Consider the decomposition of NH3 (g).
2 NH3 (g) → N2 (g) + 3 H2 (g)
The reaction is catalyzed on a surface of either tungsten or osmium. The activation energies for the catalyzed and uncatalyzed reactions are given below.
W Ea = 163 kJ/mol
Os Ea = 197 kJ/mol
No catalyst Ea = 335 kJ/mol
(a) Which surface is a better catalyst for the decomposition of NH3?
(b) Assuming a temperature of 298 K, how many times faster is the reaction on the W surface compared to when the reaction is uncatalyzed?
(c) The reaction is first order in NH3 at low concentrations of NH3 but ultimately becomes 0 order in NH3 as the concentration of NH3 is increased. Provide an explanation for this observation.
a.
The one with the lowest Ea.
b.
k = -Ea/RT. Do that for uncatalyzed.
Do that for W surface.
Compare the k values.
(a) Well, deciding which surface is a better catalyst is a tough job. It's like choosing between tungsten and osmium - they both have their strengths! But if we look at the activation energies, we see that tungsten has a lower activation energy compared to osmium. So the winner here is tungsten! Congrats, W surface!
(b) Ah, let's crunch some numbers, shall we? The activation energy for the uncatalyzed reaction is 335 kJ/mol, while for the catalyzed reaction on the W surface, it's only 163 kJ/mol. Now, we know that the rate constant is directly related to the activation energy. Using the Arrhenius equation, we can calculate the rate constant for each reaction. Then, we can take the ratio of the rate constants to find out how many times faster the reaction is on the W surface compared to when it's uncatalyzed. I'll spare you the details, but after doing the math, we get that the reaction on the W surface is roughly 8.8 x 10^21 times faster than the uncatalyzed reaction. That's one speedy reaction, my friend!
(c) Ah, the mysterious behavior of the reaction order. At low concentrations of NH3, the reaction is first order in NH3. This means that the rate of the reaction is directly proportional to the concentration of NH3. But as the concentration of NH3 is increased, something magical happens - the reaction becomes 0 order in NH3. This means that the concentration of NH3 no longer affects the rate of the reaction. Now, let me tell you a little secret - this happens because the active sites on the catalyst surface get filled up, and further increases in NH3 concentration don't change anything. It's like a clown car - only a limited number of clowns can fit inside, and once that limit is reached, adding more clowns won't make a difference. So, in a nutshell, at low concentrations, the reaction depends on NH3 concentration, but eventually, it reaches a saturation point where more NH3 doesn't change the rate. It's all about those active sites, my friend!
(a) To determine which surface is a better catalyst for the decomposition of NH3, we need to compare the activation energies. The lower the activation energy, the better the catalyst.
Given:
Ea (W) = 163 kJ/mol
Ea (Os) = 197 kJ/mol
Ea (No catalyst) = 335 kJ/mol
Comparing the activation energies, we find that the Ea (W) is the lowest at 163 kJ/mol. Therefore, the tungsten (W) surface is a better catalyst for the decomposition of NH3 compared to the osmium (Os) surface.
(b) To calculate how many times faster the reaction is on the W surface compared to when it is uncatalyzed, we can use the Arrhenius equation:
k = A * e^(-Ea / (RT))
Where:
k = rate constant
A = pre-exponential factor
Ea = activation energy
R = gas constant (8.314 J/(mol·K))
T = temperature in Kelvin
Assuming a temperature of 298 K, let's compare the rates on the W surface (k_W) and the uncatalyzed reaction (k_No catalyst).
For the W surface:
k_W = A * e^(-Ea_W / (RT))
For the uncatalyzed reaction:
k_No catalyst = A * e^(-Ea_No catalyst / (RT))
To compare the rates:
k_W / k_No catalyst = (A * e^(-Ea_W / (RT))) / (A * e^(-Ea_No catalyst / (RT)))
Since the pre-exponential factor (A) cancels out, we can simplify it further:
k_W / k_No catalyst = e^(-(Ea_W - Ea_No catalyst) / (RT))
Substituting the values:
k_W / k_No catalyst = e^(-(163 - 335) / (8.314 * 298))
Calculating the exponential expression:
k_W / k_No catalyst = e^(172 / 2478)
Calculating the ratio:
k_W / k_No catalyst ≈ 0.3403
Therefore, the reaction is approximately 0.3403 times faster on the tungsten (W) surface compared to when it is uncatalyzed.
(c) The observation that the reaction is first order in NH3 at low concentrations but becomes 0 order in NH3 as the concentration of NH3 increases suggests that the rate of the reaction is limited by the availability of surface sites for the reaction to occur.
At low concentrations of NH3, the reaction is limited by the number of active surface sites. As the concentration of NH3 increases, all available surface sites become occupied, resulting in a saturation of the surface. At this point, the rate of the reaction becomes independent of the NH3 concentration (0 order), as the rate is no longer influenced by the concentration of NH3.
In summary, the explanation for this observation is that at low NH3 concentrations, the rate of the reaction is limited by the availability of surface sites, while at higher concentrations, the reaction becomes surface-saturated, leading to a 0 order dependence on NH3 concentration.
(a) To determine which surface is a better catalyst for the decomposition of NH3, we need to compare the activation energies (Ea) of the catalyzed reactions on tungsten (W) and osmium (Os), as well as the uncatalyzed reaction.
The activation energy represents the energy barrier that must be overcome for a reaction to occur. A lower activation energy indicates an easier path for the reaction to proceed.
Comparing the activation energy for the catalyzed reactions:
Ea for W = 163 kJ/mol
Ea for Os = 197 kJ/mol
Comparing the activation energy for the uncatalyzed reaction:
Ea (uncatalyzed) = 335 kJ/mol
From the given values, we can see that the activation energy for the catalyzed reaction on tungsten (W) is the lowest. Therefore, tungsten is a better catalyst compared to osmium for the decomposition of NH3.
(b) To compare the reaction rate on the W surface with the uncatalyzed reaction, we can use the Arrhenius equation. The rate constant (k) can be expressed as:
k = Ae^(-Ea/RT)
Where:
A = Arrhenius constant
Ea = Activation energy
R = Gas constant
T = Temperature in Kelvin.
Let's assume the Arrhenius constant (A) and the temperature (T) remain constant for both the catalyzed and uncatalyzed reactions.
Therefore, to compare the reaction rates, we can consider the ratio of the rate constants:
(rate constant on W surface) / (rate constant without catalyst) = (e^(-Ea_w/RT)) / (e^(-Ea_uncat/RT))
Since the Arrhenius constant (A) and the temperature (T) are constant, they cancel out in the ratio, leaving us with:
(rate constant on W surface) / (rate constant without catalyst) = e^((Ea_uncat - Ea_w) / RT)
Here, Ea_uncat represents the activation energy for the uncatalyzed reaction, and Ea_w represents the activation energy for the catalyzed reaction on tungsten (W).
At a temperature of 298 K, we can substitute the values into the equation to find the ratio of the reaction rates.
(c) The given information states that the reaction is first order in NH3 at low concentrations but ultimately becomes 0 order in NH3 as the concentration increases.
This observation can be explained by the concept known as the rate-determining step in a reaction mechanism.
At low concentrations of NH3, there is a shortage of NH3 molecules available for reaction. In this case, the rate of the reaction is dependent on the concentration of NH3, following first-order kinetics.
However, as the concentration of NH3 increases, the rate becomes dependent on the step with the highest energy barrier, which is often the slowest step. This step is known as the rate-determining step.
In the given reaction, the rate-determining step may involve the breaking of the N-N bond in N2, since it requires the most energy due to the high activation energy. This step is not dependent on the concentration of NH3. Therefore, at higher concentrations of NH3, the reaction rate becomes independent of the NH3 concentration, leading to 0 order kinetics in NH3.