Example Problem with Complete Solution

3C-1 : Enthalpy Change of Ammonia Using the IG Heat Capacity 5 pts
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: T1 325 K T2 750 K
Find: DH1-2 = ??? J/mole DU1-2 = ??? 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/mol-K 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