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Ch 5 – The Gaseous State. Gas Phase Reactions The Empirical Gas Laws The Kinetic – Molecular Theory of Gasses. Gas Phase Reactions. Avogadro’s Law and Molar Volumes
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Ch 5 – The Gaseous State Gas Phase Reactions The Empirical Gas Laws The Kinetic – Molecular Theory of Gasses
Gas Phase Reactions • Avogadro’s Law and Molar Volumes • Avogadro’s Law: Equal Volumes of different gasses at the same temperature and pressure conditions contain equal numbers of particles. • Molar Volume (Vm): The volume occupied by one mole of any gas.
Gas Law Variables and STP Conditions Other Gas Phase Conversions Pressure: 1.0 Atmosphere = 760 mm Hg = 760 Torr = 14.2 psi = 29.92 in. Hg =1.01 x 108 pascals = 1013 millibars Temperature: 273 K = 0oC = 32oF
Gas Phase Reactions • Consider the following reaction: N2(g) + 3H2(g) 2NH3(g) • Vm ≡ Volume occupied by 1mole of any gas and contains 1 Avogadro’s number of particles of the specifed gas. ( No = 6.02 x 1023 particles ) • NOTE: No finite molar volume has been assigned because molar volume (Vm) is dependent upon Temperature and Pressure conditions associated with the specified molar volume of interest.
Gas Phase Reactions – Stoichiometry What if Temp and Pressure were specified at 0oC and 1.00 Atm Pressure?*
Gas Phase Reactions – Stoichiometry What if Conditions were specified at non-Std Temp Conditions? Pressure is kept constant. 2Vm= 44.8 L 2Vm<44.8 L 2Vm > 44.8 L
Gas Phase Reactions – Stoichiometry What if Conditions were specified at non-Std Pressure Conditions? Temperature is kept constant. 2Vm= 44.8 L 2Vm<44.8 L 2Vm > 44.8 L
Gas Phase ReactionsCorrecting for Non-Standard Conditions • The Empirical Gas Laws: • Boyles Law (V ∝ 1/P)n,T or (P ∝ 1/V)n.T • Charles Law (T ∝ V)n,P • Gay-Lussac Law (T ∝ P)n,V • Avogadro’s Law (n ∝ V)T,P • Combined Gas Law (PV ∝ nT) • Ideal Gas Law (PV/nT) ∝ Constant P = Pressure, V = Volume, n = moles & T = Temperature
Gas Phase ReactionsBoyles Law • If I have 5.6 liters of gas in a piston at a pressure of 1.5 atm and compress the gas until its volume is 4.8 L, what will the new pressure inside the piston be?
Gas Phase ReactionsCharles Law • Calcium carbonate decomposes at 12000 C to form carbon dioxide and calcium oxide. If 25 liters of carbon dioxide are collected at 12000 C, what will the volume of this gas be after it cools to 250 C?
Gas Phase ReactionsCombined Gas Law • A toy balloon has an internal pressure of 1.05 atm and a volume of 5.0 L. If the temperature where the balloon is released is 200 C, what will happen to the volume when the balloon rises to an altitude where the pressure is 0.65 atm and the temperature is –150 C?
Gas Phase ReactionsReaction Stoichiometry Calcium carbonate decomposes at high temperatures to form carbon dioxide and calcium oxide: CaCO3(s) CO2(g) + CaO(s) How many grams of calcium carbonate will I need to form 3.45 liters of carbon dioxide at STP? What volume of CO2(g) will be produced at 25oC and 775mm pressure?
Gas Phase ReactionsIdeal Gas Law • How many moles of gas are in a 30 liter scuba canister if the temperature of the canister is 300 K and the pressure is 200 atmospheres? • If I have a 50 liter container that holds 45 moles of gas at a temperature of 2000 C, what is the pressure inside the container?
Gas Phase Reactions When chlorine is added to acetylene, 1,1,2,2-tetrachloroethane is formed: 2 Cl2(g) + C2H2(g) -> C2H2Cl4 (l) How many liters of chlorine will be needed to make 75.0 grams of C2H2Cl4 at 25oC and 725mm Hg? Ethylene burns in oxygen to form carbon dioxide and water vapor: C2H4(g) + 3 O2(g) -> 2 CO2(g) + 2 H2O(g) How many liters of water can be formed if 1.25 liters of ethylene are consumed in this reaction?
Dalton’s Law of Partial Pressures • For a mixture of gasses, the total pressure is the sum of the partial pressures. PTotal = ∑Pi = P1 + P2 + … + Pn Pi Vi = niR Ti If I place 3 moles of N2and 4 moles of O2in a 35 L container at a temperature of 25° C, what will the pressure of the resulting mixture of gases be? n i = 1
Graham’s Law of Effusion Graham’s Law of Effusion: The discharge rate of a confined gas under pressure is inversely proportional to the square root of it’s molecular weight. Velosity effusion (vi) ∝ [1 / (M)1/2] V1 • √M1= v2•√M2 (Relative speed of effusion) √M1/t1 = √M2/t2 (Relative time of effusion)
Graham’s Law of Effusion • Compare the effusion rates of N2(g), H2(g), and O2(g). • For a container of N2(g), it was found that effusion of all the nitrogen took 27 seconds. For a similar container of H2(g), how long will its effusion time be?
Kinetic – Molecular TheoryGas Phase Particles • Postulates of the Kinetic-Molecular Theory • All matter is composed of particles – elements and/or molecules. • Particle-Particle interactions are by attraction or by repulsion forces. • All particles of matter are in constant motion ; i.e., translation, rotation and vibration. • The average velocity of particles of matter is directly proportional to its Kinetic Energy content. • Collisions between particles of matter are generally considered to be perfectly elastic in nature ; i.e., ∑ΔEnergy = 0.
Kinetic – Molecular TheoryGas Phase Particles • Boltzman Distribution of Gas Particle Speed/Energy Content VRMSParticle @ T1 Activation Energy VRMS Particle @ T2 VRMS = 159√T/M (m/sec) T = Kelvin Temperature M = Molecular Weight Velocity (m/sec)
Kinetic – Molecular TheoryGas Phase Particles • Root Mean Square Speed Vrms = √3RT/M = 159√T/M (m/sec) T = Kelvin Temperature M = Molecular Weight • Calculate the Root Mean Sqr Speed of O2(g) at 25oC, 30oC and 35oC. Plot Vrms∝ f(Temp). Is the trend linear or exponential?
