One day at the fertilizer factory, your boss Mr. Haber comes to you with a problem. The process used by the factory to produce ammonia,the raw material for your fertilizer, is just not optimized. He would like to modify the conditions to achieve a better yield of ammonia in the shortest possible time, and asks you to suggest One day at the fertilizer factory, your boss Mr. Haber comes to you with a problem. The process used by the factory to produce ammonia,the raw material for your fertilizer, is just not optimized. He would like to modify the conditions to achieve a better yield of ammonia in the shortest possible time, and asks you to suggest some changes. Consider the following equation,describing the process used by your factory:
N2(g) + 3 H2(g) ---> 2NH3(g) ΔHrxn=-92.4 KJ/mol
How will each of the following affect the yeild ofNH3,the equilibrium constant (K), the rate of the reaction and the value of the rate constant (k)? Assume constant pressure unless otherwise indicated, and that the rate law israte=k[N2]m[H2]n, whereboth m and n are greater than 0.
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Yield ofNH3 Equilibrium constant(K) Rate of rxn Rate constant(k)
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adding N2
removing H2
removing NH3
increasing
pressure
increasing
temp
adding catalyst
What is your recommendation to MR. Harber?
To determine how each of the changes will affect the yield of NH3, the equilibrium constant (K), the rate of the reaction, and the value of the rate constant (k), we need to understand the concepts behind each change. Let's go through each change one by one:
1. Adding N2: Adding more N2 to the reaction will increase the concentration of the reactant, according to Le Chatelier's principle. Since N2 is a reactant in the forward reaction, increasing its concentration will shift the equilibrium towards the production of NH3, resulting in an increase in the yield of NH3. The equilibrium constant K will not be affected by the change in concentration. The rate of the reaction and the rate constant k may increase if the increased N2 concentration leads to more collisions and successful reactions.
2. Removing H2: Removing H2 will decrease the concentration of one of the reactants. According to Le Chatelier's principle, removing a reactant will shift the equilibrium in the direction to compensate for the loss. In this case, the reaction will shift towards the formation of NH3 to replenish the lost H2. As a result, the yield of NH3 will increase. The equilibrium constant K will not be affected, but the rate of the reaction and the rate constant k may decrease due to the decreased concentration of H2.
3. Removing NH3: Removing NH3 will reduce the concentration of the product. According to Le Chatelier's principle, the reaction will shift towards the formation of NH3 to compensate for the loss, resulting in an increase in the yield of NH3. The equilibrium constant K will remain unchanged. However, removing NH3 will not directly affect the rate of the reaction or the rate constant k.
4. Increasing pressure: Increasing the pressure of the system can affect the yield of NH3, depending on the stoichiometry of the reaction. In this case, the reaction involves the gas-phase elements N2, H2, and NH3. Increasing the pressure will shift the equilibrium towards the side with fewer moles of gas. Since the reaction has fewer moles of gas on the product side (2 moles of NH3) compared to the reactant side (1 mole of N2 and 3 moles of H2), increasing the pressure will result in an increase in the yield of NH3. The equilibrium constant K will not be affected, but the rate of the reaction and the rate constant k may increase due to the increased collision frequency caused by the higher pressure.
5. Increasing temperature: Increasing the temperature of the system will favor an endothermic reaction (a reaction that absorbs heat) according to Le Chatelier's principle. As the forward reaction in this case is exothermic (releases heat), increasing the temperature will shift the equilibrium towards the reactant side to counteract the temperature increase. As a result, the yield of NH3 will decrease. The equilibrium constant K will not be affected, but the rate of the reaction and the rate constant k will increase due to the higher energy of the reactant molecules at higher temperatures.
6. Adding a catalyst: Adding a catalyst will not directly affect the yield of NH3 or the equilibrium constant K. A catalyst provides an alternative reaction pathway with a lower activation energy, allowing the reaction to occur more easily. While a catalyst speeds up the rate of the reaction, it does not shift the equilibrium position. Therefore, the yield of NH3 will remain unchanged, the equilibrium constant K will be unaffected, but the rate of the reaction will increase due to the presence of the catalyst. The rate constant k may also increase with the catalyst.
Based on these considerations, my recommendation to Mr. Haber would be to add more N2, remove H2, add a catalyst, and possibly increase the pressure to optimize the yield of NH3 in the shortest possible time. However, it's important to note that the specific conditions and optimization strategies may vary depending on the specific parameters and constraints of the fertilizer factory.