Ammonia gas is heated from 325 K to 750
K. Using the ideal gas
heat capacity given by the Shomate Equation, calculate the ΔU and ΔH in J/mole. 


Read : 
The Shomate Equation will yield the most accurate estimate of the enthalpy change for an ideal gas. 










Diagram: 
A diagram is not needed
for this problem. 















Given: 
T_{1} 
325 
K 



T_{2} 
750 
K 










Find: 
DH_{12} = 
??? 
J/mole 



DU_{12} = 
??? 
J/mole 










Assumptions: 
1  Assume ammonia behaves as an ideal gas. 













Equations
/ Data / Solve: 








Let's begin by
collecting the data we will need from the NIST Webbook : 

Temp (K) 
298.  1400. 








A 
19.99563 








B 
49.77119 








C 
15.376 








D 
1.921168 








E 
0.189174 










Part a.) 
The enthalpy change
associated with a temperature change for an ideal gas can be determined from : 


















Eqn 1 











The Shomate
Equation for the ideal
gas heat capacity is : 




















Eqn 2 











where : 






Eqn 3 

and : 


















Combining Eqns 1, 2 and 3
and integrating yields : 

























Eqn 4 











Plug in values for the
temperatures and the constants to get : 
DH 
18358 
J/mol 











We can determine DU using
the definition of enthalpy : 


Eqn 7 











For ideal gases, Eqn 7 becomes : 


Eqn 8 











We can then solve Eqn 8 for DU : 



Eqn 9 











R 
8.314 
J/molK 



DU 
14824 
J/mol 










Verify: 
Without knowing the
pressure, it is not possible to verify this assumption. 












Answers : 
DH 
18400 
J/mol 



DU 
14800 
J/mol 









