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Honors Chemistry

Chapter 5

Gases

5.1 Gases

• Temperature vs. Intermolecular attraction

• Atomic Gases• Noble Gases, H2, N2, O2, F2, Cl2

• Molecular Gases• Usually light molecules with weak attraction forces

• Eg: HCl, CO2, NH3, H2S, NO2

• Ionic Compounds• Strong forces; not normally gases

5.2 Pressure

• Force per unit area• P = F/A • N/m2 unit defined as Pascal (Pa)• Standard air pressure = 101.325 kPa• Also called 1 atmosphere (atm)• Measured by unequal mercury levels• Manometers and barometers• Common unit called mmHg (or Torr)• Standard air pressure = 760 mmHg

5.2 Dimensional Analysis

• Convert 75.0 kPa to mmHg

• 75.0 kPa 760 mmHg----------- x --------------- = 563 mmHg 1 101.325 kPa

• Try this one• Convert 1.25 atm to kPa

5.3 Boyle’s Law

• Pressure is inversely proportional to volume• Hold temperature and amount of gas constant• V 1/P• V = k x (1/P)• PV = k• Best used with changing conditions

• P1V1 = P2V2

5.3 Boyle’s Law Problems

• A 175 mL sample of methane is stored at 125 kPa. What pressure is needed to compress the gas to a volume of 50.0 mL?

• P1V1 = P2V2

• (125 kPa) (175 mL) = P2 (50.0 mL)• P2 = 438 kPa• Try this one

• A sample of argon occupies 476 mL at 650 Torr. Find the volume at 975 Torr.

5.3 Charles’ Law

• Also credited to Gay-Lussac• Volume is directly proportional to temperature• Hold pressure and amount of gas constant• V T• V = kT• Linear relationship• Must use Kelvins!• V1 V2

--- = ---T1 T2

5.3 Charles’ Law Problems

• A 5.00 L helium balloon is heated from 20oC to 75oC. Find its new volume.

• V1/T1 = V2/T2

• 5.00 L V2

--------- = --------293 K 348 K

• V2 = 5.94 L

• Try this one• A 670 mL sample of chlorine is stored at 50oC. At what

temperature will its volume be 450 mL?

5.3 More Gas Laws

• Another form of Charles’ Law• Pressure is directly proportional to temperature• P = kT

• P1/T1 = P2/T2

• Avogadro’s Law• Volume is directly proportional to the amount of

gas present• V n• Volume relationships in chemical reactions

5.3 Avogadro’s Law Problems

• How many liters of hydrogen are needed to completely react with 1 liter of oxygen?

• 2 H2 + O2 2 H2O• 2 mol hydrogen react with 1 mol oxygen• V n, so….• 2 L hydrogen react with 1 L oxygen• Try this one

• How many liters of ammonia are formed when 1 L of hydrogen reacts with excess nitrogen?

5.4 The Ideal Gas Equation

• Ideal Gas• No intermolecular attraction forces• Particles have no volume

• Combine Boyle’s, Charles, and Avogadro’s Laws

• PV = nRT• STP = 1 atm, 273 K• Molar volume of a gas = 22.414 L at STP• R = 0.0821 atm L / mol K

5.4 Ideal Gas Equation Problems

• A sample of fluorine occupies 3.65 L at 45oC and 2.50 atm. How many moles of fluorine are present?

• PV = nRT• (2.50 atm)(3.65 L) = n (0.0821)(318 K)• n = 0.350 mol• Try this one

• A 0.500 mol sample of propane occupies 2.15 L. If the temperature is 28oC, find the pressure.

5.4 Gas Density

• Since n = m/M….

• PV = (m/M) RT

• MPV = mRT

• Divide by V to get density (m/V)

• MP = RT

• Gas density expressed in g/L

5.4 Gas Density Problems

• Find the density of nitrous oxide at STP.

• First, find molecular mass of N2O

• MP = RT

• (44.0 g/mol)(1.00 atm) = (0.0821)(273 K)

• = 1.96 g/L

• Try this one….• A gas is found to have a density of 2.54 g/L at

15oC and 1.50 atm. Find its molecular mass.

5.5 Gas Stoichiometry

• Mass-Mass problems (review)

• Volume-Volume problems

• Volume is proportional to moles, so….

• Mol relationship from reaction can be used directly

• No conversions needed!

5.5 Volume-Volume Problem

• 2 H2 + O2 2 H2O

• If 3.25 L of oxygen react, how many liters of water vapor are formed?

• 3.25 L O2 2 L H2O------------- x ------------ = 6.50 L H2O 1 1 L O2

• Volume-Volume is just Avogadro’s Law!

5.5 Mass-Volume Problems

• Key step – get to moles!

• Mass conversion – use molecular mass

• Volume conversion – use gas equation

• Need to know temperature and pressure conditions

5.5 Mass-Volume Problems

• 25.0 g of sodium react with excess water at STP. How many liters of hydrogen are produced?

• 2 Na + 2 H2O 2 NaOH + H2

• 25.0 g Na 1 mol Na 1 mol H2

------------ x ----------- x ----------- = 0.543 mol 1 23.0 g Na 2 mol Na

• Now use ideal gas equation to get volume

5.5 Mass-Volume Problems

• PV = nRT

• (1.00 atm) V = (0.543 mol)(0.0821)(273 K)

• V = 12.2 L

• Try this one• Potassium chlorate decomposes into potassium

chloride and oxygen gas. How many grams of KClO3 are needed to produce 5.00 L of oxygen at 0.750 atm and 18oC?

• Hint: This one is backwards!

5.6 Dalton’s Law

• Partial pressure – the pressure of an individual gas in a mixture of gases

• Total pressure of a mixture equals the sum of the partial pressures of each gas

• Pt = P1 + P2 + P3 + ...

• Partial pressure is proportional to the mol fraction (X1 = n1 / nt)

• P1 = X1 Pt

5.6 Dalton’s Law

• 2.00 mol He is mixed with 1.00 mol Ar. Find the partial pressure of each at 1.75 atm pressure.

• XHe = 2.00 mol / 3.00 mol = 0.667

• XAr = 1.00 mol / 3.00 mol = 0.333

• PHe = (0.667) (1.75 atm) = 1.17 atm

• PAr = (0.333) (1.75 atm) = 0.583 atm

• Try this...• Find the partial pressure of oxygen in air if it makes up 21% of

the Earth’s atmosphere by volume. (Note: The volume gives you the mole ratio because of Avogadro’s law.)

5.7 Kinetic Molecular Theory

• Explains gas behavior in terms of molecular motion

• Energy• Work done by a moving object• Measured in SI unit Joule (J)

• Kinetic energy• Energy due to motion• K = ½ mv2

• KMT is a simplification of reality (ideal gas)

5.7 Kinetic Molecular Theory

• Gas molecules are separated by great distances

• They can be treated as “point masses”

• Gas molecules are in constant random motion

• Frequent elastic collisions (no energy lost)

• No attractive or repulsive forces

• Average K is proportional to Temperature

5.7 Distribution of Molecular Speeds

• Maxwell-Boltzmann Distribution• Molecular speeds distributed around average• Peak velocity depends on temperature and on

molec. mass

• Root Mean Square Speed

• _____vrms = √3RT/M

• Rate of diffusion

5.8 Deviations from Ideal Behavior

• We made approximations!• Point masses• No intermolecular forces

• These approximations become bad at...• High pressure• Low temperature• Liquefaction

• van der Waals Equation• (P + an2/V2) (V – nb) = nRT