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. |
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Read : |
The Shomate Equation will yield the most accurate estimate of the enthalpy change for an ideal gas. |
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Diagram: |
A diagram is not needed
for this problem. |
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Given: |
T1 |
325 |
K |
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T2 |
750 |
K |
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Find: |
DH1-2 = |
??? |
J/mole |
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DU1-2 = |
??? |
J/mole |
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Assumptions: |
1 - Assume ammonia behaves as an ideal gas. |
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Equations
/ Data / Solve: |
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Let's begin by
collecting the data we will need from the NIST Webbook : |
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Temp (K) |
298. - 1400. |
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A |
19.99563 |
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B |
49.77119 |
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C |
-15.376 |
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D |
1.921168 |
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E |
0.189174 |
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Part a.) |
The enthalpy change
associated with a temperature change for an ideal gas can be determined from : |
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Eqn 1 |
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The Shomate
Equation for the ideal
gas heat capacity is : |
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Eqn 2 |
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where : |
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Eqn 3 |
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and : |
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Combining Eqns 1, 2 and 3
and integrating yields : |
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Eqn 4 |
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Plug in values for the
temperatures and the constants to get : |
DH |
18358 |
J/mol |
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We can determine DU using
the definition of enthalpy : |
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Eqn 7 |
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For ideal gases, Eqn 7 becomes : |
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Eqn 8 |
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We can then solve Eqn 8 for DU : |
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Eqn 9 |
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R |
8.314 |
J/mol-K |
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DU |
14824 |
J/mol |
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Verify: |
Without knowing the
pressure, it is not possible to verify this assumption. |
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Answers : |
DH |
18400 |
J/mol |
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DU |
14800 |
J/mol |
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