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## Energy and Gases

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**Energy and Gases**Kinetic energy: is the energy of motion. Potential Energy: energy of Position or stored energy Exothermic • energy is released by the substance into the surroundings • less PE, more KE, so temperature rises Endothermic • energy is absorbed by the substance from the surroundings • more PE, less KE, so temperature drops**Nature of Gases**• Gases expand to fill the container that they are in • gas particles glide past one another- they are fluid • gases have low density • gases can be compressed or squeezed together • Diffusion: spontaneous mixing of two gaseous substances by their random motion. • Effusion: process by which gas particles pass through a tiny opening • Pressure: force per unit area (pressure = force/area) • units: Newtons (N), millimeters of mercury (mm Hg), torr, One atmosphere of pressure (atm), Pascal (Pa)**Gases**• Kinetic-molecular theory: particles of matter are always in motion • Ideal gas: an imaginary gas that perfectly fits all the assumptions of the kinetic molecular theory Kinetic Model theory of gases: 1) gases are tiny particles that are far apart 2) Collisions between gases particles (and container walls) are elastic (i.e: no net lose of kinetic energy) 3) gas particles are in continuous, rapid, random motion 4) No forces of attraction or repulsion between particles 5) The average kinetic energy of gas particles depends on the temperature. KE = 1/2 mv2**Gas Laws**Boyle’s Law: P1V1= P2V2 Charles’ Law: V1 = V2 T1 T2 Lussac’s Law: P1 = P2 T1 T2 Avogadro’s Law: V=kn Combined Gas Law: P1V1 = P2V2 T1 T2 Ideal Gas Law: PV = nRT Dalton’s Law of Partial Pressure: Ptotal= P1+ P2 + P3…. Graham’s Law: Rate gas 1 = √MM gas 2 Rate gas 2 = √MM gas 1**Proportionality**• PV = nRT • Pressure and Volume: are inversely proportional because they are on the same side of the equation • Opposites: one goes up…the other goes down • P α 1/V • Temperature and Volume: are directly proportional because they are on opposite sides of the equation • Same: one goes up….the other also goes up • T α V**Variables in Equations**PRESSURE (P): • Force per unit of area • Caused by collisions of gas molecules pushing on the walls of a container • Measured using a barometer • A device that allows atmospheric gases to push open mercury up through a graduated tube. • Units: “atm” (atmosphere) • Standard pressure is 1 atm • 1 atm = 760 mm Hg = 760 Torr = 101325 Pascals = 101.325 kPa = 14.7 psi = 29.92 in Hg**Variables in Equations**VOLUME (V): • The amount of space taken up • Gases expand to fill the space of the container that they are in. • Units: “L” (Liters) • 1 L = 1000 mL • @ STP 22.4 L = 1 mol (of a gas) MOLES (n): • Units: “mol” (moles) • If given grams convert using molar mass**Variables in Equations**TEMPERATURE (T): • Units: “K ” (Kelvin) • oC + 273 = K • Standard Temperature is 0 oC or 273K CONSTANT (R ): • This is not variable, but a constant • Depends on pressure units • R = 0.0821 (L * atm)/ (mol * K) • R = 8.314 (L * kPa) / (mol * K)**Ideal Gas Law**• Assume that gases behave ideally • No attractive or repulsive forces between particles • Real gases behave most like ideal gases at high temperatures and low pressures • IDEAL GAS LAW PV = nRT • n = the number of moles, • R = 0.0821 (L*atm)/(mol* K) or 8.314 J/(mol* K) • n = m/ MM moles = mass / Molar Mass • D = m/V • So.... MM = DRT or MM = gRT P PV**Stoichiometry**• Use the Ideal Gas Law to get the number of moles then use the balanced equation to go from moles X to moles Y. The use Molar Mass to get to grams! • The rates of effusion and diffusion depends on the relative velocities of gas molecules. The velocity of a gas varies inversely with the square root of the molar mass of the gas • The larger a molecule, the slower it moves. Graham’s Law**Dalton’s Law:**• Partial Pressure: the pressure that an individual gas exerts in a mixture of gases • Ptotal = P1 + P2 + P3 ……Pn • You just add the individual pressures for the various gases.**Examples:**_________ # 1) A gas travels 2.0 faster than N2. What is the molar mass of the gas?**Examples:**_________ # 2) When 0.27 L of a gas at 23oC is heated to 38oC, what will be the new volume in milliliters?**Examples:**_________ # 3) If 750 mL of a gas at 850 mm Hg is reduced to 0.90 atm, what is the new volume?**Examples:**_________ # 4) A container of gas at 1.2 atm contains O2 at 100.0 mm Hg, N2 at 425 torr, and the gas CO2. What is the pressure of CO2 in atmospheres?**Examples:**_________ # 5) 13.5 grams of NH3 are put in a 20.0 L container at 179 kPa, what is the temperature inside?**Examples:**_________ # 6) If a gas at 308 K and 525 torr is cooled to 13oC, what will be the new pressure in atm?**Examples:**_________ # 7) If 5.0 moles of gas are HELD in a flexible container with an initial volume of 89.5 mL at 25oC and 1.05 atm. If the pressure changes to 748 mm Hg and the temperature is 295 K, how much space will the new container take up?**Examples:**_________ # 8) What is the density of sulfur dioxide gas at 34.0 degrees celsius and 745 mm Hg?**Examples:**_________ # 9) If nitrogen travels at 25.0 m/sec at a certain temperature, how fast does carbon monoxide travel at the same temperature?**Examples:**_________ # 10) What is the molar mass of a gas if 18 grams are put into a 375 mL container at 28oC and 10.6 psi?