How Does Temperature Affect Reaction Rate and Activation Energy Calculation?

[stacope32]

http://antoine.frostburg.edu/chem/senese/101/kinetics/faq/temperature-and-reaction-rate.shtml

According to Rule of Thumb, the reaction rate doubles when there is a 10 degree rise in temperature.
I want to determine the activation energy for a lab, but my level of study is not advanced enough for me to actually calculate rate constant, therefore I am using the rule of thumb as substitute.

I am using the rule of thumb to determine the ratio of rate constant because I don't actually know how to calculate it for gas and I have no time left for more experiments.

Using the Arrhenius equation with Ea isolated on the left side, according to the rule of thumb, ln k2/k1 will be ln 2/1, however, there is only a 0.5 degree rise in my experiment, does that mean that my reaction rate will be x0.1?I need to find a way to calculate the activation energy without actually finding rate constant as my level of study is not high enough.

The reaction is Zn + HCl = ZnCl2 + H2
The values I have access to are temperature at time intervals, gas produced over time (reaction rate).
Thanks so much!

 

[Borek]

Can't say what you wrote makes much sense to me. Looks like you are mixing two different things in a rather incompatible way.

Rule of thumbs as given allows estimation of activation energy - it will give a reasonable order of magnitude for most reactions, however, it will tell you the activation energy is identical for every reaction. That's clearly not true.

However, you wrote you did some experiment - what kind of experiment it was, and what was its purpose?

 

[stacope32]

Can't say what you wrote makes much sense to me. Looks like you are mixing two different things in a rather incompatible way.

Rule of thumbs as given allows estimation of activation energy - it will give a reasonable order of magnitude for most reactions, however, it will tell you the activation energy is identical for every reaction. That's clearly not true.

However, you wrote you did some experiment - what kind of experiment it was, and what was its purpose?

Hi thanks for replying ! Sorry for thr confusion, I am struggling to learn things as I just stumbled upon this topic.

My report aim is to determine the activation energy for a reaction and the reaction I chose is as above, the zinc and hydrochloric acid reaction. I am using the Arrhenius equation.
I have gathered data on
1. Temperature at 30 sec, 60 sec etc in a calorimetry.
2. Reaction rate: water displacement of hydrogen gas in cm3 (amount of hydrogen gas formed over time )

However when I first researched I mixed up rate constant and reaction rate, therefore I am stuck right now with 3 unknown variables (Ea, k, A) .

I wanted to plot Ln k against 1/T on a graph to get the slope Ea but now I don't have the rate constant value and I don't know how to solve it. Is it possible to solve for it with the information I have ?

That's why I stumbled upon the rule of thumb because I saw a sample calculation that used Ln 2/1, which solved the k variable which I don't have. However in my experiment the zinc and hydrochloric acid reaction, because I used small quantities, the maximum temp rise is 0.5 celsius(while rule of thumb is 10 degrees). I don't know how to go about solving it.
I would like to find the activation energy ultimately.
I used 25ml 1M HCl and 1g Zn.

 

[DrDu]

So if the rate doubles when going from room temperature ($T_0$=298 K) to room temperature +10 K ($T_1$=308 K), then
$2=r_1/r_0=\exp(-E_a/(RT_1))/\exp(-E_a/(RT_0))=\exp(-E_a/R\cdot(1/T_1-1/T_0))$, which you can solve for $E_a/R$. Now you can use this to calculate the change of rates for any two temperatures you like.

 

[epenguin]

If you are using the same concentration of hydrochloric acid and the same amount of zinc in each experiment (and it was finely divided, more big lumps) and only varied the temperature, then since what you use for the calculation is the ratio, the ratio of rate constants would be the same as the ratio of rates so you are OK for a calculation.

And anyway I have my doubts about 'rate constant'. A heterogeneous reaction of somewhat complicated mechanism, I guess you could define an 'empirical rate constant' depending on the concentration of HCl and the 'concentration'of zinc. On third thoughts and, As you have probably not had the time to look into varying these are systematically, I expect it would be better to stay just with rates.

And then you say you have measured measured rates. Actually you have measured volume of hydrogen involved, and evolution of temperature basically (not sure what you mean by the vague 'calorimetry'. To call anything a rate measurement, you need to measure parameters like this at various times, yes which apparently you have done. So how well did the time course of these two parameters compare? Was the comparison the same (after suitable corrections) at the different temperatures?

We are quite often have questions like this and it is quite difficult to comment when we don't see the detail of how the experiment was done nor any results. But one thing not to worry, it is quite difficult to do studies like this very conclusively inside the timeframe of the class experiments.