Page 90 - Physical Chemistry

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Of course, the main hurdle is step 3. Because of the many equations in physical Section 2.12
chemistry, it might seem a complex task to find the right equation to use in a problem. Problem Solving
However, there are relatively few equations that are best committed to memory. These
are usually the most fundamental equations, and usually they have fairly simple forms.
For example, we have several equations for mechanically reversible P-V work in a
closed system: dw rev PdV gives the work in an infinitesimal reversible process;
2
w rev PdV gives the work in a finite reversible process; the work in a constant-
1
pressure process is P V; the work in an isothermal reversible process in a perfect gas
is w nRT ln (V /V ). The only one of these equations worth memorizing is dw rev
1
2
PdV, since the others can be quickly derived from it. Moreover, rederiving an
equation from a fundamental equation reminds you of the conditions under which
the equation is valid. Do not memorize unstarred equations. Readers who have invested
their time mainly in achieving an understanding of the ideas and equations of physical
chemistry will do better than those who have spent their time memorizing formulas.
Many of the errors students make in thermodynamics arise from using an equa-
tion where it does not apply. To help prevent this, many of the equations have the con-
ditions of validity stated next to them. Be sure the equations you are using are
applicable to the system and process involved. For example, students asked to calcu-
late q in a reversible isothermal expansion of a perfect gas sometimes write “dq
C dT and since dT 0, we have dq 0 and q 0.” This conclusion is erroneous.
P
Why? (See Prob. 2.63.)
If you are baffled by a problem, the following suggestions may help you. (a) Ask
yourself what given information you have not yet used, and see how this information
might help solve the problem. (b) Instead of working forward from the known quanti-
ties to the unknown, try working backward from the unknown to the known. To do this,
ask yourself what quantities you must know to find the unknown; then ask yourself
what you must know to find these quantities; etc. (c) Write down the definition of the
desired quantity. For example, if a density is wanted, write r m/V and ask yourself
how to find m and V. If an enthalpy change is wanted, write H U PV and
H U (PV) and see if you can find U and (PV). (d) In analyzing a ther-
modynamic process, ask yourself which state functions stay constant and which
change. Then ask what conclusions can be drawn from the fact that certain state func-
tions stay constant. For example, if V is constant in a process, then the P-V work must
be zero. (e) Stop working on the problem and go on to something else. The solution
method might occur to you when you are not consciously thinking about the problem.
A lot of mental activity occurs outside of our conscious awareness.
When dealing with abstract quantities, it often helps to take specific numerical
values. For example, suppose we want the relation between the rates of change
dn /dt and dn /dt for the chemical reaction A 2B → products, where n and n B
A
A
B
are the moles of A and B and t is time. Typically, students will say either that dn /dt
A
1
2 dn /dt or that dn /dt dn /dt. (Before reading further, which do you think is
B
A
B
2
right?) To help decide, suppose that in a tiny time interval dt 10 3 s, 0.001 mol
of A reacts, so that dn 0.001 mol. For the reaction A 2B → products, find
A
the corresponding value of dn and then find dn /dt and dn /dt and compare them.
B
B
A
In writing equations, a useful check is provided by the fact that each term in an
equation must have the same dimensions. Thus, an equation that contains the expression
2
2
U TV cannot be correct, because U has dimensions of energy mass length /time ,
3
whereas TV has dimensions of temperature volume temperature length . From
the definitions (1.25) and (1.29) of a derivative and a partial derivative, it follows that
( z/ x) has the same dimensions as z/x. The definitions (1.52) and (1.59) of indefinite
y
b
and definite integrals show that fdx and fdx have the same dimensions as fx.
a
When writing equations, do not mix finite and infinitesimal changes in the same
equation. Thus, an equation that contains the expression PdV V P must be wrong