Page 56 - Basic physical chemistry for the atmospheric sciences

42 Basic physical chemistry

2 . 2 7 . Show that i f a chemical reaction occurs a t pressures near 1
atm and involves only solids and/or liquids
dH = d U
where dH and dU are the changes in enthalpy and internal
energy of the system during the chemical reaction. If, on the
other hand, gases are involved in the chemical reaction,
show that

dH = dU + R*Tdn + R*ndT
where dn is the change in the number of moles of gas during
the chemical reactions and dT the change in temperature.
a
2 . 2 8 . Show that for n ideal gas
dq ev dT d p
r
-- = c P - - R -
T T p
where the symbols have the same meanings as those defined
2
in Section . 3 .
2.29. Electrochemical cells (i. e . , "wet" batteries) are powered by
s
chemical reaction . Derive an expression for the number of
moles (n) of electrons that are transferred through a cell in
terms of the change in the Gibbs free energy (aG) of the
system due to the chemical reaction, the difference in volts
(il.E) across the terminals of the battery, and the charge in
coulombs (F) on one mole of electrons. (Hint: Use the result
from E x ercise 2. 1 8 . Also, recall that when a charge of 1
coulomb passes through a potential difference of 1 volt, 1 J
of work is involved. )

Notes
If the internal energy of a gas depend s on its temperature only (and not its volume),
it is said to obey Joule's law. One of the requirements of an ideal gas is that it obey
Joule's law.
2 Note that the standard temperature is defined as 0°C (see Section I . I), but standard
states are defined at a temperature of 25°C (or 298 K).
3 Although one atmosphere (I aim) is not the SI unit of pressure, it does not matter
here because the pressures in Eq. (2.39) occur as a ratio (dplp).