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

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

PCl5= 5.203



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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
    [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="">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.

    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

Jun 8th, 2015

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