣﺌﻮﯾﺔ‬30.98 ‫ ﺗﺒﻠﻎ درﺟﺔ ﺣﺮارة ﺛﺎﻧﻲ أﻛﺴﯿﺪ اﻟﻜﺮﺑﻮن اﻟﺤﺮﺟﺔ‬،‫ﻋﻠﻰ ﺳﺒﯿﻞ اﻟﻤﺜﺎل‬.‫ درﺟﺔ ﻣﺌﻮﯾﺔ ﻣﻦ أﺟﻞ ﺗﺴﯿﯿﻠﮫ‬30.98 ‫إﻟﻰ أﻗﻞ ﻣﻦ‬ Liquefaction of gases do not occur at temperatures above the critical temperature ? At temperature above the critical temperature value, the ‫ﻋﻨﺪ درﺟﺔ ﺣﺮارة أﻋﻠﻰ ﻣﻦ ﻗﯿﻤﺔ درﺟﺔ اﻟﺤﺮارة‬ ‫ ﺗﺘﻤﺘﻊ اﻟﺠﺰﯾﺌﺎت ﺑﺎﻟﻄﺎﻗﺔ اﻟﺤﺮﻛﯿﺔ اﻟﻜﺎﻓﯿﺔ‬،‫اﻟﺤﺮﺟﺔ‬ molecules have sufficient kinetic energy so that no amount ‫ﺑﺤﯿﺚ ﻻ ﯾﻤﻜﻦ ﻷي ﻗﺪر ﻣﻦ اﻟﻀﻐﻂ أن ﯾﺠﻌﻠﮭﺎ ﺿﻤﻦ‬ ‫ﻧﻄﺎق ﻗﻮى اﻟﺠﺬب اﻟﺘﻲ ﺗﺘﺴﺒﺐ ﻓﻲ اﻟﺘﺼﺎق اﻟﺠﺴﯿﻤﺎت‬ of pressure can bring them within the range of attraction ‫ﺑﺒﻌﻀﮭﺎ اﻟﺒﻌﺾ‬ forces that causes the particles to stick together  If pressure is applied to a gas, the molecules are brought within the range of van der Waals forces and pass into the liquid state. Because of these forces, liquids are considerably denser than gases and occupy a definite volume ‫ ﯾﺘﻢ وﺿﻊ اﻟﺠﺰﯾﺌﺎت ﺿﻤﻦ ﻧﻄﺎق ﻗﻮى ﻓﺎن دﯾﺮ ﻓﺎﻟﺲ وﺗﻤﺮ إﻟﻰ اﻟﺤﺎﻟﺔ‬،‫إذا ﺗﻢ ﺗﻄﺒﯿﻖ اﻟﻀﻐﻂ ﻋﻠﻰ اﻟﻐﺎز‬ ‫ ﺗﻜﻮن اﻟﺴﻮاﺋﻞ أﻛﺜﺮ ﻛﺜﺎﻓﺔ ﺑﻜﺜﯿﺮ ﻣﻦ اﻟﻐﺎزات وﺗﺸﻐﻞ ﺣﺠﻤﺎ ﻣﺤﺪدا‬،‫ ﺑﺴﺒﺐ ھﺬه اﻟﻘﻮى‬.‫اﻟﺴﺎﺋﻠﺔ‬ b. Effect of pressure: Critical pressure (Pc ) The critical pressure of a gas is the minimal pressure required to liquefy it at the critical temperature ‫اﻟﻀﻐﻂ اﻟﺤﺮج ﻟﻠﻐﺎز ھﻮ اﻟﺤﺪ اﻷدﻧﻰ ﻣﻦ اﻟﻀﻐﻂ اﻟﻤﻄﻠﻮب ﻟﺘﺴﯿﯿﻠﮫ ﻋﻨﺪ درﺟﺔ اﻟﺤﺮارة اﻟﺤﺮﺟﺔ‬ The critical temperature serves as a rough measure of the attractive forces between molecules because at temperatures above the critical value, the molecules possess sufficient kinetic energy so that no amount of pressure can bring them within the range of attractive forces that cause the atoms or molecules to “stick” together. ‫ ﺗﻤﺘﻠﻚ اﻟﺠﺰﯾﺌﺎت طﺎﻗﺔ ﺣﺮﻛﯿﺔ ﻛﺎﻓﯿﺔ‬،‫ﺗﻌﻤﻞ درﺟﺔ اﻟﺤﺮارة اﻟﺤﺮﺟﺔ ﻛﻤﻘﯿﺎس ﺗﻘﺮﯾﺒﻲ ﻟﻠﻘﻮى اﻟﺠﺬاﺑﺔ ﺑﯿﻦ اﻟﺠﺰﯾﺌﺎت ﻷﻧﮫ ﻓﻲ درﺟﺎت ﺣﺮارة أﻋﻠﻰ ﻣﻦ اﻟﻘﯿﻤﺔ اﻟﺤﺮﺟﺔ‬.‫ﺑﺤﯿﺚ ﻻ ﯾﻤﻜﻦ ﻷي ﻗﺪر ﻣﻦ اﻟﻀﻐﻂ أن ﯾﺠﻠﺒﮭﺎ ﺿﻤﻦ ﻧﻄﺎق اﻟﻘﻮى اﻟﺠﺬاﺑﺔ اﻟﺘﻲ ﺗﺘﺴﺒﺐ ﻓﻲ "اﻟﺘﺼﺎق" اﻟﺬرات أو اﻟﺠﺰﯾﺌﺎت ﺑﺒﻌﻀﮭﺎ اﻟﺒﻌﺾ‬ Water Helium Critical Temperature 647 K 5.2 K Critical Pressure 218 atm 2.26 atm The high critical values for only the weak London water result from the strong force attracts helium dipolar forces between the molecules, and, molecules and particularly the consequently, this hydrogen bonding that exists element must be cooled to the extremely low temperature of 5.2 K before it can be liquefied. Above this critical temperature, helium remains a gas no matter H2O what the pressure. Exercise: The following gases have the given Critical temperature and Critical Pressure values, which gas easier to liquify ? CO2 Helium Nitrogen Critical 304 K 5.2 K 126 K Temperature Critical 72.9 atm 2.26 atm 33.5 atm Pressure  Aerosols Aerosols are pharmaceutical preparations in which the drug is dissolved or suspended in a propellant. Aerosols depend in their action on the concept of gas liquefaction and the reversible change of state. Aerosol = Propellant gas + drug solution or suspension Propellant gas is a material that is liquid under the pressure conditions existing inside the container but that forms a gas under normal atmospheric conditions Gases can be liquefied under high pressures in a closed chamber as long as the chamber is maintained below the critical temperature. When the pressure is reduced, the molecules expand and the liquid reverts.to a gas. The container is so designed that, by depressing a valve, some of the drug– propellant mixture is expelled owing to the excess pressure inside the container. If the drug is nonvolatile, it forms a fine spray as it leaves the valve orifice; at the same time, the liquid propellant vaporizes off.