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UMass Amherst CHEM 110 - Chemistry Chapter 10

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Chemistry Chapter 10● Atoms and molecules are in constant motion●Physical StatePackingInteractionbetweenMoleculesKinetic(motion)energy ofmolecules(howfast they aremoving)SolidClosely packedStrongLeastLiquidIntermediatelypackedIntermediateIntermediateGasWidely spacedWeakGreatest● Pressure:○ Force per unit area (N/m2) exerted on the container walls by colliding ofmolecules○ Pressure inside the container will depend on: V, T, n○1 atm= 1.013 bar(bar)= 101.3 kPa(kilopascal)= 60 mm Hg(millimeters of mercury)= 760 torr(torr)= 14.7 psi(pounds per squareinch)● Boyle’s Law:○ For the same amount of gas at constant temperature○ P is inversely proportional to V○ PV = Constant○ High pressure small volume, low pressure large volume.○ P1V1 = P2V2● Charles's Law:○ For the same amount of gas at constant pressure○ V is directly proportional to T○ V/T is Constant○ High temperature, large volume, low temperature small volume○ V1/T1 = V2/T2■ T2 = T1 x V2 / V1● Avagadro’s Law:○ Volume of a gas is directly proportional to the moles (n) (number of molecules) ofthe gas when pressure and temperature are held constant. Bigger moles = biggervolume.○ V1 x n1(initial) = V2 x n2(final)■ V2 = V1 x n2 / n1● Increasing the temperature increases pressure, decreasing the temperature decreasespressure.● Combined Gas Law:○ P1 x V1 /T1 = P2 x V2 /T2○ V2 = V1 x P1 x T2 /P2 x T1○ P2 = P1 x V1 x T2 /V2 x T1○ T2 = T1 x P2 x V2 /P1 x V1● Ideal Gas Law:○ PV = nRT○ V = nRT/P○ T = PV/nR○ P = nRT/V○ P = dRT/M■ M = dRT/P■ d = PM/RT○ n = PV / RT■ P: Pressure(usually atm, based on what R is)■ V: Volume(L)■ n: moles■ R: Gas constant(determines on what unit of pressure is used)■ T: Temperature(K)■ d: Density■ M: Molar mass○ Ptotal = ntotal x (RT/V)○ ntotal = (Ptotal x V) /RT○ P2 = P1 x (V1 / (V1+V2))● Gas Mixtures○ Dalton’s Law of partial pressures states that the pressure of a gas mixture isequal to the sum of the partial pressures of the individual gases.○ Found using Mole Fraction.■ Mole Fraction molecule A = moles of molecule A / moles of molecules A +moles of molecule B(Total number of moles)■ Partial Pressure of molecule A = mole fraction of molecule A x totalpressure● Graham’s Law of effusion?○ Diffusion: Two gases reaching an equilibrium when a barrier is removed to beequally distributed.○ Effusion: When you have a gas trapped on one side of a barrier(concentratedside), and you open a slit, the molecules will move from the more concentratedside to the less concentrated side.■ The rate at which the molecules effuse = 1 / square root of the molecularweight.■ As molecule gets larger the rate slows down.■ Rate 1 / rate 2 =(molecular weight of molecule 2 / molecular weight ofmolecule 1)^1/2● Or (rate 1)^2 / (rate 2)^2 = molecular weight molecule 2 /molecular weight molecule 1● (Time 2 / time 1)^2 = molecular weight 2 / molecular weight 1● (Avg speed 2 / avg speed 1) = (molecular weight 1 / molecularweight 2)^1/2○ Molecular weight = molar mass● Kinetic Molecular Theory:○ The size of gas molecules is insignificant to the volume they occupy○ Molecules of a gas are in continuous, rapid and random motion○ The average kinetic energy (K.E) of gas molecules is determined by the gastemperature, all gas molecules at the same temperature, regardless of mass,have the same average kinetic energy○ Collisions are elastic (no loss of energy)● Boltzmann Distribution○ For gasses there is a distribution of energy. The most probable speed of themolecule is at the top of the curve.● Conditions for Non-Ideal Behavior: Real Gases○ For an ideal gas PV = nRT, therefore PV/nRT = 1 at any pressure○ At high pressure and low temperature, gases deviate from ideal behavior, andthey start to react with each other.● Root Mean Squared Velocity:○ Average velocity.○ Urms = (3RT / M)^½■ The bigger the molar mass, the smaller the velocity■ R = 8.3145 kg m2s-2mol-1K-1■ M = molar mass in kg mol-1● Real Gases: The van der Waals Equation○ (P measured + an^2/V^2 total) (V total - nb)○ P = [(nRT)/(v-nb)] - [(an^2)/(v^2)]○ Percent difference = how attracted molecules are to each other or how big themolecules are in space.○ Mass % = (mass of a component divided by the total mass of the mixture) x 100○ % difference = 100 x (Pideal- Pvan der Waals) /


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