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For the reversible reaction $\ce{N2 + 3H2 <--> 2NH3}$

When $\ce{N2}$ is increased, the the forward reaction is favored, increasing the yield of $\ce{NH3}$ and decreasing the yield of $\ce{H2}$. I read from multiple textbooks that the $\ce{H2}$ decreases in concentration to a greater extent than $\ce{NH3}$ increases in concentration, such that the final concentration of $\ce{NH3}$ is greater than that of $\ce{H2}$. Why is this so?

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The final concentration of H$_2$ is lower than the concentration of NH$_3$ because for each NH$_3$ you produce, you need 1.5 H$_2$. So the rate of consumption of hydrogen is higher than the rate of production of ammonia.

Here you can read about the multiple steps in the synthesis of ammonia, also called the Haber-Bosch Process. As you mention, by increasing the concentration of nitrogen, you can increase the rate. The rate limiting step is separation of the nitrogen atoms in N$_2$

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The first bit:

the $\ce{N2}$ decreases in concentration to a greater extent than NH3 increases in concentration

This is very easy to explain. If you look at the stoichiometrically balanced equation, you need 3 molecules of $\ce{H2}$ for every 2 molecules of $\ce{NH3}$. Consequently, when H2 concentration decreases, it will do so less than $\ce{NH3}$ increases (2 < 3).

To answer the second bit,

the final concentration of $\ce{NH3}$ is greater than that of $\ce{H2}$

To explain this part, we need to think about what it means to say "the forward reaction is favored." This is to say that energetically $\ce{2NH3}$ releases more energy into the system whereas $\ce{N2}$ and $\ce{3H2}$ store more energy in bonds.

To figure out the extent to which an equation favors one side or the other, we would need to look at the energy levels specifically. But for many gas equations, there's a nice way to guess -- which is related to gas laws. Looking at the ideal gas law (P = nRT/V), the amount of energy expressed in pressure is a function of "n" if Temperature and Volume are constant. Thus when n goes down, the amount of energy needed goes down. By reducing the number of molecules, we lower (2 is less than 4).

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  • $\begingroup$ Thank you! Regarding your explanation to the second part, what did you mean by "energetically NH3 releases more energy into the system"? I'm confused as to how energetics might play a part in whether the reaction is favored or not. And if we were to "look at the energy levels specifically", which energy levels in particular would we have to consider? $\endgroup$ – b3nj4m1n Feb 13 '17 at 1:35
  • $\begingroup$ bond energy of N-N + N = N + N (triple bond) N and 3x H - H vs. N-H bonds x 3 x 2 (see the chart here for general values labs.chem.ucsb.edu/zakarian/armen/…) $\endgroup$ – virmaior Feb 13 '17 at 4:58

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