Gases Characteristics of Gases

Gases Characteristics of Gases • Gases are the most chaotic, dispersed, free flowing phases of matter. • Gases are composed of particles that are moving randomly around very fast in their container(s). • The volume of a gas (under ideal conditions) is its container. – Gases occupy a vessel uniformly. • Gases can expand (they diffuse) or be contracted. – Gas particles can expand indefinitely. It is the size of the container which restricts its expandability. – Free space between gas particles allows for the contraction of a gas. The Four Properties of Gases • Pressure – Units: • atm (Ideal Gas Law) • mmHg or Torr • Volume – Units: • Liters (L) • Temperature: – Units: • Kelvin (k) • Amount: mole Pressure • The pressure of a gas is the result of the constant movement of the gas particles and their collisions with the surfaces of the container. – Gaseous particles exert a force when they collide with a surface or with other gaseous particles. • Collisions create pressure. • Pressure is the force exerted per unit area by gas molecules as they strike the surfaces around them. 𝐹𝑜𝑟𝑐𝑒 • • Pressure = 𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 Units: – atm (atmosphere) • Conversions • 1 atm is equivalent to : – 760 mm Hg or 760 Torr – 29.9 inches Hg • SI unit is PASCAL (Pa), where 1 atm = 101.325 kPa Reference credit: academic.greensboroday.org Gas Pressure Factors As noted: the pressure of a gas is the result of gas particles striking (i.e. colliding) with the container. • Total pressure of a gas depends on the concentration of gas particles and volume of the container. – The greater the concentration (i.e. number of gas particles per given volume), the greater the pressure. • Force per unit area increases, therefore the greater the gas pressure. • Example: – Low density of gas particles = less gas pressure. » This in turn results in fewer collisions, which leads to a lower pressure. – Average speed of the gas particles. • KE = ½ mv2 Gas Laws Boyle’s Law: P1V1 = P2V2 • Boyle’s experiment noted: if amount and temperature were kept constant that pressure (P) and volume (V) had an inverse relationship. Charles’ Law: • 𝑽𝟏 𝑻𝟏 𝑽 = 𝑻𝟐 𝟐 Charles’ experiment noted: when the temperature rises the volume of gas will expand (if allowable): meaning that volume and temperature have a direct relationship. Amonton/Gay-Lussac’s Law: • 𝑃 = 𝑇2 2 This law looks at the pressure and temperature relationship of a gas, where amount and volume are kept constant. & V are kept constant. Experimental evidence indicated that there is a direct relationship between P & T. Avogadro Law: • 𝑃1 𝑇1 𝑽𝟏 𝒏𝟏 = 𝑽𝟐 𝒏𝟐 This law looks at the relationship between the volume of a gas and the amount (moles) of gas particles, when P & T are kept constant. Experimental evidence indicate that V and n are directly related. The Ideal Gas Law: Bringing Together the Properties of Gases • The properties of gases, how they affect each others' behaviors has been investigated and summarized in a variety of laws. – Boyle’s: • Investigates P& V with T & amount (moles = n) constant – Charles’s: • Investigates T & V with P & n constant – Avogadro's: • Investigates V & n with P & T constant – Gay-Lussac/Amonton’s: • Investigates P & T with V & n constant • The ideal gas law, derived experimentally, is a representative of all these laws: PV = nRT *where R is the universal gas constant (0.0821 L atm/K mol) Problem: Methane is an alternative combustible fuel to gasoline. It is estimated that 665 g CH4 would replace 1 gallon of gasoline burned. Determine the volume of methane gas that would replace 1 gallon of gasoline at 745 mmHg and 25.0 oC. R = 0.0821 L•atm/K•mol Derivations of the Ideal Gas Law • The Ideal Gas Law can be used to solve for a the density of a gas, or determine the molecular mass of a gas. Ideal Gas Law: PV = nRT – n is for moles and a mole is defined: • mole = Ideal Gas Law PV = • rearranging • MM = dRT P 𝑠𝑎𝑚𝑝𝑙𝑒 𝑚𝑎𝑠𝑠 (𝑔) 𝑔 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 (𝑚𝑜𝑙) or 𝑔 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 (𝑀𝑀) gRT MM gRT MM = PV Where 𝑚𝑎𝑠𝑠 (𝑔) 𝑣𝑜𝑙𝑢𝑚𝑒 (𝐿) is density (d) Problem#1: Determine the molecular mass and identity of the diatomic gas pressure of the gas is 760 torr and the temperature is 17.0 oC. The density of the gas is 0.0897 g/L. R = 0.0821 L•atm/K•mol Problem#2: Determine the volume of hydrogen gas produced when 8.88 g Ga is mixed with excess HCl (aq) at the conditions of 723 mmHg and at 27.0 oC R = 0.0821 L•atm/K•mol Ga (s) + HCl (aq) → GaCl3 (aq) + H2 (g) Dalton’s Law of Partial Pressure Dalton’s Law of Partial Pressure states that the TOTAL PRESSURE in a container EQUALS the SUMMATION of the PARTIAL PRESSURES of ALL the gases present in the container. Reference credit: OpenStax2017 • If equal-volume cylinders containing gas A at a pressure of 300 kPa, gas B at a pressure of 600 kPa, and gas C at a pressure of 450 kPa are all combined in the same-size cylinder, the total pressure of the mixture is 1350 kPa. Representations of Dalton’s Partial Pressure Law • Dalton’s Law of partial pressures Ptotal = PA + PB + ... • This version is often used when information given states “ a volatile gas was collected in water.” Ptotal = PH2O + Pgas Reference credit: OpenStax2017 – There is a table of partial pressures for PH2O at a specific temperature. • This version is used when moles or mole fractions are given. Ptotal = PA x Ca Ca is the notation for the mole fraction of gas A Mole fraction (Ca)is defined as Ca = na (na + nb+ nc + ….) Problem: A 5.73 L flask, having a temperature of 25.0 oC contains 0.0388 mol N2, 0.0803 mol H2 and 0.147 mol CO. R = 0.0821 L•atm/K•mol Determine: 1. Pressure of each gas in atm 2. The total pressure of the gas in the flask. 3. The mole fraction of each gas. Gases Diffuse & Gases Effuse Diffuse • DIFFUSION is: a. a. the gradual, spontaneous mixing of gas particles of different gases; Reference credit: 2012books.lardbucket.org b. the spontaneous movement of gas particles to fill a container equally. • High to low concentration. • Factors that effect rate of diffusion: – Temperature – Type of gas particle b. – KE = ½ mv2 Reference credit: sites.google.com Gases Diffuse & Gases Effuse Effuse • EFFUSION is the movement of molecules through a small hole into an empty container. • Factors that affect the rate of effusion of gases. – Temperature – Size of gas particle • KE = ½ mv2 • Rate = (moles/time) that is proportional to temperature but is inversely proportional to molecular mass . Reference credit: chem.libretexts.org Graham’s Law of Diffusion (Effusion) • Formula representation: 𝒓𝒂𝒕𝒆𝒂 = 𝒓𝒂𝒕𝒆𝒃 𝑴𝒃/𝑴𝒂 Thomas Graham, 1805-1869. Professor in Glasgow and London. Reference credit: www.livebinders.com • Graham’s law governs effusion and diffusion of gas molecules. – Rate of effusion of a gas is inversely proportional to the molar mass of the gas (M) Overview of the Kinetic Theory of Gases Assumptions: ▪ Gases particles have a random motion (i.e. gas particles are constantly moving about a container). ▪ Gas pressure results from the particle collisions with container walls. ▪ Collisions are elastic in nature, where with the container wall or with other gas particles. ▪ When gas particles collide with the container or each other there is no attractive or repulsive forces between the gas particles. ▪ Collisions elastic. ▪ The volume of gas particles are negligible, therefore the volume of the flask is the volume of the gas. ▪ All gases have the same average kinetic energy (KE) when at the same temperature; independent of their mass. ▪ It is assumed that gas particles are in constant motion, therefore they have all have kinetic energy (KE). ▪ As temperature increases, the KE & speed of particle also increases. Molecular Velocities & Kinetic Energy of Gases • Individual gas particles have varying speeds at the same temperature. – Because of the great number of gas particles and number of random collisions between particles and container, the overall molecular speed distribution and average speed of gas particles is considered constant. – The Maxwell-Boltzmann distribution of molecular speed mathematically illustrates the relative numbers of molecules of a gas at a given speed. urms = 𝟑𝑹𝑻/𝑴𝑴 Where: urms is the root mean speed • MM is the molar mass of the gas in kg/mol • T is temperature in Kelvin (K) • The speeds of gas particles will change as temperature changes because kinetic energy is temperature dependent. – Particle speed INCREASES with increasing temperature; there is an increase in KE of the gas particles with increasing temperature. When not at Ideal Conditions As long as we stay away from extremes in pressures ( very high) & temperatures (very low ~ 0 K) the ideal gas law works. Reason: • Intermolecular forces (e.g. the attractions between molecules and ions such as dispersion forces) are negligible for gases at normal-low pressures and at normal to high temperatures. – Why is this important: • Gas volumes decrease with attractions between particles. • An increase in attraction between gas particles during collisions with each other or the container reduces gas pressure. • Volume of the gas particles do not take up an appreciable space, so that the volume of the gas can be assumed to be the volume of the container. Reference credit: OpenStax2017 van der Waals Equation • To account for attractions between gas particles with other gas particles and the container during collisions (inelastic) as well as the volume of the gas particle itself, corrections must be made to the Ideal Gas Law. – The accounts for VAN DER WAALS’s EQUATION volume of particles & intermolecular interaction (forces) between gas particles. Reference Credit: OpenStax2017