Review of Equilibrium Review of Equilibrium

ANDAND

Calculation ofCalculation ofEquilibrium Equilibrium

ConcentrationsConcentrations

a high school dance!!!a high school dance!!!

(sponsored by FBLA!)(sponsored by FBLA!)To make this far fetched….To make this far fetched….

1 male + 1 female --> 1 dancing 1 male + 1 female --> 1 dancing

couplecouple

To Review Equilibrium,Let’s Consider an analogy--

the forward reaction rate:the forward reaction rate:

1 male + 1 female --> 1 dancing 1 male + 1 female --> 1 dancing couplecouple

Rate Rate ff = k = kff [GUYS][girls] [GUYS][girls]At the start of the dance,At the start of the dance, the the

concentrations of [GUYS] and concentrations of [GUYS] and [girls] will be high-- so the forward [girls] will be high-- so the forward reaction predominates. reaction predominates.

As the number of dancing couples As the number of dancing couples increaseincrease what happens?what happens?

Did you say the forward reaction Did you say the forward reaction

decreases with time?decreases with time?

If a couple wishes, they may stop dancing, soIf a couple wishes, they may stop dancing, so dancing --> 1 male + 1 female dancing --> 1 male + 1 female

couple couple ( a reverse reaction)( a reverse reaction)

RateRateReverseReverse = K = KR R [Couples][Couples]

At the start of the danceAt the start of the dance

[Couples] is small, so reverse [Couples] is small, so reverse reaction is slow. But as time reaction is slow. But as time progressesprogresses what happens?what happens?

Did you say the reverse reaction Did you say the reverse reaction increases with time?increases with time?

There will always be some number of There will always be some number of couples starting to dance and others couples starting to dance and others

who decide to quit. At some pointwho decide to quit. At some point

# starting(# starting(forwardforward) = ) = #quitting(#quitting(reversereverse))

and we haveand we have

Equilibrium!Equilibrium!

The Equilibrium Constant The Equilibrium Constant

KKff[GUYS][girls]=[GUYS][girls]=

kkrr[couples][couples]

KKeqeq= = [couples][couples] [GUYS][girls][GUYS][girls]

The rates of the forward and The rates of the forward and reverse reactions depend on reverse reactions depend on

““experimental conditionsexperimental conditions””, such , such asas

Type of Music being playedType of Music being played Whose talking to who?Whose talking to who?

what else?what else?

BUT.. The ratio of BUT.. The ratio of [couples]/[GUYS][girls] = K[couples]/[GUYS][girls] = K

Today we have to tackle the Today we have to tackle the next problem?next problem?

If 150 GUYS and 200 girls go to a dance, If 150 GUYS and 200 girls go to a dance, what will be the [GUYS], [girls] and what will be the [GUYS], [girls] and

[couples][couples] AT EQUILIBRIUMAT EQUILIBRIUM

GIVEN:GIVEN:

KKEQEQ = 1.8 x 10 = 1.8 x 10-2-2

Or to use a chemical reaction...Or to use a chemical reaction...

Reaction:Reaction: H H22(g) + I(g) + I22(g) <---> 2HI(g)(g) <---> 2HI(g)

KKeqeq = = 7.1 x 107.1 x 102 2 at 25at 25o o CC

PROBLEM:PROBLEM:

Calculate the equilibrium Calculate the equilibrium

concentrations concentrations if if a 5 L a 5 L vessel initially contains vessel initially contains

15.7 g of H15.7 g of H22 and 294 g of I and 294 g of I22. .

The key is toThe key is to

determine the direction determine the direction of the reaction. of the reaction.

TO DO THIS WE TO DO THIS WE COMPARE COMPARE Q to KQ to K

WHAT IS Q? WHAT IS Q? YOU SAY…YOU SAY…

A Reaction Quotient(Q)A Reaction Quotient(Q)

can be utilized to predict the can be utilized to predict the direction in which the reaction direction in which the reaction will go to achieve equilibrium.will go to achieve equilibrium.

All reacting chemical systems can be characterized by their All reacting chemical systems can be characterized by their REACTION QUOTIENT, QREACTION QUOTIENT, Q..

Q = =0.350.25

= 1.40

Q = the reaction quotientQ = the reaction quotient

If Q = K, then system is at equilibrium.

To reach EQUILIBRIUM[Iso] must INCREASE and [n] must DECREASE.

Since K =2.5, system NOT AT EQUIL.

[iso][n]

Q has the same form as K, . . . but uses existing concentrations

n-Butane iso-Butane 0.25 0.35

In short--In short--

Q is calculated just like the Q is calculated just like the equilibrium constant equilibrium constant

EXCEPT EXCEPT

values substituted are EXISTING values substituted are EXISTING values NOT Equilibrium Values.values NOT Equilibrium Values.

Rule 1:Rule 1:

If If Q is EQUAL to KQ is EQUAL to K, , the system isthe system is

AT AT

EQUILIBRIUM!!EQUILIBRIUM!!

Rule 2Rule 2

If Q is Greater than K, mathematically, there is too

much product present.

The system will shift to the The system will shift to the LEFTLEFT

(or the reverse reaction will speed (or the reverse reaction will speed up)up) to reach equilibrium. to reach equilibrium.

Rule 3: Rule 3:

If If Q is less than KQ is less than K, there is , there is too much reactant present. too much reactant present.

The system will shift to the The system will shift to the RIGHTRIGHT

(or the forward reaction will speed up)(or the forward reaction will speed up) to reach equilibrium.to reach equilibrium.

Consider AGAIN: Consider AGAIN: H H22(g) + I(g) + I22(g) <---> 2HI(g)(g) <---> 2HI(g)

K= 7.1 x 10K= 7.1 x 102 2 at 25at 25o o CCPredict the direction that the system will Predict the direction that the system will

shift if: shift if: a) Q= 427a) Q= 427

b) [b) [HH22]] =0.081M=0.081M

[ I[ I22]=0.44M]=0.44M [HI]=0.58M[HI]=0.58M

KKeqeq = = 7.1 x 107.1 x 102 2 at 25at 25o o CC

PROBLEM:PROBLEM:

Calculate the equilibrium Calculate the equilibrium

concentrations concentrations if if a 5 L a 5 L vessel initially contains vessel initially contains

15.7 g of H15.7 g of H22 and 294 g of I and 294 g of I22. .

A SAMPLE PROBLEM- GIVEN H2(g) + I2 (g) <---> 2HI(g)

[ [ HH22]] =15.7g/2g/5L=1.56M=15.7g/2g/5L=1.56M

[ I[ I22]=294g/254g/5L= 0.232M]=294g/254g/5L= 0.232M

[HI]=0.00[HI]=0.00

Q = [HI]Q = [HI]2/ 2/ [ [ HH22]] [ I[ I22] ]

=0/(1.56)(0.232)= 0=0/(1.56)(0.232)= 0

Initially--

Q<K,Q<K, the reaction will go to the the reaction will go to the

RIGHTRIGHT

IFIFQQ

WASWAS > THAN K, > THAN K,

IT WOULD HAVE GONE TO THE IT WOULD HAVE GONE TO THE LEFT!!LEFT!!

NEXT WE --NEXT WE --

Set up a Table of Initial and Set up a Table of Initial and Final ConcentrationsFinal Concentrations

which looks like…which looks like…(we will do this for all (we will do this for all equilibrium problems!)equilibrium problems!)

HH22 I I22 HI HI

IINITIAL NITIAL 1.56M -0.23M 1.56M -0.23M 0 0

CCHANGE HANGE ? ? ? ? ? ?

AT AT

EEQUILIBRIUMQUILIBRIUM

THIS IS CALLED

AN

ICEBOX or RICEBOX!!!!!

REACTION

SINCE WE KNOWSINCE WE KNOW Q<K,Q<K,

the reaction will go to the the reaction will go to the RIGHT RIGHT

WE WE Do a Limiting reagent Do a Limiting reagent stoichiometry problemstoichiometry problem

HH22(g) + I(g) + I22(g) <---> 2HI(g)(g) <---> 2HI(g)1.56 mol ---> 3.12 mol1.56 mol ---> 3.12 mol 0.232 mol --> .464 mol0.232 mol --> .464 molTherefore- ITherefore- I2 2 is limiting is limiting

HH22 I I22 HI HI

INITIAL INITIAL 1.56M 0.23M 0 1.56M 0.23M 0

CHANGECHANGE -0.23M -0.23M -0.23M -0.23M 0.464M0.464M

EQUIL.EQUIL. 1.328M 0 0.464M 1.328M 0 0.464M

Now we fill in the ICEBOX

However, the reaction does However, the reaction does not go all the way to not go all the way to

completion.completion.

There will be some There will be some amount of Iamount of I22 left over. left over.

LetLet’’s call it X.s call it X.

Our chart then becomes:Our chart then becomes:

HH22 I I22 HI HIinitial 1.56M 0.23M 0initial 1.56M 0.23M 0

reacting -0.23M -0.23Mreacting -0.23M -0.23M

final 1.328M final 1.328M +x+x 0 0 +x+x 0.464M 0.464M -2x-2x

DO YOU SEE WHY

X IS ADDED TO REACTANT SIDE

AND

SUBTRACTED FROM PRODUCT?

Since the reaction is fairly Since the reaction is fairly complete, (K is large) we complete, (K is large) we

cancan Make an assumptionMake an assumption

(HEREAFTER DESIGNATED AS(HEREAFTER DESIGNATED AS22))

Assumption: x is small compared Assumption: x is small compared to 1.36 and 0.464to 1.36 and 0.464

Thus, here are our final values we will Thus, here are our final values we will substitute into the K expression.substitute into the K expression.

HH22 I I22 HI HI initial 1.56M -0.23M 0initial 1.56M -0.23M 0

reacting -0.23M -0.23Mreacting -0.23M -0.23M

final final 1.328M x 0.464M1.328M x 0.464M

K = [HI] K = [HI] 22// [ [ HH22]] [ I[ I22]]

710=(0.464)710=(0.464) 2 2/ (1.32)(X)/ (1.32)(X)

X = [IX = [I22]= 2.28 x 10 ]= 2.28 x 10 -4 -4 MM

Therefore, at equilibriumTherefore, at equilibriumOUR ANSWER BECOMESOUR ANSWER BECOMES

[HI] = 0.464 M[HI] = 0.464 M

[ [ HH22]] = 1.328 M = 1.328 M

[I[I22] = 2.28 x 10 ] = 2.28 x 10 -4 -4 M M

WERE WE CORRECT IN MAKING WERE WE CORRECT IN MAKING AN ASSUMPTION????AN ASSUMPTION????

We could test our assumptionWe could test our assumption 2 ways2 ways

1. 1. TEST 1!!TEST 1!! Substitute our final Substitute our final values and see if we get the values and see if we get the value of Kvalue of Keqeq

2. 2. TEST 2!!TEST 2!! Our assumption is Our assumption is justified justified if and only ifif and only if x is less x is less than 5% of a valuethan 5% of a value

Is 2.28 x 10Is 2.28 x 10 -4 -4 less than 5% of less than 5% of 1.32? 1.32? YesYes

Is 2.28 x 10Is 2.28 x 10 -4 -4 less than 5% of less than 5% of 0.464? 0.464? YesYes

SHOULD the answer to SHOULD the answer to

Our TEST questions be Our TEST questions be NONO, a quadratic , a quadratic

equation must be equation must be solved!!solved!!

The most IMPORTANT The most IMPORTANT questionquestion

in doing Equilibrium Problems isin doing Equilibrium Problems is

““What does the value of K tell What does the value of K tell me about the extent of the me about the extent of the

reaction?reaction?””if K is smallif K is small, the reaction will stay far , the reaction will stay far

to the to the leftleft

if K is largeif K is large, the reaction will stay far to , the reaction will stay far to the the rightright

Use the following steps to solve Use the following steps to solve equilibria problems. equilibria problems.

STRONGLY SUGGESTED:STRONGLY SUGGESTED:STRONGLY SUGGESTED:STRONGLY SUGGESTED:To REVIEW at homeTo REVIEW at home

GO to GO to http://www.wwnorton.com/college/chemistry/gilbert2/tutorials/http://www.wwnorton.com/college/chemistry/gilbert2/tutorials/

interface.asp?chapter=chapter_15&folder=solving_equilibriuminterface.asp?chapter=chapter_15&folder=solving_equilibrium!!

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SOLVING EQUILIBRIUM PROBLEMSSOLVING EQUILIBRIUM PROBLEMS

LetLet’’s utilize the rest of the s utilize the rest of the period to WORK some period to WORK some SAMPLE Equilibrium SAMPLE Equilibrium

Problems.Problems.Homework!!Homework!!

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Equilibrium ProblemsEquilibrium Problems