[HoneyDumplings]

I measured the change in pressure for the decomposition of hydrogen peroxide in the presence of a manganese(IV) oxide catalyst at 5 different temperatures:

         MnO₂(s)
2H₂O₂(l)  O₂(g)+2H₂O(l)

Is there any way that I can find concentrations and then find the rate constant, k? And, using them, make an Arrhenius graph to find activation energy (including the catalyst)? Any help would be much appreciated.

Change in pressure was found using a Vernier Gas Pressure Sensor. The starting concentration of hydrogen peroxide was 3% or 0.88mol. The starting pressure was always around 98kPa. The catalyst and hydrogen peroxide were mixed together after the stopper was put on the flask. The increasing pressure was measured and the highest it went to (at 70C) was around 145kPa.
Here is an example of what I have done so far to try and find the rate constant to plot on an Arrhenius graph:

At 303.15K
PV=nRT
P/(RT)=n/v, which is the same as concentration.
120.3/(8.314*303.15) = 0.477 mol/dm^3
0.477mol/dm^3 is the final concentration of oxygen created after 180s had elapsed.
0.477mol/dm^3/180s = 0.00265 mol/dm^3/s
The ratio between oxygen and hydrogen peroxide is 1:2, therefore the rate at which hydrogen peroxide was depleted at is 0.0053 mol/dm^3/s
The ending concentration must be 0.88M - (0.0053mol/dm^3/s x 180s) = -0.074 mol/dm^3
And this is where I think something has gone wrong... The pressure continued to increase even after this 180s so I do not think the reaction went to completion.

I would then use the equation k = rate / [final concentration hydrogen peroxide] to find k.

I have already posted about this question but it got confusing so I think this post is much more clear what I am asking for. I hope this is ok.

[mjc123]

The ratio between oxygen and hydrogen peroxide is 1:2, therefore the rate at which hydrogen peroxide was depleted at is 0.0053 mol/dm^3/s

The molar ratio is 1:2, not the concentration ratio (because H₂O₂ is in solution and O₂ in the gas phase). In this case you need to work out the number of moles of O₂ produced, hence the number of moles of H₂O₂ consumed, then convert this to concentration. For this you have to know both the solution volume and the gas volume.

[HoneyDumplings]

Guess it’s not possible from just knowing change in pressure and not the volume of oxygen then... well thank you anyways!

[mjc123]

You can't find absolute rate constants, but you can find relative rate constants at the different temperatures and determine the activation energy. (The unknown multiplication factor will affect the intercept but not the slope of the Arrhenius plot.)
If you're using the method of initial rates (which is suggested by your observation that the reaction is not complete after 180 s) then
Rate = dP_O2/dt ∝ k (assuming initial [H₂O₂] is the same in all experiments)

[HoneyDumplings]

You can't find absolute rate constants, but you can find relative rate constants at the different temperatures and determine the activation energy. (The unknown multiplication factor will affect the intercept but not the slope of the Arrhenius plot.)
If you're using the method of initial rates (which is suggested by your observation that the reaction is not complete after 180 s) then
Rate = dP_O2/dt ∝ k (assuming initial [H₂O₂] is the same in all experiments)

Yes the concentration is the same in all experiments. Is Rate = dP_O2/dt ∝ k the Clapeyron equation? So the pressure of oxygen divided by the temperature? What exactly does dP and dt stand for? I have not seen this equation before.
But after I do that what exactly does rate refer to? the initial rate? the average rate?
Thank you very much again!

[mjc123]

dP/dt is the rate of change of pressure with time. Have you studied differentiation?

[HoneyDumplings]

dP/dt is the rate of change of pressure with time. Have you studied differentiation?

No, not yet. Is there a way I could just put my numbers into an online calculator or something of the sort to do this equation?
For the rate of change of pressure with time would that be the derivative of the change in pressure divided by time? ex 120(final pressure) - 98(initial pressure) = 22kPa
Then the something with the derivative of 22kpa/180s ?

[mjc123]

It is rather fundamental to kinetics, which is about rates of change!
However, if you're doing an initial rate experiment (that is, one where the change in concentration of the reactant is negligible over the timescale of the experiment - 180 s in your case - so you can assume the reaction rate is constant over that time) you can estimate the rate as (final pressure - initial pressure)/reaction time.

[HoneyDumplings]

It is rather fundamental to kinetics, which is about rates of change!
However, if you're doing an initial rate experiment (that is, one where the change in concentration of the reactant is negligible over the timescale of the experiment - 180 s in your case - so you can assume the reaction rate is constant over that time) you can estimate the rate as (final pressure - initial pressure)/reaction time.

Alrighty then! What about measuring the tangent from time=0, would that still be initial rate as well? And then my rate of reaction units would be in kpa/s right?
Anyways what you're saying is that trying to find the activation energy would be too complicated for me?

[mjc123]

How many data points have you got? I thought you only had initial and t = 180 s. If you have more, and can draw an accurate tangent at t = 0, that will give you the initial rate.
If you have 5 initial rate values at different temperatures, you can do an Arrhenius plot to get the activation energy.

[HoneyDumplings]

How many data points have you got? I thought you only had initial and t = 180 s. If you have more, and can draw an accurate tangent at t = 0, that will give you the initial rate.
If you have 5 initial rate values at different temperatures, you can do an Arrhenius plot to get the activation energy.

I took a measurement of pressure every 5 seconds so something like 36 points for each trial? And I did 5 trials at 5 different temperatures. I have 5 average initial rates in kPa/s.

[HoneyDumplings]

5 trials per temperature so a total of 25 trials.