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**Macroscale Chemistry Ch 5 Gases—transition to macroscale**

Ch 6-8 Equilibrium Ch 9 Thermochemistry Ch 10 Thermodynamics Ch 15 Kinetics Applications

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Gases Ch 5

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IMF and Gases

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11 Gaseous Elements

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**Gases: Macroscopic Observation**

Gases fill the container into which they are placed Gases are compressible Gases mix completely and evenly when confined to the same container Gases have much lower densities than solids or liquids (g/L)

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Gases: Molecular View Fill space evenly and completely: randomly, fast moving particles Low density and compressibility: large distances between particles Idealized assumptions Gas particles have no volume Gas particles have no interaction, so identity of gas particle is inconsequential

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**Gases: Historical View**

Molecular basis Kinetic energy of molecules much greater than intermolecular forces Historical studies precede the atom First we will look at non-molecular properties

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Torricelli ( ) 1 atm = 760 torr

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**Pressure Velocity = distance / time (m/s)**

Acceleration = change in velocity / time (m/s2) Force = mass x acceleration (kg m/s2 = N) Pressure is the force of the gas pressing on a given area P = F/A (N/m2 = Pa) Ability to cut with a knife doesn’t depend simply on amount of force

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Test the concept

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**Pressure Pressure = Force/Area Force = mass * acceleration**

Acceleration = g = pull of gravity mass = r*V = r*h*A where r=density of Hg, h= height of Hg, A = cross-sectional area of column Force = r*h*A*g Pressure=(r*h*A*g)/A = r*h*g P height and density If the density of mercury is 13.6g/ml, what is the height of a column of water under vacuum at atmospheric pressure? (76 cm =2.5 ft)

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Pressure Conversions 1 atm = 14.7 lb/in2 = 760 mmHg = 760 torr = kPa

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Manometer

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**Experimenting with Gases**

Robert Boyle ( ) As P (h) increases V decreases

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**Plot of Pressure vs Volume**

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Boyle’s Law V =k/P

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**Boyle’s Law P 1/V , when one sample is kept at constant temperature**

Acts as an “Ideal Gas”

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Ideal Gas Pressure is inversely proportional to volume at a range of constant temperatures and sample sizes k changes value at different temperatures, but is constant…well, almost constant Also notice that identity of gas matters little, and all approach same ideal (all data from 1 mol samples at 0 oC)

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**Ideal Gas Molecular perspective Assumptions Good assumptions?**

Molecules occupy no space Molecules do not interact with each other Good assumptions?

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**Test your Understanding**

When you blow up your tire, you increase the pressure and volume simultaneously. According to Boyle, pressure and volume are inversely proportional. What gives?

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**Charles’s Law Jacque Charles (1746-1823) Solo balloon flight**

At constant pressure, volume increases linearly with temperature Write Law

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Charles’s Law (1783) V T T in Kelvin K = oC + 273 Absolute zero

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**Pressure and Temperature**

Draw Pressure as a function of Temperature at constant volume

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**Avagadro’s Law (1811) In light of Dalton’s Atomic Theory (1808)**

Based on Gay-Lussac Law of combining volumes

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Avogadro’s Law At constant P and T, the volume of a gas is proportional to the amount of gas molar volume Vm = V/n V n Little known historical fact: Junior High nickname happened to be “The Mole”

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**Combined Ideal Gas Law V proportional to 1/P V proportional to T**

V proportional to n 𝑉=𝑅 𝑛𝑇 𝑃 PV = nRT

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**Problem Types If three variables known, calculate fourth**

Some conditions change—how does it affect others? Stoichiometry Determine a molar mass

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**Molar Volume Molar Volume = Vm Vm at STP = 22.41 L/mol**

Defined as the volume taken up per mole of gas Vm at STP = L/mol Standard Pressure is 1 atm What is standard temperature in Celcius?

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**Strategy/Sketch: Answer: 7.0 x 102 oC**

A flask that can withstand an internal pressure of 2500 torr, but no more, is filled with a gas at 21.0 oC and 758 torr and heated. At what temperature will it burst? Strategy/Sketch: Answer: 7.0 x 102 oC

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**Change in State of Ideal Gas**

If the stopcock is opened, the total pressure is atm. What was the original pressure of the red bulb? Strategy: Logic Check: 2.00L Ar at 360 torr 1.00 L Ar unknown pressure Assumption Check: According to ideal gas, would the total pressure change if the right bulb were filled with 1 L of carbon dioxide? Answer: x 103 torr

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**Gas Density 𝑃𝑉=𝑛𝑅𝑇 𝑃𝑉 𝑚 = 𝑛𝑅𝑇 𝑚 where m = mass in grams**

𝑚 𝑉 = density in grams/Liter 𝑚 𝑛 = molar mass in g/mol 𝑃 𝜌 = 𝑅𝑇 𝑀 where ρ = density & M = molar mass

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**Experimental Importance**

𝑃 𝜌 = 𝑅𝑇 𝑀 If you had a sample of an unknown gas, what could you measure experimentally? What could you determine about the gas?

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**Dalton’s Law of Partial Pressures**

Extension of ideal gas assumptions For a mixture of two gases A and B, the total pressure, PT, is PT = PA + PB “Partial Pressure” Since two gases by definition are at same V and T, 𝑛 𝑎 𝑛 𝑏 = 𝑃 𝑎 𝑃 𝑏 Useful case: 𝑛 𝑎 𝑛 𝑡𝑜𝑡𝑎𝑙 = 𝑃 𝑎 𝑃 𝑡𝑜𝑡𝑎𝑙 An example of early utility of Dalton’s atomic theory

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Mole Fraction Mole fraction (χ) is the number of moles of one component of a mixture divided by the total moles in the mixture: 𝑛 𝑎 𝑛 𝑡𝑜𝑡𝑎𝑙 χ A + χ B + χ C = 1 The partial pressure of any gas, A, in a mixture is given by: PA = χ A ( PT )

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**Collecting a Gas Over Water**

Gases collected by water displacement are a mixture of the gas and water vapor. All liquids have a certain amount in the gas phase. This is known as the Vapor Pressure of the liquid. It is temperature dependent. PT = Pgas + PH2O

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**Experimental Determination of R**

Name Mass Mg (g) Moles Mg Moles H2 T (Celsius) T (Kelvin) PT (mm Hg) PH2O (mm Hg) PH2 (mm Hg) PH2 (atm) VH2 (mL) VH2 (L) R (L-atm/mol-K) Joe Dirk 0.0295 21.8 731 19.59 30.5 0.03 0.0291 Anne Marie, Emily 0.0293 21.0 18.65 31.5 20.0 17.54 31.6 31.1 Anthony Nick 0.0302 22.0 19.83 31.9 0.0287 22.7 20.57 30.2 0.0285 23.3 21.32 30.0 Jon Josh 0.0301 21.5 19.32 32.0 0.0313 33.4 0.0319 20.5 18.08 mike jeremy 0.0305 23.5 18.50 24.2 32.5 0.0298 23.8 31.7 Marissa, Natalie, Katie 23.0 21.07 19.35 32.6 0.0297 31.4 Kim, Dave 0.0296 31.0 19.11 Marshall, Brian 0.028 24.0 22.38 29.9 21.58 30.8 0.029 32.1 Alysha, Ashley 0.0279 29.8 0.0277 29.2 0.0274 28.4 Ryan, Valerie 30.3 0.0299 22.8 20.82 Toni, Bryson 24.5 22.92 28.0 0.0286 28.8 0.0282 22.9 28.5

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**Kinetic Molecular Theory**

Describes gases at the molecular level 1. Gases consist of small particles separated by large distances (assume no volume.) 2. Constant, random motion. Collisions with wall cause pressure 3. Gas particles have no interaction with one another (no intermolecular forces.) Collisions occur continuously and are elastic (no gain/loss of KE). 4. KE T, average kinetic energy only changes when temperature changes.

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**Ideal Gas Law from Theory: Qualitative**

Connect Atomic level (velocity, mass, collisions) to macroscopic (P, V, n, T) P ∝ 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑐𝑜𝑙𝑙𝑖𝑠𝑖𝑜𝑛 ( 𝑐𝑜𝑙𝑙𝑖𝑠𝑖𝑜𝑛𝑠 𝑠𝑒𝑐𝑜𝑛𝑑 ) P ∝ 𝑚𝑎𝑠𝑠 𝑎𝑣𝑒 𝑠𝑝𝑒𝑒𝑑 [ 𝑎𝑣𝑒 𝑠𝑝𝑒𝑒𝑑(#𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠) 𝑣𝑜𝑙𝑢𝑚𝑒 ] P ∝ (𝑚 υ 2 )(#𝑚𝑜𝑙𝑒𝑠) 𝑣𝑜𝑙𝑢𝑚𝑒 ∝ 𝑘𝑖𝑛𝑒𝑡𝑖𝑐 𝑒𝑛𝑒𝑟𝑔𝑦 (#𝑚𝑜𝑙𝑒𝑠) 𝑉𝑜𝑙𝑢𝑚𝑒 P ∝ 𝑇 𝑛 𝑉

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**Is KMT consistent with Observation?**

Compressibility Boyle – P and V Charles – V and T, P and T Avogadro – V and n Dalton’s Partial Pressures

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**Ideal Gas Law from Theory: Quantitative**

Error in text (total force does not equal sum of component) 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 2 = 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑥 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑦 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑧 2

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Derivation of KMT See handout

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**The meaning of Temperature**

𝑃𝑉 𝑛 = 2 3 (KE)ave and 𝑃𝑉 𝑛 = RT KEave = 3 2 RT where R = J/mol K Kelvin temperature is measurable quantity that is directly proportional to the random motion (kinetic energy) of the particles

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**Velocity of particles in Gas**

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**Velocity of particles in Gas**

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**Maxwell-Boltzmann Distribution**

f(u)=4𝜋 𝑚 2𝜋𝑘𝑇 3/2 𝑒 (− 𝑚𝑢2 2𝑘𝑇 ) How does this function form the shape of the distribution? How does high mass shift curve? How does high T shift curve?

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**Maxwell/Boltzmann Distribution**

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**“Typical” Velocities at 298 K in m/s**

These gases are at the same temperature, so they have the same __________ but they have different average velocities because they have different _________________.

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**Three ways to describe a “typical velocity”**

Most probable Average RMS

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**Determination of RMS velocity**

KEave = 3 2 RT = Na 1 2 𝑚 𝑢 2 𝑢 2 = 3𝑅𝑇 𝑚 𝑁 𝑎 Root mean square velocity

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Root Mean Square Speed

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**Test your understanding**

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**Gas Motion on a Molecular Level**

Effusion Diffusion

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**Diffusion and Effusion**

Diffusion – mixing due to motion Effusion – passage of a gas through a small hole into an evacuated space Ratio of effusion or diffusion rates depends on relative velocities of gases 𝑒𝑓𝑓 𝑜𝑟 𝑑𝑖𝑓𝑓 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑔𝑎𝑠 1 𝑒𝑓𝑓 𝑜𝑟 𝑑𝑖𝑓𝑓 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑔𝑎𝑠 2 = 3𝑅𝑇/𝑚1 3𝑅𝑇/𝑚2 = 𝑚2 𝑚1

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Real Gases Nitrogen gas At 200K

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**Real Gases: Check Assumptions**

1. Gases consist of small particles separated by large distances (assume no volume.) 2. Constant, random motion. Collisions with wall cause pressure 3. Gas particles have no interaction with one another (no intermolecular forces.) Collisions occur continuously and are elastic (no gain/loss of KE). 4. KE T, average kinetic energy only changes when temperature changes.

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Assumptions that Fail Gases have no contribution to volume. Is this assumption equally valid at all states?

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Assumptions that Fail Gases velocity is unaffected by attraction to other particles.

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When Is a Gas Most Ideal?

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**Make a “Real Gas” Law Points to consider**

Volume: must factor in _________and __________ of particles Pressure: must factor in ___________ and ___________ of interaction

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**( ) } } Van der Waals equation nonideal gas an2 P + (V – nb) = nRT V2**

corrected pressure } corrected volume Does this experimental data match theory?

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