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Key Thoughts to Date

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:

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Key Thoughts to Date

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  1. 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: • 1.125 0.889 0.0139 Which 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.

  2. 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

  3. 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

  4. 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?

  5. 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.

  6. 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.

  7. 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

  8. 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

  9. 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?

  10. 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!!

  11. It’s all about your state of mind • There are really two key thoughts that the student must be comfortable with: • I will never ask you a question that is not fully solvable based solely upon previously covered/discussed material • There is nothing I can ask that you can’t do.

  12. 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

  13. 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?

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