Use the ClausiusClapeyron equation to estimate the vapor
pressure, in kPa, of ammonia at 25^{o}C. The normal
boiling point of ammonia is 33.34^{o}C and the latent heat of vaporization at this temperature is 1370 kJ/kg. 

ammonia 
SI with C 






151.4713 

Read : 
The keys here are to
know that the normal boiling point is the boiling point at 1atm
and that the ClausiusClapeyron Equation provides a relationship between the rate at which vapor pressure changes
and the latent heat of vaporization. Knowing that P*(33.34^{o}C) = 101.325 kPa and the latent heat of vaporization at this
temperature allows us to evaluate both the slope and the intercept in the ClausiusClapeyron Equation and then use the result to estimate the vapor pressure at any other temperature. We should keep in mind
that this estimate is only reasonably accurate at temperatures close to the one known value, 33.34^{o}C in this case. 














101.2561 
151.4713 
Diagram: 
A diagram is not
needed in the solution of this problem. 

1399.072 












29.53419 

Given: 
T_{1} 
33.34 
^{o}C 



T_{2} 
25 
^{o}C 

1369.538 



239.81 
K 




248.15 
K 

23.32359 


P_{1}* 
101.325 
kPa 



DH_{vap} 
1370 
kJ/kg 

















MW 
17.03 
g/mole 



R 
8.314 
J/moleK 
















Find: 
P_{2}* 
??? 
kPa 






















Assumptions: 
1  ClausiusClapeyron applies: 






 The saturated vapor is an ideal gas 






 The molar volume of the saturated vapor is much, much greater than the molar volume of the saturated liquid. 






 The latent heat of vaporization is constant over the temperature range
of interest. 
















Equations
/ Data / Solve: 
























We can estimate the latent heat of vaporization using
the Clausius Clapeyron Equation. 























Eqn 1 

















If we plot Ln P* vs. 1/T(K), the slope is 
DH_{vap}/R. Don't forget to use T in Kelvins in Eqn 1. 

















So, the next thing we
need to do is use the given value of the latent heat to estimate this slope. 


















Eqn 2 


DH_{vap} 
23331 
J/mole 










Slope 
2806.242 
K 

















Next, we can use the
one known value of the vapor pressure (at 33.34^{o}C) to evaluate the constant (C) in the ClausiusClapeyron
Equation. 


















Eqn 3 

C 
16.320 


















Evaluating C in this manner has a catch. This value of C only
applies as long as the same units of pressure are used in Eqn 1. Since we used P_{1}* in kPa, we must always use P in kPa
whenever we use this value of C. 

















Now, we can use the
values of the slope and intercept that we have determined
to subsititute back into Eqn 1 to estimate the vapor pressure of ammonia at a temperature other than 33.34^{o}C, in this case 25^{o}C. 























P_{2}* 
150.1 
kPa 
















Verify: 
Only the ideal gas assumption can be
verified using the data in the problem statement. 

















Ideal
Gas EOS : 





Eqn 4 

















Solve for molar volume : 




Eqn 5 

















Plug in values based upon
the results we obtained above : 





















V_{1} 
1.97E02 
m^{3}/mol 



V_{2} 
1.37E02 
m^{3}/mol 





19.7 
L/mol 




13.7 
L/mol 

















Because the molar volume of the saturated vapor at both (33.34^{o}C, 101.325
kPa) and (25^{o}C, 150.1 kPa) is less than 20 L/mole, it is not accurate to treat the saturated
vapors as ideal gases. This is a more serious problem at 25°C and 150.1 kPa. 

















The 2nd and 3rd
assumptions required to use the ClausiusClapeyron
Equation cannot be verified with the information
provided in the problem statement.
However, based on data available in the Ammonia
Tables, these two assumption are valid under the
conditions in this problem. 

















The Ammonia
Tables also tell us that: 


P_{2}* 
151.5 
kPa 

















Our answer based on
the ClausiusClapeyron Equation
is accurate to within about 1%. This is surprisingly
good in light of the fact that the ideal gas
assumption for the
saturated vapor is not valid! 
















Answers: 
P_{2}* 
150.1 
kPa 





















