##### The equilibrium constant, K, for the following reaction is 5.37E-2 at 540 K. PCl

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The equilibrium constant, K, for the following reaction is 5.37E-2 at 540 K.

PCl5(g) PCl3(g) + Cl2(g)

An equilibrium mixture of the three gases in a 18.5 L container at 540 K contains0.167 M PCl5,   9.48E-2 M PCl3 and 9.48E-2 M Cl2. What will be the concentrations of the three gases once equilibrium has been reestablished, if the equilibrium mixture is compressed at constant temperature to a volume of 9.64 L?

 [PCl5] = M [PCl3] = M [Cl2] = M

It says you have to use the quadratic formula

Jun 8th, 2015

PCl5= 5.203

PCl3=4.27

Cl2=0.16

Jun 8th, 2015

wrong. look

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 V2
 [PCl5>   =  0.167 M 18.5 L =  0.320 M 9.64 L

 [PCl3>   =  9.48E-2 M 18.5 L =  0.182 M 9.64 L

 [Cl2>   =  9.48E-2 M 18.5 L =  0.182 M 9.64 L

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 [PCl5]

 Q = (0.182)(0.182) =  0.103 > K (0.320)

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.

PCl3 (g) PCl5 (g) + Cl2 (g) Initial (M) 0.320 0.182 0.182 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 [PCl5] (0.363)

Jun 8th, 2015

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Jun 8th, 2015
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Jun 8th, 2015
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