at high temperatures, ammonia decomposes to N2 and H2.
2 NH3(g)--> N2 (g) + 3H2(g)
Delta H for the reaction is positive and delta S is positive.
Estimate the temperature at which this reaction becomes spontaneous
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Use the tables in your text/notes to evaluate dHo for the rxn and dSo for the rxn and set those up as dGo = dHo - TdSo. Then set dGo = 0 and solve for T. That will be the point at which the rxn is spontaneous/non-spontaneous (or the reverse). dH often doesn't change much with T and dS often doesn't change much with T so this allows one to estimate (note that word in the problem) the change over point.
Well, the temperature at which this reaction becomes spontaneous is when ammonia is feeling hot enough to decompose on its own. It's like ammonia is saying, "I'm way too hot to stay together as one molecule, I need to break free!"
Now, since both delta H and delta S are positive, it means that ammonia values its freedom and disorder over staying as a single molecule. It's breaking free, but it's doing so in a fancy and somewhat chaotic manner.
To estimate the temperature, we can use the equation ΔG = ΔH - TΔS, where ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy, ΔS is the change in entropy, and T is the temperature in Kelvin.
When the reaction becomes spontaneous, ΔG will be equal to zero. So we can rewrite the equation as 0 = ΔH - TΔS.
Now, we want to solve for T. But we're not math bots, we're clown bots! So instead of throwing equations at you, let me tell you a joke to lighten the mood:
Why did the ammonia molecule go to therapy?
Because it couldn't stop decomposing under pressure!
Okay, back to the question. To estimate the temperature, we need the values of ΔH and ΔS. Without those, it's like trying to tell a joke without a punchline. So, if you provide me with ΔH and ΔS, I'll be more than happy to calculate the temperature for you.
To determine the temperature at which a reaction becomes spontaneous, we need to consider the Gibbs free energy change (ΔG) of the reaction. The Gibbs free energy change is given by the equation:
ΔG = ΔH - TΔS
Where:
ΔG is the Gibbs free energy change
ΔH is the enthalpy change
T is the temperature in Kelvin
ΔS is the entropy change
In this case, you have mentioned that ΔH is positive (indicating an endothermic reaction) and ΔS is positive (indicating an increase in disorder). For a reaction to be spontaneous at a given temperature, ΔG must be negative. This means that the entropy-driven factor (TΔS) needs to be larger than the enthalpy-driven factor (ΔH).
To estimate the temperature at which this reaction becomes spontaneous, we set ΔG = 0 and solve for T:
0 = ΔH - TΔS
Rearranging the equation:
TΔS = ΔH
T = ΔH / ΔS
Now, let's substitute the given values:
ΔH = Positive value (you mentioned it is positive)
ΔS = Positive value (you mentioned it is positive)
By dividing ΔH by ΔS, you will obtain the temperature at which this reaction becomes spontaneous.