Comments re Chapter 1 Problems


Definitions. Levine's true/false problems encourage very careful thinking.Note that an intensive variable (like P or T) does not depend on the amount of the substance while an extensive variable (like V or n) does.The difference is important because adding or subtracting intensive variables often results in nonsense.The terms homogeneous and heterogeneous are defined beginningat the bottom of pg 5.A homogeneous system must be composed of one phase;a system containing pure liquid water and pure ice has only one substance but is not homogeneous.If there is more than one component (or, substance) present then the mixing must be at the molecular (or atomic or ionic) level for the system to be homogeneous.


Still more definitions.The reasoning necessary for part a, which is true, is very subtle.See pg. 14.To be really correct Levine should have specified the normal boiling point.Note that at the normal boiling point the pressure is 1 atm (for historical reasons) rather than 1 bar.
Note that Levine calls the equation PV=nRT the perfect gas law.Levine reserves the term ideal gas for monatomic gases like He, Ne, and Ar.All gases become more perfect as the pressure is reduced or the temperature raised.Remember that n = m/Mr, where m is the mass and Mr is the molar mass.


A basic exercise in doing conversions.It is useful to remember that there are 760 torr (or, mm Hg) in an atmosphere and 750 torr in a bar.There are 105 Pa (the SI unit for pressure) in 1 bar.(The SI unit for pressure is seldom used because it is inconveniently small).


Mole relationships in an equilibrium reaction. Dalton's Law of Partial Pressures is important.(Daltonís Law says that the total pressure, which is what would be measured with a barometer, is the sum of the pressures of the individual gases.The pressures of the individual gases would not change if all the other gases were removed from the system).Being able to do problems like this one will become important in Chpt 6.


An exercise in symbolic manipulation and in spotting a common error.


How good is a good vacuum?This problem can be solved by using the perfect gas law.




More about pressure. How does the density of the fluid in a manometer or barometer affect the height of the column? Does the cross-sectional area of the column have any effect?(See pp. 11-12 of the textbook).


An exercise in taking total differentials.(Please note that the answer in the Solutions Manual appears to be the answer to a different problem).
Remember that the total differential for a function z = f(x,y) is:
dz = (z/x)ydx + (z/y)xdy


More practice with partial derivatives.


Yet more practice with partial derivatives.Tthis problem is not short.It is important to avoid making mistakes while doing it.
In showing that (P/T)V = a/k it will be necessary to
(1)know that a = (1/V)(V/T)P and that k = -(1/V)(V/P)T, and
(2)use the cyclic rule.That rule says the (z/x)y(x/y)z(y/z)x = -1.This rule is easy to remember because each of the three variables must appear once in the numerator, once in the denominator, and once as the value held constant.Be careful about the negative sign.


Calculation of a , k , and their ratio from simple density measurements. The derivative is approximated by small differences, eg, (V/T)P @ (DV/ DT)P for small changes.
Look at the sizes of the calculated terms. Note also that most of the answers are given to two significant digits even though the densities have six significant digits. The values of DV are given by the difference between the inverses of the densities. These inverses differ in only the 5th and 6th digits.
[It is interesting that it makes sense to add and subtract the inverses of densities (e.g., mL/g) when it is nonsense to add and subtract the densities themselves (e.g., g/mL).The inverse of the density is effectively an extensive property if the masses for the two values being added or subtracted are the same.Densities themselves are intensive properties cannot be added or subtracted unless the two values correspond to the same volume, which is seldom the case.]

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