450 
In order to decide whether we are dealing with the same phase of 
silver oxide at high and low temperatures, we will determine from a 
change of the decomposition pressure between 302° and 445° the heat 
of decomposition of the silver oxide occurring at these temperatures, and 
compare this value with the one obtained at ordinary temperatures by 
other methods. 
The heat of decomposition may be found from the change of pressure 
with the temperature, by the aid of the equation of van’t Hoff, which 
in this case has the form, 
dinp Q 
aT Re (1) 
where p is the decomposition pressure, T the absolute temperature, R 
the gas constant, and Q the heat absorbed when 2-gram molecules of 
silver oxide decompose according to the equation, 
2 Ag.O = 4 Ag-+0,. 
This equation of van’t Hoff is not strictly exact, but is derived with the 
aid of two assumptions from the equation of Clausius, 
: dp..: QQ". 
aT T (v¥—V) (2) 
where v is the molecular volume of oxygen at the temperature T and the 
pressure p, V is the total change of volume of the solid system—that is, 
it is the volume of 2-gram molecules of silver oxide less that of 4-gram 
molecules of silver. Q represents the heat absorbed during the decom- 
position and may be replaced by the expression U + p (v —V), where U 
is the increase in internal energy accompanying the decomposition, and 
p (v—V) is the work done. In the integration of the van’t Hoff equa- 
tion U is usually regarded as constant, but since we are dealing with a 
pretty wide range of temperature we shall obtain a more accurate result 
by regarding it as a linear function of the temperature according to the 
equation 
U=U,—CT (3) 
Where C is the diminution in the heat capacity of the system during the 
decomposition of two gram-molecules of silver oxide. We may therefore 
write in place of the equation 2, 
dp ms U,— CT + p (¥=V)} 
qn T (v—V). (4) 
In order to obtain equation 1 from equation 2 or 4, it is necessary 
to make two assumptions; first that the oxygen obeys the gas law, and 
second, that the volume V is negligible compared with v. Since the 
deviation of oxygen from the gas law is small at ordinary temperatures ‘ 
7 Amagat (1. ¢.). 
