TBR GC Equilibrium Example 3.9 page 174 => inferring shift magnitude

[saoj]

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He says, like 23423 + 234234 / 23 = 1111 was as obvious as 2 + 2 = 4

(I know, I know, I am the dumb one, not the book...)

"In this case, Keq is less than 1.0, and the reaction starts with all products. The value of x is going to be significant (more than half shifts over)."

Great, but how did this conclusion pop in your brain? 😕

Here is the question: http://notes.soliveirajr.com/docs/TBR3.9.png

 

[ljc]

He says, like 23423 + 234234 / 23 = 1111 was as obvious as 2 + 2 = 4

(I know, I know, I am the dumb one, not the book...)

"In this case, Keq is less than 1.0, and the reaction starts with all products. The value of x is going to be significant (more than half shifts over)."

Great, but how did this conclusion pop in your brain? 😕

Here is the question: http://notes.soliveirajr.com/docs/TBR3.9.png

A Keq of 1 means at equilibrium, there will be as many products as reactants. A Keq of greater than 1 means more products than reactants, and less than 1 means less products than reactants.

All he's saying is that since Keq is small, there will be a lot more reactants than products.
Once you realize this, it is simply a matter of plugging in some numbers:
At most, since you started with "X" amount of products, you can get "2X" reactants (this is seen by the stoichiometric coefficients, which they provide). Since X is 0.2, you could get 0.4 reactants if ALL of the products converted over. This won't be the case, since there has to be equilibrium. This means option D is out.
Since we just said we'll have more reactants than products at equilibrium, you can eliminate A, because 0.025 is way too small for this.
Now for B: you know you convert 2 reactants from 1 product. So to get 0.2 NO2, you'd use up 0.1 N2O4. This would leave you with 0.1 N2O4, giving you a 1:1 ratio of reactants to products. We just said at equilibrium you need more reactants than products! So this is out too.
C is the best answer.

 

[saoj]

Since we just said we'll have more reactants than products at equilibrium, you can eliminate A, because 0.025 is way too small for this.

You can say that 0.0125 from right moved to the left to form 0.025, right? So you would end up with more products than reactants => 0.025 on left and (0.2 - 0.0125) on right. Not possible. GOT IT!

Now for B?

To get 0.2 on the left side, I need to move 0.1 from the right side. That gives me 0.2 on the left side and (0.2 - 0.1) on the right side. THAT'S MORE REACTANTS THAN PRODUCTS, NO?

Why do you say it is 1-to-1 ratio ???

Now for B: you know you convert 2 reactants from 1 product. So to get 0.2 NO2, you'd use up 0.1 N2O4. This would leave you with 0.1 N2O4, giving you a 1:1 ratio of reactants to products. We just said at equilibrium you need more reactants than products! So this is out too.

Why do you say it is 1-to-1 ratio and not 2-to-1 ratio?

😕😕😕😕😕😕

 

[ljc]

Woops. Made a mistake. You are correct!

Now that you have those numbers, plug them into the equilibrium expression, and see if 0.2 pops out:

0.1/(0.2^2) = 0.1/0.04 = 2.5. 2.5 is not 0.2, and it's not even close, so we can throw it out.

For completeness' sake:
Now try it with C:
To make 0.35atm of NO2, you'd use up 0.175atm of N2O4. This leaves you with 0.025atm. Plug into equilibrium:

0.025/(0.35^2) = 0.025/~0.11 ~ 0.2. This is the closest we'll get.

Sorry for the mistake!