Honors Chem Chapter 5 Test

Kinetic Theory of Gases

Kinetic Energy: Energy of movement Kinetic Theory of Gases: All gases behave similarly as far as particle motion is concerned.

Partial Pressure

Ptot = P₁ + P₂ (P₃ + P₄ +...) *Dalton's Law: The total pressure of a gas mixture is the sum of the partial pressures of the components of the mixture. P₁ = (n₁RT)/V, P₂ = (n₂RT)/V *Ptot = (ntotRT)/V* Example: PH2 = 2.46 atm PHe = 3.69 atm Ptot = 6.15 atm

Effusion (definition)

The flow of gas particles through tiny pores or pin holes → This ✓ is the validity of calculations made from the Kinetic Theory of Gases

The Law of Combining Volumes

The volume ratio of any two gases in a reaction at a constant temperature and pressure is the same as the reacting mole ratio. 2H₂O(l) → 2H₂(g) + O₂(g) V=n! *Volume directly proportional to moles Electrolysis of H₂O → 2x as much (volume or moles) H₂ gas as O₂ gas!

Effusion of Gases - Graham's Law

rate 2/rate 1 = √M₁/M₂ *Rate of effusion depends on • Pressure • Speed of particles *High molar mass effuse more slowly than lower molar mass. (Rate of Effusion 2) / (Rate of Effusion 1) = u₂/u₁ u₂/u₁ = √M₁/M₂ rate 2/rate 1 = √M₁/M₂ *Can determine molar mass of gases!

Density

• Can use the ideal gas law to get the general equation for density...which is what was done in two steps in example 5.5 o Density = m/V o PV = m/M RT o Density = MP/RT o Density is dependent on: Pressure: Compressing, ↑ Density Temperature: ↑ Temp, ↓ Density Molar Mass: Lower M, ↓ Density

Molecular Model of the Kinetic Theory of Gases

• Gases are mostly empty space • Gas molecules are in constant, chaotic motion (increase temperature) • Collisions are electric → won't stick *Shooting pool! • Gas pressure is caused by collisions of molecules with the wells of the container * ↑P↓ Temperature and Amount (They are directly proportional) *Air undergoes about 10 billion collisions per second

Molar Mass

• Molar mass of a gas can be determined from the ideal gas law. *Can also be applied to volatile liquids • All we need to know is... o m = M x n (PV = nRT) o Mass of sample o Confined container/fixed volume o Temperature and pressure o Example 5.4 and 5.5 o n = m/M o PV = m/M RT

Attraction Forces

(Vm - V°m)/V°m < 0 Vm = Molar Volume (Experimentally Observed) V°m = Molar Volume (From Ideal Gas Law) From molar volume table all are negative (less than expected) gas particles move closer to one another...reduce space between and attract!

Particle Volume

(Vm - V°m)/V°m > 0 Vm = Molar Volume (Experimentally Observed) V°m = Molar Volume (From Ideal Gas Law) Larger particles account for deviations of molar volume at high pressures where particles are close to one another. *Larger can't pack as well

Average Kinetic Energy of Translational Motion, Et

* Motion of molecules Et = (3RT)/2Nα Nα = Avogadro's Number = 6.022 * 10²³ molecules/mole 3 Constants (³/₂, R, Nα) 1 variable T → In Kelvin *At a given temperature in different gases they must all have the same Kinetic Energy of translation motion. *The average translational Kinetic Energy of a gas molecule is directly proportional to the temperature (T) in Kelvin.

Ideal Gas Law Formula and Symbol Meaning

*PV = nRT* (V) Volume = Liters (P) Pressure = atm (n) Amount = usually moles T = Kelvin R = 0.0821 L x atm/(mol x K) R = 8.31 J/(mol x K) R = 8.31 x 10³ g x m²/(s² x mol x K)

Avogadro's Number

6.022 * 10²³ molecules/mole

Partial Pressure and the Mole Fraction Example Problem: Chemical analysis of dry air (NOT wet) shows the mole fraction of nitrogen, oxygen, and argon are 0.781, 0.210, and 0.009. Calculate the partial pressure of each of these gases on a day when the barometric pressure is 747 mmHg (total pressure).

747 mmHg * 1 mol/760mmHg = 0.983 atm 0.781 (0.983 atm) = 0.768 atm Nitrogen 0.210 (0.983 atm) = 0.206 atm Oxygen 0.009 (0.983 atm) = 0.009 atm Argon

Graham's Law (definition)

At a given temperature and pressure, the rate of effusion of a gas, in moles per unit time, is inversely proportional to the square root of its molar mass.

cm³ --> m³ Conversion

Cm³ = 1 * 10⁻³ m³

Effusion of Gases/Graham's Law Example: In an effusion experiment, argon is allowed to expand through a tiny opening into an evacuated flash of volume 120mL for 32.0 sec, at which point the pressure in the flash is formed to be 12.5mmHg. This experiment is repeated with a gas x of unknown molar mass at the same temperature and pressure. It is found that the pressure in the flask builds up to 12.5mmHg after 48.0 sec. Calculate the molar mass of gas x.

Comparing the two rates in moles per second: rate Ar/rate X = (n/32.0 s)/(n/48.0 s) = 48.0/32.0 = 1.50 Applying Graham's Law: 1.50 = √M x/M Ar Solving by squaring both sides and substituting M Ar = 39.95 g/mol M x = (39.95 g/mol) × (1.50)² = *89.9 g/mol*

Average Speed (Extra Credit)

Distribution Chart: Page 132 u = √(3RT)/M u₂/u₁ = √T₂/T₁ u₂/u₁ = √M₁/M₂ Different R value *Page 119 R = 8.31 (g x m²)/(s² x mol x K) • Directly proportional to the square root of the absolute temperature → Gas at two different temperatures (T₂ + T₁), the M is constant u₂/u₁ = √T₂/T₁ • Inversely proportional to the square root of molar mass (M) for two different gases 1 and 2 at the same constant temperature u₂/u₁ = √M₁/M₂

Wet Gases, Partial Pressure of H₂O

Electrolysis of H₂O → Molecules of H₂O escape and enter the gas phase. Ptot = PH₂O + PH₂ Ptot = Measured pressure PH₂O = A fixed value for water vapor → Vapor pressure at a given temperature *Appendix 2 (mmHg) "Vapor pressure" - physical characteristic PH₂ = determined by subtraction From this we can determine nH₂ using the ideal gas law (PV = nRT)

Gas (definition)

Fills the volume of it's container... For example, the air in this room... All gases behave physically VERY similarly! *Their volumes respond exactly the same way to changes in pressure, temperature, or amount of gas.

Pressure (definition)

Force per unit area Example: PSI (Pounds per Square Inch) in tires Barometer measures atmospheric pressure

Real Gases (definition)

Gases actually deviate from experimentally observed data...especially at high pressure or low temperature (close to liquefying!).

Wet Gas Partial Pressure of H₂O Example Problem: You prepare a sample of Hydrogen gas by electrolyzing water at 25 degrees Celsius. You collect 152 mL of H2 at a total pressure of 758 mmHg. Using Appendix 1 to find the vapor pressure of water. Calculate: 1) The partial pressure of hydrogen. 2) The number of moles of hydrogen collected.

0.99 atm = 0.0313 atm + PH₂ PH₂ = 0.9587 atm PH₂V = nRT PH₂ = 0.006 mol

L --> cm³ Conversion

1 L = 1 * 10³ cm³

L --> mL Conversion

1 L = 1 * 10³ mL

Pa --> Bar Conversion

1 Pa = 1 x 10⁻⁵ Bar

mmHG ---> atm Conversion

1 atm = 760 mmHg

Stoichiometry of Gaseous Reactions Practice Problems • Hydrogen Peroxide (hair bleach) What mass of H₂O₂ must be used to produce 1.00 L of O₂ gas at 25 degrees Celsius and 1.00 atm? 2H₂O₂(aq) → O₂(g) + 2H₂O(l) Balance equation Find moles using ideal gas law • Octane in gasoline (C₈H₁₈). When burned (combustion) produces CO₂ and H₂O. How many liters of O₂ measured at 0.974 atm and 24 degrees Celsius are required to burn 1.00 g of octane? 2 C₈H₁₈(l) + 25 O₂(g) → 16 CO₂(g) + 18 H₂O(l)

1. 2.78 g H₂O₂ 2. 2.73 L

Molecular Model

1. Gases are mostly empty space: The total volume of the molecules is negligibly small compared with that of the container to which they are confined. 2. Gas molecules are in constant, chaotic motion: They collide frequently with one another and with the container walls. As a result their velocities are constantly changing. 3. Collisions are elastic: There are no attractive forces that would tend to make molecules "stick" to one another or to the container walls. 4. Gas pressure is caused by collisions of molecules with the walls of the container: As a result, pressure increases with the energy and frequency of these collisions.

Ideal Gas Law

1. Volume is directly proportional to amount V = n (constant T, P) 2. Volume is directly proportional to absolute temperature (Charles' Law) V = T (Constant n,P) 3. Volume is inversely proportional to pressure (Boyle's Law) V = 1/p (constant n, T) So... V = constant (gas constant) x nT/P R= 0.0821 L x atm/mol x K *Ideal Gas Law: pY = mRT*

Bar --> atm --> mmHg Conversion

1.013 bar = 1 atm = 760 mmHg

Monometer (definition)

Measures pressure of a confined gas (example: blood pressure cuffs)

Partial Pressure and the Mole Fraction

Mixture containing gases 1(+2) P₁ = (n₁RT)/V Ptot = (ntotRT)/V P₁/Ptot = n₁/ntot *The fraction n₁/ntot is called the mole fraction of gas 1 in the mixture... it is the fraction of the total number of moles that is accounted for by gas 1 use X₁ → Mole fraction X₁ = n₁/ntot So... P₁ = X₁ Ptot X₁ = n₁/ntot *The partial pressure of a gas in a mixture is equal to its mole fraction multiplied by the total pressure. • Used to calculate partial pressure of gases in a mixture when the total pressure and the composition of the mixture is known.

Molar Volume

Molar Volume = Vm = V/n with the molar volume calculated from the ideal gas law V°m: V°m = RT/P *In general, the closer a gas is to the liquid state, the more it will deviate from the ideal gas law.

Real Gases (factors)

Molar Volume page 133 Charts From a molecular standpoint deviations result from the ideal gas law because it neglects two factors: 1) Attractive forces between gas particles: From molar volume table all are negative (less than expected) gas particles move closer to one another...reduce space between and attract! 2) Particle Volume: Larger particles account for deviations of molar volume at high pressures where particles are close to one another. *Larger can't pack as well

Kinetic Theory of Gases Equation

P = (Nmu²)/3V N = # of molecules m = mass of molecule u = average speed *The ratio N/V = concentration of gas molecules in container more molecules at a given volume, ↑ collision frequency, ↑ Pressure *Product of mu2: The energy of collision → More mass at greater speed, MORE energy transferred, ↑ Pressure

Converting Farenheit to Celsius

TF = 1.8 TC + 32

Converting Kelvin to Celsius

TK = TC + 273.15