Chemical Forums
Chemistry Forums for Students => Undergraduate General Chemistry Forum => Topic started by: edoble on November 05, 2012, 07:17:20 PM
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Here is the problem, any help would be really helpful, thank you.
At T=350°, the value for Kc for the reaction N2 (g) +3H2 (g) = 2NH3 (g) is 8. If 2 moles of N2, 1 mole of H2, and 2 moles of NH3 are put into an empty 2L flask, what will be the concentration of H2 at equilibrium?
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Write down the law of mass action for this reaction.
Then you have to think that some of the chemicals will convert and disappear and new product is formed, for this you use x. Some x will go away and some in a ratio will be produced.
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I made the ICE Chart but after that I am confused because I need to use the Method of Successive Approximations to get my X. This is what I have so far:
N2 + 3H2 = 2NH3
I 1 0.5 1
C -x -3x +2x
E 1-x 0.5-3x 1+2x
Kc = (1+2X)^2 = 8
(1-x)*(0.5-3x)^3
At this point I need to use Method of Successive Approximations to solve for X. I do not know how to do it since my Kc formula is complicated.
Is my ICE chart correct?
Any help would be much appreciated, thank you.
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Can you assume that x will be negligible for any of those concentrations?
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I made the ICE Chart but after that I am confused because I need to use the Method of Successive Approximations to get my X. This is what I have so far:
N2 + 3H2 = 2NH3
I 1 0.5 1
C -x -3x +2x
E 1-x 0.5-3x 1+2x
Kc = (1+2X)^2 = 8
(1-x)*(0.5-3x)^3
At this point I need to use Method of Successive Approximations to solve for X. I do not know how to do it since my Kc formula is complicated.
Is my ICE chart correct?
Any help would be much appreciated, thank you.
I think this should be correct. Of course you need a math program to solve for x. But you can try to simplify the formula by using the binomial formulas.
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Can you assume that x will be negligible for any of those concentrations?
I dont think so.
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eg:
http://did.mat.uni-bayreuth.de/~wn/BLK/Poly/poly.html
http://www.numberempire.com/equationsolver.php
http://www.solvemymath.com/online_math_calculator/algebra_combinatorics/polynomial_calculator/polynomial_roots.php
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I used www.wolframalpha.com to solve that above equation and this is what I get :
216x4-324x3+122x2-23x=0
The real root is X= 1.0628
When I use that X value to find Concentration of H2 at equilibrium I get:
From ICE chart: H2=0.5-3x
H2=0.5-[3(1.0628)]
H2= - 2.6884
I get a negative solution...I believe something is wrong...please help I am confused, thank you.
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You have to choose another x. 1.0628 is not the solution we looking for.
I have to change my answer to XGen. He was right.
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First things first - what is the method of successive approximations?
Edit: something is wrong, I got the same 1.0628 with a different approach. Are you sure about the Kc value? I seem to remember it is much lower.
Edit2: ROFL, everything is OK. Nice question :) 1.0628 is not the only real root.
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If all values true I think 1 *10-16 is the right x. What means not much change.
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Perhaps looking at Q prior to doing any calculations might be helpful.
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What is in this case the Q. Because I cannot see without calculation whats going on.
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I used www.wolframalpha.com to solve that above equation and this is what I get :
216x4-324x3+122x2-23x=0
The real root is X= 1.0628
I used Wolfram too and got two roots; not one:
(https://www.chemicalforums.com/proxy.php?request=http%3A%2F%2Fwww4b.wolframalpha.com%2FCalculate%2FMSP%2FMSP47601a3iffa9fi1big7c000043cg330e154b6haa%3FMSPStoreType%3Dimage%2Fgif%26amp%3Bs%3D61%26amp%3Bw%3D300%26amp%3Bh%3D190%26amp%3Bcdf%3DCoordinates%26amp%3Bcdf%3DTooltips&hash=12ced4d42eb8dddf9f422492a8940ca46ef4df69)
Why do you only see one root?
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At this point I need to use Method of Successive Approximations to solve for X. I do not know how to do it since my Kc formula is complicated.
Rearrange your equality to get:
[tex]
x=1-\frac{(1+2*x)^2}{8*(0.5-3*x)^3}
[/tex]
Now choose any reasonable guess for x. Already 0≤x≤1 seems the domain from your ICE chart.
Use this guess to calculate a new x. You'll find this converges to a solution (often, not always).
In less than 4 iterations I have your Wolfram solution.
e.g. Starting from x=0.1
0.10
-21.5000
0.9992
1.0721
1.0617
1.0630
1.0628
Starting from x=0.9
0.90
1.0920
1.0592
1.0633
1.0628
etc.
Note this only gives one solution. Which is the key in this problem. :)
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Why do you think that ammonia is formed. May be it decomposes and negative root of the equation should be used.
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Why do you think that ammonia is formed. May be it decomposes and negative root of the equation should be used.
Does it have a negative root? Thought the only roots are 0 and 1.0628.
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What is in this case the Q. Because I cannot see without calculation whats going on.
See for instance http://dwb4.unl.edu/Chem/CHEM869V/CHEM869VLinks/learn.chem.vt.edu/tutorials/equilibrium/rxnquotient.html or similar
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I used www.wolframalpha.com to solve that above equation and this is what I get :
216x4-324x3+122x2-23x=0
The real root is X= 1.0628
I used Wolfram too and got two roots; not one:
(https://www.chemicalforums.com/proxy.php?request=http%3A%2F%2Fwww4b.wolframalpha.com%2FCalculate%2FMSP%2FMSP47601a3iffa9fi1big7c000043cg330e154b6haa%3FMSPStoreType%3Dimage%2Fgif%26amp%3Bs%3D61%26amp%3Bw%3D300%26amp%3Bh%3D190%26amp%3Bcdf%3DCoordinates%26amp%3Bcdf%3DTooltips&hash=12ced4d42eb8dddf9f422492a8940ca46ef4df69)
Why do you only see one root?
Using Wolfram Alpha to solve for X : 216x4-324x3+122x2-23x=0
The real solutions are:
X=0
X=1.06284
So thats why I quoted only X=1.06284
Is there something wrong with this problem; and YES I copied the question correctly from my chemistry book...word for word. Could be there is an error in the book..not sure.
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But 1.0628 is not the solution what gives the right hydrogen amount.
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What is x?
What does x=1.0628 mean?
What does x=0 mean?
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What is in this case the Q. Because I cannot see without calculation whats going on.
See for instance http://dwb4.unl.edu/Chem/CHEM869V/CHEM869VLinks/learn.chem.vt.edu/tutorials/equilibrium/rxnquotient.html or similar
We used Kp for that. p = pressure. I learned Q is used for heat capacity. But in different countries different letters for variables in use.
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We used Kp for that. p = pressure. I learned Q is used for heat capacity. But in different countries different letters for variables in use.
Kp to me suggests the conditions at equilibrium, not necessarily the conditions at the start of the reaction. which is what Q is used for in this case.
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x = 0 means we are already at equilibrium. So far so good, but if I want to calculate the hydrogen (0,5-3x)3 = c(H2) we get 0.125 mol/l but we put 0.5 mol/l in?????
For ammonia (1+2x)2 = c(NH3) give 1 mol/l and also for nitrogen (1-x) give 1 mol/l. Why it doesnt fit for hydrogen.
the whole term give 1/0.125 = 8 = K
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x = 0 means we are already at equilibrium. So far so good, but if I want to calculate the hydrogen (0,5-3x)3 = c(H2) we get 0.125 mol/l but we put 0.5 mol/l in??
For ammonia (1+2x)2 = c(NH3) give 1 mol/l and also for nitrogen (1-x) give 1 mol/l. Why it doesnt fit for hydrogen.
the whole term give 1/0.125 = 8 = K
Check your units.
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Wow right. Its for hydrogen 0.125 (mol/l)3 so need 3rd. root what gives 0.5 mol/l Also for ammonia I need square root. (1+x)2 gives (mol/l)2.
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Using Wolfram Alpha to solve for X : 216x4-324x3+122x2-23x=0
The real solutions are:
X=0
X=1.06284
So thats why I quoted only X=1.06284
Is there something wrong with this problem; and YES I copied the question correctly from my chemistry book...word for word. Could be there is an error in the book..not sure.
Nothing wrong in the problem. But ignoring a zero root is the problem. That is the relevant root in your case.
They tricked you by giving you a system already at equilibrium. ;D
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Q is usually used for the reaction quotient.
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Why do you think that ammonia is formed. May be it decomposes and negative root of the equation should be used.
Does it have a negative root? Thought the only roots are 0 and 1.0628.
If one of the solutions is exactly zero then we are at the equilibrium point.
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Why do you think that ammonia is formed. May be it decomposes and negative root of the equation should be used.
Does it have a negative root? Thought the only roots are 0 and 1.0628.
If one of the solutions is exactly zero then we are at the equilibrium point.
Yep. That's exactly the case here.