Introduction to the course Thoughts about problems about thoughts ◄ Abstract
Key Thoughts to Date
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Transcript of Key Thoughts to Date
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Key Thoughts to Date• Summary-the four equations-3 variable systems• a/b=c• b/a=c• 1/(a*b)=c• a*b=c• Applications:
It is known that a & c are directly related and that a & b are inversely related. If a=9 and b=8, what is c?
There are four mathematically possible results:72 1.125 0.889 0.0139Which is it?a=c (from a & c being direct)a*b=c (from a & b being inverse which also requires that b & c
be direct)Thus, the answer is 72.
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• Binary Changes of State• Direct: • state1= a1/b1
– Assume you are going to be solving for a2 => a1/b1 = a2 (this is not strictly true)
– Since the relationship between a and b is direct, b2 must be written on the same level as a2, yielding: (a1/b1)*b2 = a2
• In general one can describe the solution of all changes of state involving directly related variables as fitting the following general algorithm:
• (Fully defined state written as a ratio with the term identical to the missing term written as the numerator)*given variable=missing value
• Inverse• state1= a1*b1
• a1*b1=b2
• (a1*b1)/a2=b2
• In general:
(fully defined state written as a product)/given variable=missing variable
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What about dimensions?
• The text in sections 1.5 and 1.9 discusses SI units, both fundamental and derived. In gen chem, we are most interested in mass, volume, moles and T, as well as a number of derived units.
• By next Tues (10/7),The student needs to be comfortable and be able to readily (as in instantaneously) convert between the following:– mass: mg,g,kg – vol: L,mL,cm3
– If practice is needed, there are web pages available.
• Other dimensions will be introduced as appropriate
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Mass, volume and density-a study in intrinsic and extrinsic properties
• Intrinsic-not dependent on quantity, source or method of preparation• Extrinsic-not intrinsic• Key thought-most of what we measure/observe is sample dependent-or
at least we don’t know that it isn’t.• The value of intrinsic properties lies in their transferability to any
sample. Pick up any reference text and it contains only intrinsic information
• The key process then is the conversion of measured properties(extrinsic most often) into intrinsic ones
• An obvious example of this transition is the relationship between mass, volume and density.
– No one is likely to argue against mass and volume being sample dependent– density is then defined as mass per unit volume => d=m/V where m is
usually in grams and V can be cm3,mL or L.– density is said to be intrinsic-why? What does that say about the rules of
the universe?
• Is “mass per unit volume” a good definition of density?
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Looking at d=m/V• What does d=m/V say about the relationships between the
variable pairs? Is it what you would logically expect?
• d=1.00g/mL is roughly the density of water at RT. It’s often useful to frame discussions with that as a reference
• if d>1.00 what quick relationship can you see between m and V-assuming that all of the dimensions are consistent?
• What about d<1.00?
• What is really significant about d=m/V is that it is the classic three variable equation. Master this and you’ll be able to handle the majority of “problems” you’ll encounter in the course.
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Density Problems• Since this is a three variable system, it clearly provides
three basic questions-given any two what’s the third. Hardly rocket science.
• Working problems in lecture is one way to fill 100mins, but it has several shortcomings. In particular, problem solving is not a spectator sport. What is useful, is the discussion of common pitfalls or error traps which the instructor will lay for you.
• The student should realize that a major role of the instructor in a testing environment is to cause the student to make a mistake. It’s a game. The instructor is trying to make you err and you are trying to avoid those errors. To be frank, the instructor likes to lose.
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Avoiding the Pitfalls• What is the volume in liters of a sample of a liquid with a density of 0.732g/mL
and a mass of 0.670kg?• Line up your ducks
– m=0.670kg=670.g– V=? (in liters)– d=0.732g/ml
• Recall that when d<1.00 V>m so V>670. If you are going to apply this, be certain that the dimension of the given variable matches that of the density.
• now you can play the algebra game d=m/V to V=m/d or you can simply realize that the only combination of 670 and 0.732 that yields an answer greater than 670 is 670/0.732
• either yields V=915.300546448087431693398907103825• hopefully you’ll round this to the allowed three sig figs =915mL• note:students commonly write out the correct calculation and then perform it
incorrectly. The most common errors being switching multiplication and division or inverting a ratio. More than one student would multiply instead of divide the above and get 490. That answer would be accepted and put in one of those “magic boxes”.
• you see your initial note that the answer is to be in liters and convert it to 0.915L
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A few density facts• water(l)=1.00g/mL
• gas densities tend to be about 1/1000 or less than that of liquids and are often presented as g/L.
• metals tend to be in the range of
10-20g/cm3
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Questions without solutions• What is the volume of 345g of a material
with d=1.17g/cm3
• A liquid has a volume of .465L and a mass of .756kg. What is its density?
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Question of the Day
Why are you having us calculate densities in dimensions like kg/mL? Seems like a total waste of time. I’ve got lots of things going on besides this class, you know!!
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It’s all about your state of mind
• There are really two key thoughts that the student must be comfortable with:
1. I will never ask you a question that is not fully solvable based solely upon previously covered/discussed material
2. There is nothing I can ask that you can’t do.
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Tuesday’s Quiz- A Change of State?• How many grams of hydrogen are present in a sample of
ammonium carbonate that contains 0.13moles of oxygen?• yes=42 No=107 Who cares=98• (NH4)2CO3
• State 1 is fully defined by the formula which contains 8.00g of H and 3 moles of O
• State 2 contains 0.13moles of O• mass of H and moles of O are directly related• You should be able to see readily that the answer must be less
than 0.80g of H but more than 0.08g. Why?• setting it up as a direct change of state (a1/b1)*b2=a2
• (8.00g of H/3moles of O)*0.13moles=0.347g of H• what are these #s : 0.0487 185• 3/8*.13 8/.13*3 • notice that both fail our test
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Getting ahead of the game-n and T
• For purposes of this exercise, ignore any issues involving temperature of which you may be aware.
• A gas system is kept at constant P and V• Initially, T=400K and n=0.45moles.• If constant P and V are maintained-what will T be
when n=0.057 moles?