Thank you for the opportunity to help you with your question!
Step 1. Determine the concentrations immediately after the volume has been reduced, before the system responds to the disturbance.
|Rearranging the relationship M1V1 = M2V2 gives M2 = M1||V1|
|[PCl5> = 0.167 M||18.5 L||= 0.320 M|
|[PCl3> = 9.48E-2 M||18.5 L||= 0.182 M|
|[Cl2> = 9.48E-2 M||18.5 L||= 0.182 M|
Step 2. Predict the direction in which the reaction will proceed to reach equilibrium.
- PCl5(g) [img src="http://cxp.cengage.com/contentservice/assets/T=1432835347244/owms01h/mediaarchives/GenChem/Image/Doublearrow.GIF">PCl3(g) + Cl2(g) K = 5.37E-2
Le Chatelier's Principle predicts that reducing the volume of the system will cause the system to shift to the left, forming fewer moles of gas.
It is also possible to compare Q to K.
|K =||[PCl3>[Cl2]||= 5.37E-2|
|Q =||(0.182)(0.182)||= 0.103 > K|
This also predicts a shift towards reactants as the system comes to equilibrium.
Step 3. Set up an ICE table to define equilibrium concentrations in terms of x.
|PCl5 (g)||+||Cl2 (g)|
|Change (M)||+ x||- x||- x|
|Equilibrium (M)||(0.320 + x)||(0.182 - x)||(0.182- x)|
Step 4. Substitute the equilibrium concentrations into the equilibrium constant expression and solve for x.
|K =||[PCl3>[Cl2]||=||(0.182 - x)(0.182 -x )||= 5.37E-2|
|[PCl5]||(0.320 + x)|
Rearrange to get an expression of the form ax2 + bx + c = 0 and use the quadratic formula (see the information page) to solve for x. This gives:
x = 4.23E-2, 0.375
The second value leads to results that are not physically reasonable.
Step 5. Use x = 4.23E-2 to solve for the final equilibrium concentrations.
[PCl5] = 0.320 + 4.23E-2 = 0.363 M
[PCl3] = 0.182 - 4.23E-2 = 0.140 M
[Cl2] = 0.182 - 4.23E-2 = 0.140 M
Step 6. Check to see that the system is at equilibrium.
|Q =||[PCl3][Cl2]||=||(0.140)(0.140)||= 5.37E-2 = K|
Content will be erased after question is completed.