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1 mol of ammonia gas and 3 mol of methane are mixed in a 3 L container at 20oC. What is the entropy of mixing (in J/K.mol)?

1 mol of ammonia gas and 3 mol of methane are mixed in a 3 L container at 20oC. What is the entropy of mixing (in J/K.mol)?

Chemistry: Matter and Change
Chemistry: Matter and Change
1st Edition
ISBN:9780078746376
Author:Dinah Zike, Laurel Dingrando, Nicholas Hainen, Cheryl Wistrom
Publisher:Dinah Zike, Laurel Dingrando, Nicholas Hainen, Cheryl Wistrom
Chapter15: Energy And Chemical Change
Section: Chapter Questions
Problem 80A
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1 mol of ammonia gas and 3 mol of methane are mixed in a 3 L container at 20oC. What is the entropy of mixing (in J/K.mol)?

Expert Solution
Step 1 entropy

The randomness of of a system is known as entropy. 

Step 2 calculation

When two system are added then entropy of mixing is defined as,

delta S = -R(XalnXa  + XblnXb )

where , Xa = mole fraction of gas a and R = gas constant 

Xa = Na/ (Na + Nb)

Similarly for gas b 

Mole of methane(a) = 1mol, mole of methane (b) = 3mole

Mole fraction of (a) = 1/4 

Mole fraction of (b) = 3/4

 

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