Page 33 - Bruno Linder Elementary Physical Chemistry

August 25, 2010 9:36 9in x 6in b985-ch02 Elementary Physical Chemistry

18 Elementary Physical Chemistry

2.10. Heat Capacity

The heat capacity, as noted earlier, is the heat absorbed divided by the
change in temperature. C = q/∆T or, in differential form, C =dq/dT .
The heat capacity depends on the amount of material. Most often used
are the molar heat capacity (heat capacity per mole), C mol , and specific
heat capacity (heat capacity per gram), c g . In scientific work, the use of
molar heat capacity is standard.
In addition to characterizing the heat capacity by the amount of
material, it is also necessary to specify the condition under which the
change takes place. The heat capacities most often used are molar heat
capacity at constant volume, C V,m, and molar heat capacity at constant
pressure, C P,m . In the absence of work other than PV work, dU =dq−PdV
and dH =dU + PdV + V dP =dq + V dP. Obviously, at constant
volume, dq v /dT =(∂U/∂T) V = C V and at constant pressure, dq P /dT =
(∂H/∂T) P = C P .Itis pointed outthatdq P =dU + PdV [Eq. (2.16)].
For one mole of an ideal gas, PV = RT ,and so

C P,m − C V,m =dq P /dT − dq v /dT = P(∂V/∂T ) P = PR/P = R (2.19)

2.11. Enthalpy Changes in Chemical Reactions
What makes the enthalpy particularly useful is that the integral is
independent of the path of integration. For example, if one wants to know
the enthalpy change for
1
C+ O 2 → CO (2.20)
2
which is difficult to produce, one can obtain the result from the following
reactions, which are easy to measure
C+ O 2 → CO 2 ; ∆H = −94.1kcal mol −1 (2.21)
1 −1
CO 2 → CO + O 2 ;∆H =+67.6kcal mol (2.22)
2
Adding the two reactions gives Eq. (2.20) with ∆H = −26.5kcalmol −1 .

2.12. Standard Enthalpy
o
Standard enthalpy, denoted as H , is the enthalpy of a system at one bar
¯
◦
pressure and a specified temperature (usually 25 C). Standard enthalpy