Transcript Gas Laws
Gas Laws Properties of Gases • • • • • • Particles far apart Particles move freely Indefinite shape Indefinite volume Easily compressed Motion of particles is constant and random Gas Pressure • Gas pressure is the result of collisions of particles with their container. • More collisions = more pressure • Less collisions = less pressure • Unit = kPa or atm Units of Pressure • • • • 1 atm = 101.3 kPa =760 torr = 760 mmHg 1 atm = 101,325 Pa 1 atm = 14.70 lb/in2 1 bar = 100,000 Pa = 0.9869 atm atm = atmosphere Amount of Gas • If you add gas, then you increase the number of particles • Increasing the number of particles increases the number of collisions • Increasing the number of collisions = increase in gas pressure • Unit = mole Volume • Decreasing the volume of a container increases the compression. • Increasing compression results in more collisions with the side of the container and therefore an increase in gas pressure • Unit = L Temperature • If the temp. of a gas increases, then the kinetic energy of the particles increase. • Increasing KE makes the particles move faster. • Faster moving particles hit the sides of the container more and increase gas pressure. • Unit = Kelvin (K) (K = °C + 273) STP • Standard Temperature and Pressure Standard Temp = 273K Standard Pressure = 1 atm (101.3kPa, 760torr, 760mmHg) Gas Laws • • • • • • • Boyle’s Law Charles’s Law Gay-Lussac’s Law Avogadro’s Law Combined Gas Law Ideal Gas Law Dalton’s Law of Partial Pressures Boyle’s Law • As pressure of a gas increases, the volume decreases (if the temp is constant). • Inverse relationship P1V 1= P2V2 Charles’s Law • As temperature of a gas increases, the volume increases (if pressure is constant). • Direct relationship V 1= V2 T 1 T2 Gay-Lussac’s Law • As temperature of a gas increases, the pressure increases (if volume is constant). • Direct relationship P 1= P2 T 1 T2 Combined Gas Law P1V1 = P2V2 T1 T2 Avogadro’s Law • Equal volumes of gases at the same temperature and pressure contain an equal number of particles V 1= V2 n 1 n2 Dalton’s Law of Partial Pressure • The sum of the partial pressures of all the components in a gas mixture is equal to the total pressure of the gas in a mixture. • So…all the individual pressures add up to the total pressure. Ptotal = P1 + P2 + P3 + … Ideal Gas Law • An Ideal Gas does not exist, but the concept is used to model gas behavior • A Real Gas exists, has intermolecular forces and particle volume, and can change states. Ideal Gas Law PV = nRT P = Pressure (kPa or atm) V = Volume (L) n = # of particles (mol) T = Temperature (K) R = Ideal gas constant 8.31 (kPa∙L) (mol∙K) or 0.0821 (atm∙L) (mol∙K) At what temperature would 4.0 moles of hydrogen gas in a 100 liter container exert a pressure of 1.00 atm? Ideal Gas Law PV = nRT Use Ideal Gas Law when you don’t have more than one of any variable T = PV/nR = (1.00atm)(100L) (4.0mol)(.0821atm∙L/mol∙K) = 304.5 K 300K Problem #1 • Oxygen occupies a volume of 66L at 6.0atm. What volume will it occupy at 920kPa? Problem #2 • At 25°C a gas has a volume of 6.5mL. What volume will the gas have at 50.°C? Problem #3 Initially you have gas at 640mmHg, 2.5L, and 22°C. What is the new temperature at 750mmHg and 5L? Extensions! • PV = nRT n is moles. If we know the chemical formula for the gas we can convert moles to mass or to particles using Dimensional Analysis! We could also use the fact that: moles = mass or n = m molar mass MM Plugging this in, we have PV = mRT MM This can be rearranged to solve for Density which is m/V m = P∙MM V R∙T or D = P∙MM R∙T What is the density of water vapor at STP? D = P∙MM R∙T D = (1 atm)(18.02g/mol) (.0821atm∙L)(273K) mol∙K D = 0.804 g/L NOTE: STP is exact and does not count towards Sig Figs. Constants don’t either…so actually this problem doesn’t have a method to calculate SFs!