Gas Laws Review I. Variables Used to Describe a Gas A. Pressure (P) kpa, atm, mmhg (torr) -Pressure=force exerted per unit area (force/area) -Generated by collisions within container walls (more collisions=more pressure) -Dependent on velocity of gas particle -Collision frequency dependent on velocity of gas particle and distance of container walls B. Volume (V) liters -Inverse relationship with pressure C. Temperature (T) Kelvin -Direct relationship with pressure -Kelvin is preferred over Celsius because there are no negative values D. Number of moles (n) -Direct relationship with pressure II, Development of the Ideal Gas Law A. Boyle s Law -Discovered the inverse relationship between pressure and volume of a gas -More volume= less pressure & less volume=more pressure temperature is unchanging B. Charles s Law -Discovered direct relationship between volume and temperature -Volume and temperature will increase and decrease together pressure and gas amount unchanging C. Lussac s Law -Discovered direct relationship between pressure and temperature -Pressure and temperature will increase and decrease together volume unchanging D. Avogadro s Law -Discovered direct relationship between number of moles in a gas and the volume -Equal volumes of gas contain equal numbers of molecules/ atoms (moles) -Volume and number of moles increase and decrease together temperature and pressure unchanging
E. The Combined Gas Law -When Boyle s Law, Charles s Law, and Lussac s Law are COMBINED -Formula: = (1=initial condition; 2=final condition) F. The Ideal Gas Law -Shows the relationship between P,V, T, and n -More useful than the Combined Gas Law because it takes in account the number of moles or particles -Formula: -R: universal gas constant i. The Different Sides of R -Selection of R is based on the units given in the problem -Conversions are often necessary to make the units compatible -Usually given with problems (don t have to be memorized) -Main values of R: 1) 0.0821 L*atm/ mol-k 2.) 8.314 L*kPa/mol-K 3.) 8.314 J/mol-K III. Standard Temperature and Pressure (STP) -Standard Pressure: 1 atmosphere (atm) -Standard Temperature: 0 C = 273 K -Absolute Zero: lowest possible temperature ( 0 K or -273 C) -1mole of an ideal gas has a volume of 22.4 L -1 atm=101.3 kpa=760 mmhg (torr) IV. Gas Stoichiometry A. Deriving the Molar Mass -Given Ideal Gas Law: ; n(# of moles) = -Substitute: -Rearrange algebraically: ; =grams per liter=density(d) -Therefore, B. Molar Volume or -Given Ideal Gas Law : ; = molar volume -Rearrange algebraically: = C. Mole Fraction -The number of moles of component in a mixture out of the total number of moles in the mixture
-Formula: = -Rearrange algebraically: = ; V. The Kinetic Molecular Theory (KMT) -Used to describe the behavior of all gases at the level of individual particles A. Developed mainly by Boltzmann, Clausius, and Maxwell B. Main Points: 1. Molecules or atoms in gases are in constant random motion 2. Collisions of particles within are the cause of pressure from gas 3. Volume occupied by particles in gas is negligibly small (zero) 4. There are no attractive or repulsive forces between atoms/molecules in a gas 5. The average kinetic energy of a molecule/atom in gas is directly proportional to Kelvin temperature of gas C. Average Kinetic Energy -The higher the temperature=more motion -The Total Kinetic Energy of a Gas Sample: K); T=temperature (K); n=# of moles) (R=gas constant (8.31 J/mol -Average Kinetic Energy of Single Gas Molecule: = or = (m=mass of molecule (kg); v= speed (meters/sec)) D. Graham s Law of Effusion -Effusion: The rate at which a gas escapes through a tiny hole in a container; more collisions=higher probability of hitting hole and escaping; lower mass will diffuse faster -Diffusion: when molecules move from high low concentration until equilibrium is reached; doesn t have to be restricted in a container -Formula between rates of effusion and molar mass: = ( = lower mass; =higher mass) E. Root Mean Square Velocity -Formula: = ( = average speed of a gas molec. (meters/sec); T=temperature (K); M= molecular weight (kg/mol); R=8.31 J/mol K) VI. Real Gases vs. Ideal Gases -Ideal gas: no volume, no attractive/repulsive forces according to KMT
-Real gas (nonideal gas): cooled and/or compressed; distance between particles decreases due to more attraction; volume is no longer ignored; smaller pressure than ideal gas due to less collisions -Van der Waals Equation adjusts ideal gas equation by taking nonideal conditions into account -Equation: (P=pressure (atm); V=volume (L); n=# of moles; T=temperature (K); R=0.0821 L-atm/mol-K; a= constant that is different for each gas and takes in account attractive forces; b=constant that is different for each gas and takes in account the volume of each molecule) VII. Dalton s Law of Partial Pressures -Total pressure is equal to the sum of pressures of individual gases in mix -Equation: -Partial pressure: pressure exerted by each individual gas VIII. Collecting Gas Over Water -There will always be some water vapor in the collecting bottle -Pressure of water vapor depends on temperature -Pressure of gas generated can be calculated through Dalton s Law of Partial Pressures
Gas Laws Review Questions 1. A rigid 5.00 L cylinder contains 24.5 g of N2 (g) and 28.0 g of O2 (g). a.) Calculate the total pressure, in atm, of the gas mixture in the cylinder at 298 K. b.) The temperature of the gas mixture in the cylinder is decreased to 280 K. Calculated the mole fraction of N2 (g) in the cylinder. 2. What volume will 2.50 mol of N2 occupy at 45 degrees C and 1.50 atm of pressure? 3. Nitrogen gas was collected over water at a temperature of 40 degrees C, and the pressure of the sample was measured at 796 mm Hg. If the vapor pressure of the water at 40 degrees Celsius is 55 mmhg, what is the partial pressure of the nitrogen gas? 4. A sample of CO has a pressure of 58 mm Hg and a volume of 155 ml. When the CO is quantitatively transferred to a 1.00 L flask, what will the pressure of the gas be? 5. A balloon occupies a volume of 1.0 liter when it contains 0.16 grams of helium at 37 degrees C. and 1 atm pressure. If helium is added to the balloon until it contains 0.80 grams while pressure and temperature are kept constant, what will be the new volume of the balloon? 6. If ideal gas behavior is assumed, what is the density of neon at STP? 7. A mixture of helium and neon gases has a total pressure of 1.2 atm. If the mixture contains twice as many moles of helium as neon, what is the partial pressure due to neon? 8. Equal quantities of two gases, O2 and H20 are confined in a closed vessel at a constant temperature. a.) Which gas, if any, has the greater partial pressure? b.) Which gas, if any, has the greater density?
Gas Law Review Answers 1a.) First, find the moles of both N2 and O2 by multiplying them with the mass/molar mass ratio. 24.5 g N2 x (1 mol N2/ 28.0 g N2) = 0.875 mol N2 28.0 g O2 x (1 mol O2/ 32.0 g O2) = 0.875 mol O2 Next, add the two molarities together and substitute that as n for the formula P=nRT/V P= [(0.875+0.875)mol x (0.0821 L-atm/mol-K) x 298 K]/5.00 L = 8.56 atm 1b.) Plug the molarities into the mole fraction formula: =[0.875 mol N2/ (0.875 mol N2+ 0.875 mol O2)] =0.500 2.) Plug values into formula V= nrt/p (Don t forget to convert Celsius to Kelvin) V= [(2.50 mol) x (0.0821 L-atm/mol-K) x (318K)]/ (1.50atm) =43.5 L 3.) From Dalton s law, the partial pressures of nitrogen and water vapor must add up to the total pressure in the container. Thus, 796 mmhg 55 mm Hg= 741 mm Hg 4.) Plug the values into the formula = (Don t forget to convert ml to L) 58 mm Hg (155 x 10^-3 L) = (1.00 L) = 8.99 mm Hg 5.) Based on the ideal gas laws, at constant temperature and pressure, the volume of a gas has a direct relationship to the number of moles in the gas. Increase the number of grams by a factor of 5 ([0.16][5]= [0.80]) which increases the number of moles by a factor of 5 as well. In response, the volume increases by 5 so (5) x (1L) = 5 L 6.) Density= m/v and STP means 1 atm, 273 K, and 22.4 L per mole; therefore, plug in the mass of neon over the liters to find the density Density= (20.2 g)/ (22.4 L) = 0.901 g/l 7.) From Dalton s law, the partial pressure of a gas depends on the number of moles of the gas that are present. Since the mixture holds twice as many moles of helium as neon, then the mixture must be 1/3 neon. Thus, (1/3) (1.2 atm) = 0.4 atm 8a.) Partial pressures depend on the total number of moles present in the gas. Since both gases have the same number of moles, the partial pressures are the same. 8b.) O2 has a greater density because oxygen s molecules are heavier. Since density is mass per unit volume, oxygen s heavier mass makes it the denser one of the two gases.