Exercises †††††† answers to p3

 

1.†††††††† All gases consist of particles. What type of particles?

 

††††††††††† The particles could be atoms or molecules.

 

2.†††††††† A gasí volume is determined by its container, not by the size of individual molecules. Why?

 

††††††††††† The spaces between gas molecules are much bigger than the little molecules themselves. They are also moving from one point to another and they will always reach the edges of their container. So how far they reach is counted as the space they take up, but thereís a lot of emptiness in between.

 

3.†††††††† What are the differences between a liquid and a gas from a molecular point of view?

 

Gases

Liquids

  • Translate, rotate and vibrate
  • compressible
  • Molecules always fill a closed container
  • Ideal gas molecules do not attract each other; real gas attractions are still weaker than those between liquid molecules
  • Size of molecules do not affect total gas volume
  • Rotate and vibrate but do not translate
  • Not compressible
  • Molecules will not always fill a closed container
  • There are strong attractions between liquid molecules
  • Size of liquid molecules will influence volume

 

 

 

4.†††††††† How is the behaviour of suspended dust particles (Think of dislodged dust in a room as sunlight beams through) evidence for the idea that gases are in constant motion?

 

††††††††††† Even when there is no wind, air molecules move and bump into dust particles, preventing them from coming straight down.

 

5.†††††††† a.†††††††† Do all particles at the same temperature necessarily have the same speed? Explain. (Hint: if two class averages are equal, does everyone have the same mark?)

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They have the same average speed (assuming that they are all of the same mass) but not all will have the same individual speeds.

When comparing molecules of different masses, heavier molecules will have a lower average speed.

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††††††††††† b.†††††††† If a gas particle's kinetic energy increases, what happens to its speed?

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Molecular speed increases proportionally with increasing kinetic energy.

If the speed increases by afactor of x, then kinetic energy will increase by a factor of x2. If kinetic energy has increased by a factor of x then mass increased by a factor of the square root of x. This is because of the relationship E = 0.5mv2.

 

6.†††††††† If the temperature of a material is high, does it necessarily contain a lot of heat? Explain.

 

††††††††††† If there is very little material (low mass) at that temperature it could contain very little heat.

††††††††††† Conversely, the temperature can be moderate but if there is a lot of mass at that temperature, then the heat content is high.

 

7.†††††††† At the same temperature, which of these gasesí particles will move faster, on average? Kr, CO2, C2H6 or O2?

 

††††††††††† Get the molar mass of each one. C2H6 has the lowest molar mass (2*12 + 6*1 = 30 g/mole) so it will have the highest average speed.

 

8.†††††††† Consider two molecules, A and B, of different mass, mA and mB, each at the same temperature. Use Ek = 0.5mv2, where Ek = kinetic energy; m = mass; v = velocity of the particles to derive a formula revealing that small molecules move faster if they have as much energy as larger molecules.

 

Start with 0.5mAvA2 = 0.5mBvB2 and algebraically solve for the ratio VB/VA , where VB = velocity of the bigger molecule. Donít give up.

 

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9.†††††††† Which of these is more likely to be behave like an ideal gas: Ne or NH3?

 

††††††††††† Ne. In NH3,nitrogen is greedier than hydrogen, and nitrogen pulls on the three pairs of electrons at the base of the pyramid-shaped molecule creating a dipole(+ and - part of molecule).

 

  A note about head -on collisions between molecules. (Based on an in-class question: a student wondered

why the speed of two colliding molecules would not cancel.)

 

The molecules just move in the opposite direction with the same speed if the collision is perfectly elastic and if no chemical reaction takes place.

There are no forces cancelling out since the molecules do not decelerate(F= ma =m(0)= 0). What drives them apart?

It's just electron repulsion---no fender benders to reduce speed to zero!

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