According lo the first paragraph of the attached paper, in the petrochemical ind

Question

According lo the first paragraph of the attached paper, in the petrochemical industry, ethanol (C_2 H_5 OH) is produced from the catalytic hydration of ethylene (C_2 H_4), according to the reaction: C_2 H_4 + H_2 O C_2 H_5 OH Assume the solutions are ideal and at 298 K a) Estimate the concentration of C_2 H_4 of an initially 0.02 M of C_2 H_5 OH if it all dissociates. b) Find the degree of dissociation a of C_2 H_5 OH in an initially 0.02 M solution of C_2 H_5 OH at equilibrium, if the equilibrium constant K_a is 0.2. Do not assume alpha is small. c) Calculate Delta_r G for the reaction when (C_2 H_5 OH] = 0.003 M, and [C_2 H_4] - 0.2 M. Then point out what the corresponding direction of spontaneous reaction, (show work and justify your answer)

Explanation / Answer

a) Write down the reverse reaction:

C2H5OH <-----> C2H4 + H2O

As per the balanced stoichiometric equation the molar ration of C2H5OH and C2H4 is 1:1, i.e, 1 mole of C2H5OH dissociates completely to 1 mole of C2H4.

Hence, given complete dissociation, 0.02 M C2H5OH will give 0.02 M C2H4 (ans).

b)Set up the ICE chart as below:

C2H5OH <---------> C2H4 + H2O

initial                                        0.02                          0        0       

equilibrium                        0.02(1 – )                0.02 0.02

is the degree of dissociation.

Write out the expression for the equilibrium constant Ka.

Ka = [C2H4]/[C2H5OH] = (0.02)/0.02(1 – )

===> 0.2 = /(1 – )

===> 0.2= /(1 – )

===> 0.2 – 0.2 =

===> + 0.2 – 0.2 = 0

===> 1.2 = 0.2

The values of are given by

= 0.2/1.2 = 0.1667 0.17

The degree of dissociation is 0.17 (ans). Note that we have omitted the concentration of water here since the concentration of water is usually taken as unity.

c) Find Ka first.

Ka = [C2H4]/[C2H5OH] = (0.2 M)/(0.03 M) = 6.667 6.7

Employ the relation

rG = -RTln Ka = -(8.314 J/mol.K).(298 K).ln (6.7) = -4712.608 J/mol = -4.712 kJ/mol -4.7 kJ/mol.

Since rG is negative, the reaction will be spontaneous in the direction

C2H5OH <------> C2H4 + H2O

Therefore, more C2H4 and H2O are produced.

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