Equilibrium. Limiting reagent Concentrations become constant Dynamic situation Reversible reactions.

Equilibrium

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Equilibrium•Limiting reagent•Concentrations become constant

•Dynamic situation•Reversible reactions


2NO2 N2O4

a b c d

time


2NO2 N2O4


Equilibrium Constant (K)

represents a ratio of the concentrations ofproducts to reactantsat equilibrium:aA +bB cC + dD



[C]c[D]d

[A]a[B]bK=

Equilibrium, or K,expression



• “[]” represents concentration in mol/L for (g) and (aq), only

• Each “[]” must be raised to the power of its coefficient



• K < 1 indicates little product formation

• K > 100 indicates great amount of product formation



• Write the K expression for the dimerization of nitrogen dioxide.



[N2O4] [NO2]2

What will the units ofK be in this example?

K= L/mol



• At 25°C, the equilibrium concentrations of NO2 and N2O4 are 0.0370M and 0.2315M. What is the value of K at this T?



[0.2315] [0.037]2

K=

K=0.2315mol/L 0.001369mol2/L2

K=169 L/mol


N2 + 3H2 2NH3

• Write the K expression for the synthesis of ammonia.



[NH3]2

[N2][H2]3

What will the units ofK be in this example?

K= L2/mol2



• At 300°C, the equilibrium concentrations are:

[N2]eq= 2.59M[H2]eq=2.77M[NH3]eq=1.82M

What is the value of K at thistemperature?



[1.82]2

[2.59][2.77]3K=

K=3.3124mol2/L2 55.05mol4/L4

K=0.0602 L2/mol2



• Small K (<1) means…• Big K (>100) means…• Different manner of

solving problems



• If a reaction is reversed, then the value of K for the reversed reaction is the reciprocal of K.



• So, if the dimerization of NO2 is reversed to be the decomposition of N2O4…



• K = (169 L/mol)-1 or

0.00592 mol/L



• At 25°C, the initial concentration of N2O4 is 0.750M. What are the eq. conc. of both species at this temperature?



• You will make an equilibrium chart to indicate the initial, change, and equilibrium concentrations.



[N2O4] [NO2]

Initial 0.750 0

Change

Eq.



[N2O4] [NO2]

Initial 0.750 0

Change -x +2x

Eq.



[N2O4] [NO2]

Initial 0.750 0

Change -x +2x

Eq. 0.75 - x 2x



[2x]2

[0.75 – x]0.00592=

[2x]2

[0.75]0.00592=

4.44 x 10-3=4x2



1.11 x 10-3=x2

0.0333=x



5% rule…is what youremoved less than 5%of the smaller initialvalue?



If so, then yourassumption that whatyou removed was so small it is negligibleis correct



5% rule test:1(0.0333)1x

0.75X 100 =

4.44% < 5%…assumption is good



[N2O4] [NO2]

Initial 0.750 0

Change -0.0333 +2(0.0333)

Eq. 0.7167 0.0666



[0.0666]2

[0.7167]K=

Check your answer:

K=0.00619



• At 25°C, the initial concentration of NO2 is 0.500M. What are the eq. conc. Of both species at this temperature? Remember that K = 169L/mol.



Since K is big, lots of productwill be made. Thus, almost allof the initial amount of reactantwill be used. You need to maketwo charts for a big Kproblem…Stoichiometry andEquilibrium



Stoichiometry Chart[NO2] [N2O4]

Initial 0.500 0

Change

Final




Initial 0.500 0

Change -0.5 +0.25

Final




Initial 0.500 0

Change -0.5 +0.25

Final 0 0.25



Equilibrium Chart[NO2] [N2O4]

Initial (=final)

0 0.25

Change

Eq.




Initial 0 0.25

Change +2x -x

Eq.




Initial 0 0.25

Change +2x -x

Eq. 2x 0.25-x



[0.25 - x] [2 x]2

169=

[0.25]4x2

169=

676x2=0.25



3.70 x 10-4= x2

0.0192= x


5% rule test:1(0.0192)1x

0.25X 100 =

7.69% > 5%…assumption is bad


Since the assumption that xwas so small it was negligibleis bad, then you must re-insert xand solve the equation with xpresent.


[0.25 - x] [2 x]2

169=

[0.25 - x] 4x2

169=

676x2=0.25 - x


676x2 + x – 0.25 = 0

ax2 + bx + c = 0

x = -b ± b2 – 4ac2a


You will get two values of x. Ifboth are positive, then you willalways select the smaller one. If one is positive and the othernegative, you will select thepositive one.


x = -1 ± 12 – 4(676)(-0.25)2(676)

x = -1 ± 1 – (-676)1352


x = -1 ± 6771352

x = -1 ± 26.021352


x = 25.02 1352

x = -27.02 1352

= -0.0200

= 0.0185

OR

*acceptthis one



Initial 0 0.25

Change +2(0.0185)

-0.0185

Eq. 0.037 0.2315


[0.2315] [0.037]2

K=

Check your answer:

K=169L/mol

Equilibrium. Limiting reagent Concentrations become constant Dynamic situation Reversible reactions.

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