Chapter 6

Question 1

miscible

Answer 1

• capable of being mixed in any proportion without reacting chemically
• gases are miscible
• many liquids are immiscible, such as oil and water

Question 2

How do gases differ from liquids and solids?

Answer 2

1. Unlike with liquids and solids, the volume occupied by a gas changes significantly with pressure
   
   1. altitude impacts volume
2. volume of a gas changes with temp
3. gases are miscible
4. gases are typically much less dense than liquids or solids.
   
   1. we can tell b/c gas densities are g/L while liquids are g/mL

*these 4 ideas are consistent with the fact that particles of a gas (molecules OR atoms) are farther apart than those of liquids and solids.

Question 3

atmospheric pressure(P_atm)

Answer 3

• the force exerted by the gases surrounding Earth on Earth’s surface and on all surfaces of all objects
  
  • Pressure = Force/Surface Area

Question 4

devices used for measuring gas

Answer 4

• barometer: measures atmospheric pressure
  
  • 1 meter tube is inverted and open end is immersed in mercury
  • gravity pulls mercury down, atmospheric pressure pushes mercury up into tube due to force of collision of N2 and O2 molecules with mercury
  • the net effect of these opposing forces causes the heigh of the mercury in the tube which is the measurement
• manometer: measures the pressure exerted by a gas

Question 5

Boyle’s Law

Answer 5

• constant T and quantity of gas
  
  • P = 1/V
• As the volume of a constant amount of gas(at constant temp) increases, the pressure of the gas decreases b/c of fewer collisions
• As the volume of the gas decreases, its pressure increases because of more collisions
• PV = constant
• P₁V₂=P₂V₂

Question 6

Charles’s Law

Answer 6

• the principle that the volume of a fixed quantity of gas at constant pressure is directly proportional to its absolute temperature
  
  • temperature in Kelvin
    
    • Kelvin are always positive!
  • V/T = constant
  • V₁ / T₁=V₂ / T₂

Question 7

Avogadro’s Law

Answer 7

• amount of gas is not constant
  
  • obviously volume depends of amt of gas
• constant P and T
  
  • V/n = constant
    
    • when P and T are constant

Question 8

ideal gases + ideal gas law

Answer 8

• atoms or molecules are assumed not to interact with one another
  
  • instead they move independently with speeds that are related to their masses and the temp of gas
• most gases exhibit ideal behavior at the P and T typically encountered in the atmosphere
  
  • STP: P=1atm T=0˚C
  • n=m/mw
• PV=nRT
  
  • R=0.08206 Latm/molK
• combined gas law
  
  • P₁V₁/T₁ = P₂V₂/T₂

Question 9

partial pressure

Answer 9

• the contribution to the total pressure made by one gas in a mixture of gases

Question 10

mole fraction (X_x)

Answer 10

• the ratio of the number of moles of a componrnt in a mixture to the total number of moles in the mixture
  
  • 1) unlike molarity, mole fractions have no units
  • 2) unlike molarity, mole fractions are based on numbers of moles and can be used for any mixture or solution
  • 3) the mole fractions of all the componenets in a mixture must sum to 1
• relationship btwn partial pressure and total pressure
  
  • P_x=X_xP_total

Question 11

kinetic molecular theory

Answer 11

• a model that describes the bahvior of ideal gases

Assumptions

1. gas molecules have tiny volumes compared to the total volume they occupy so their individual volumes are negligible
   
   1. they are point masses(have essentially no volume)
   2. separated by large distances(mostly empty spaces)
2. gas molcules move constantly and randomly
3. the motion of these molcules is associated with an average KE that is proportional to the absolute temp of the gas
   
   1. all populations of gas molecules have same avg KE
   2. KE is determined by temp
4. gas molecules continuously collide elastically (no net energy transfer to the walls)
   
   1. avg KE is NOT affected by these collisions and is constant as long as temp is unchanged
5. each gas molecule acts independently of all other molecules. we assume there are no forces of attraction or repulsion btwn the molecules

Question 12

molecular speeds and KE

Answer 12

• KE=1/2(mu²)
  
  • m is mass
  • u is speed
• collisions btwn gas molecules cause molecules in a sample to have a range of speeds
• root-mean-square speed(u_rms): speed of a molecule possessing the avg KE.
• At a given temp, the pop. of molecules in a gas has the same avg. KE as every other pop. of gas molecules at the same temp this KE_avg is
  
  • KE_avg=1/2(m)(u_rms)²
• u_rms=√(3RT/M)
  
  • M=molar mass
  • R=8.314

Question 13

effusion vs. diffusion

Answer 13

• effusion: the process by which a gas escapes from its contained through a tiny hole into a region of lower pressure
  
  • Graham’s law of effusion: rate of effusion of a gas is inversely proportional to the √molar mass
    
    • r_x/ry = √M_y/M_x
  • gas with greater rms speed leaks at a higher rate
  • the escape of gas molecules requires encountering the microscopic holes in the balloon. The faster a molecule moves, the more likely it is to find one of these holes.
• diffusion: the spread of one substance through another

Question 14

Why the ideal gas law isn’t good enough

Answer 14

1. The ideal gas law considers gas molecules to have no volume at all, however, at high pressures, more molecules are squeezed into a given volume and it becomes significant
2. KMT assumes molecules don’t interact, but real molecules do attract one another, so ideal gas law only works when molecules are really far apart
   
   1. as pressure increases gas molecules are pushed together and IMF become significant
   2. likewise, lowering temp slows molecule movement resulting in more attractions and more deviations from ideal behavior

Question 15

van der waals equation

Answer 15

Accounts for the fact that:

• the free volume of a real gas is less than the total volume b/c its molecules occupy significant space
• the observed pressure is less than the pressure of an ideal gas b/c of intermolecular attractions

a and b are constants!

• a term: related to attractive/repulsive forces
• b term: takes into account volume of gas particle

Question 16

Dalton’s Law

Answer 16

• Since gas molecules are far apart we assume they behave independently
• Mixture of gases: each individual gas exerts its own pressure(partial pressure)
• Dalton’s Law: P_total = P₁+P₂+P₃+……