Calculating the Equilibrium Constant

~ ICE tables ~

**Calculating the Equilibrium Constant**

aA+ bB --> cC +dD

<--

K << 1: reverse reaction is favored

K = 1: neither direction favored

K >> 1: forward reaction is favored

I

1.0M 0.0M

C

-0.3 +0.5

E

0.7

0.5

Kc = _[Z]_

[X]

Solution:

Initial:

The concentration that is given for the beginning reaction

C

hange:

The change that occurred in the concentrations to reach equilibrium

E

quilibrium:

The final concentrations after the reaction reached equilibrium

I-C-E

An Introduction

I-C-E

An example:

Solution:

Now determine the equilibrium constant:

The equilibrium constant (K)

What does K mean?

By: Anmol Arora

University of New Mexico

CAPS Supplemental Instruction Program

~ a way to quantify the concentrations of reactants and products at equilibrium

K = _[C]_[D]__

[A] [B]

c

d

a b

3X --> 5Z

<--

Find equilibrium constant, Kc, given initial 1.0 M X, 0.0 M Z, and equilibrium 0.5 M of Z.

3

X -->

5

Z

<--

0.5

mol Z *

3

mol X =

0.3mol

X being used

/

5

mol Z

-> Since

0.5

moles of Z are produced, we use this number with Stoichiometric Coefficients for the ratio from balanced equation to determine how much X is used to produce

0.5

moles of Z when the ratio is

3

X:

5

Z

-> To determine how much X is left over, we simply subtract 0.3 from initial 1.0 M to get 0.7 equilibrium concentration

What to do:

-Make an ICE table

-Determine what is given

-Use stoichiometry to determine how much of the reactant is being used or product is being produced

-Find equilibrium concentrations

-Determine Kc

5

3

-> Use equilibrium concentrations from the ICE table (last row) to determine Kc

Kc = _

[0.5]

_

[0.7]

5

3

==> _

0.03125

_ ==>

Kc = 0.09

0.343

-> Can be concluded that reverse reaction is favored (K<<1)

I-C-E

Practice yourself:

1) 3.7 M H2 (g) reacts with 2.90 M I2 (g) to produce some amount of product, 2HI (g). At equilibrium, 0.09 M of I2 (g) remain. Determine the equilibrium constant for this reaction.

2) 0.1 M I2 (g) and 0.1 M Cl2 (g) react together to produce some amount of product, 2 ICl (g). The equilibrium constant, Kc, for this reaction was determined to be 81.9. Find equilibrium concentrations of I2, Cl2, and ICl.

I-C-E

Another example:

Find equilibrium concentrations of reactants and product, given initial 1.0 M CO (g), 2.0 M NH3 (g) that react to form HCONH2 (g). The equilibrium constant for this reaction is 0.700.

CO (g) + NH3 (g) --> HCONH2 (g)

<--

CO (g) + NH3 (g) --> HCONH2 (g)

<--

I

1.0M 2.0M 0.0M

C

-x -x +x

E

(1-x) (2-x) x

Kc = _[HCONH2]_

[CO]*[NH3]

0.7 = ____[X]____ => 0.7(1-x)(2-x) = x

[1-x]*[2-x]

0.7(2-x-2x+x) = x => 1.4-2.1x+0.7x = x

2

2

->Use Quadratic to determine, x, the change

in: 0.7x-3.1x+1.4 = 0

x = 0.5

Therefore, equilibrium concentrations:

CO = 1-0.5= 0.5 M

NH3 = 2-2(0.5) = 1.0 M

HCONH2 = 0.5 M

-> manipulate equation to write in Quadratic form

-x

-x

2