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

Chemistry
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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

Thank you for the opportunity to help you with your question!

PCl5= 5.203

PCl3=4.27

Cl2=0.16

Please let me know if you need any clarification. I'm always happy to answer your questions.
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)0.3200.1820.182
    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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