Example Problem with Complete Solution

3C-1 : Enthalpy Change of Ammonia Using the IG Heat Capacity 5 pts
Determine the enthalpy change and internal energy change of ammonia in J/mole, as it is heated from 350 K to 600 K, using the ideal gas heat capacity given by the Shomate Equation.
               
Read : The Shomate Equation will yield the most accurate estimate of the enthalpy change for an ideal gas.
Given : T1 350 K T2 600 K
Find : ΔH1-2 = ??? J/mole
Assumptions:
a.) Nitrogen behaves as an ideal gas.
b.) Nitrogen behaves as an ideal gas with a linear relationship between Cp and T.
This is equivalent to using a constant value of Cp that is equal to the average of Cp(T1) and Cp(T2).
c.) Nitrogen behaves as an ideal gas with a constant heat capacity.
Solution : 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 :
Equation 1 Eqn 1
The Shomate Equation for the ideal gas heat capacity is :
Equation 2 Eqn 2
where : Equation 3 Eqn 3
and : Equation 4
Combining Eqns 1, 2 and 3 and integrating yields :
Equation 5
Eqn 4
Plug in values for the temperatures
and the constants to get :
ΔH 10302 J/mol
Equation 6 Eqn 5
Equation 7 Eqn 6
Equation 8 Eqn 7
R 8.314 J/mole-K ΔU 8224 J/mol