Aceticacid can be manufactured by combining methanol with...

Aceticacid can be manufactured by combining methanol with carbon monoxide, an example of a carbonylation reaction: $$ \mathrm{CH}_{3} \mathrm{OH}(l)+\mathrm{CO}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{COOH}(l) $$ (a) Calculate the equilibrium constant for the reaction at $25^{\circ} \mathrm{C}$. (b) Industrially, this reaction is run at temperatures above $25^{\circ} \mathrm{C}$. Will an increase in temperature produce an increase or decrease in the mole fraction of acetic acid at equilibrium? Why are elevated temperatures used? (c) At what temperature will this reaction have an equilibrium constant equal to $1 ?$ (You may assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are temperature independent, and you may ignore any phase changes that might occur.)

Aceticacid can be manufactured by combining methanol with carbon monoxide, an example of a carbonylation reaction:
$$
\mathrm{CH}_{3} \mathrm{OH}(l)+\mathrm{CO}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{COOH}(l)
$$
(a) Calculate the equilibrium constant for the reaction at
$25^{\circ} \mathrm{C}$. (b) Industrially, this reaction is run at temperatures above $25^{\circ} \mathrm{C}$. Will an increase in temperature produce an increase or decrease in the mole fraction of acetic acid at equilibrium? Why are elevated temperatures used? (c) At what temperature will this reaction have an equilibrium constant equal to $1 ?$ (You may assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are temperature independent, and you may ignore any phase changes that might occur.)

Key Concepts

Equilibrium Constant

The equilibrium constant is a dimensionless number that expresses the ratio of product activities to reactant activities at equilibrium. It is closely tied to the thermodynamic state of the system and can be calculated using the Gibbs free energy change of the reaction, reflecting how far a reaction proceeds under a set of conditions.

Gibbs Free Energy and Its Relationship to Equilibrium

Gibbs free energy (?G) is a thermodynamic quantity that predicts the spontaneity of a reaction. The relationship ?G = -RT ln K connects ?G with the equilibrium constant (K), allowing one to determine how changes in free energy influence the equilibrium position of a reaction.

Van't Hoff Equation

The van't Hoff equation describes how the equilibrium constant changes with temperature by relating it to the enthalpy change (?H) of the reaction. This equation is essential for understanding whether an increase in temperature will favor the formation of products or reactants and for calculating the temperature at which the equilibrium constant reaches a specific value.

Le Chatelier's Principle

Le Chatelier's Principle explains how a system at equilibrium responds to disturbances such as changes in temperature or pressure. It predicts that a system will adjust its equilibrium position to counteract any imposed change, which is pivotal in understanding how temperature variations affect the mole fractions of reactants and products.

Reaction Kinetics and Industrial Process Considerations

While thermodynamics determines the equilibrium position, reaction kinetics deals with the rate at which equilibrium is reached. In industrial processes, conditions like elevated temperatures are often used even if they might slightly compromise the equilibrium position because they significantly enhance the reaction rate, ensuring that production is economically viable.

Transcript

00:03 We are asked to consider the manufacture of acetic acid that is accomplished by combining methanol with carbon monoxide.

00:11 Our first order of business is to calculate the equilibrium constant for this reaction at 25 degrees celsius.

00:30 Okay, so in order to do this we are going to have to figure out our delta g, whatever here, hang on one second.

00:48 So let's go ahead and figure out our delta g.

01:00 We'll be equal to the sum of our delta g of formation of our products minus the sum of our delta g of formation of our reactants.

01:32 We can look these up and we will get for our product we will have, we've got no coefficients here, so i'm going to take 1 times negative 392 .4, just look this number up, and we will minus 1 times negative 166 .23 plus 1 times negative 137 .2.

02:03 Whoops, i'm going to have to erase a little bit here because i forgot that i was using a different platform for recording this and i don't have quite as much room on my margins.

02:18 And these are all moles times kilojoules per mole and this will equal, when i'm done, negative 89 kilojoules.

02:48 So now we can find our equilibrium constant by taking the ln of our equilibrium constant will be 89, negative 89 kilojoules divided by 8 .314.

03:07 And we'll take that times 10 to the minus third kilojoules per k times our t which will be 298 kelvin and that'll give us the ln will be 35 .9.

03:32 So k will be 10 to the 35, whoops, e to the 35 .9.

03:39 That was almost tragic there.

03:42 And my k will be equal to 3 .9 times 10 to the 15th.

03:51 There's my first answer.

03:57 Now we're going to go to the next page and do part b.

03:59 Part b will ask us, um, will, uh, let's run above.

04:12 Industrial b, its temps are greater than 225 degrees.

04:31 Will an increase in temp produce an increase or decrease in the mole fraction of acetic acid at equilibrium? why are elevated temperatures used? okay, let's get ready for this part.

05:44 So the reaction is exothermic.

05:49 Let's do our delta h calculation.

05:54 This is going to be the same thing as our last calculation, except we're going to use, um, our delta hs.

06:03 These are just values you can look up in your data tables.

06:36 So my heat of reaction is negative 137 .9.

06:43 This is an exothermic reaction...

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