This is a very strange question. I don't really see how the Arrhenius equation is directly relevant to this kind of process, but I can play along.
First, you need to identify what is actually being asked for. Rate is generally speaking a function of something per unit time. In chemistry this is usually a unit of mass or moles per unit time, or even something non-dimensional like "reaction turnovers", but we aren't given anything that obvious here. The question is asking to calculate time for a process. So I'm going to call the something a unit of 1 egg, so that the rate is "eggs per time". I'm guessing "an egg boils in t seconds" means "an egg goes from an initially uncooked state to a fully cooked state in t seconds". The reaction here is the "cooking of the egg". Cooking is obviously a series of chemical reactions, although the way it's presented here is rather abstract. I guess in that sense it could be modeled by Arrhenius kinetics, although how the activation energy is being determined isn't really clear. Anyway, my interpretation of the question is that it wants to you to use Arrhenius equation to determine the amount of time it takes to fully boil one egg when the temperature is 363 K, based on the amount of time it takes to boil one egg when the temperature is 373 K. The pressures given, I'm assuming, have no direct bearing on the solving of the problem. They are only there to specify the state of the system - i.e., to explain why the temperature is changing. The question could have just as easily, and less confusingly, left it as "at sea level" and "on a mountain". I make this conclusion because of the use of the word "boiling" - the temperature of which is determined by the pressure.
So, when it comes down to it, you basically have
Rate 1 = 1 egg per t1 seconds
Rate 2 = 1 egg per t2 seconds
Given t1 and the Arrhenius expression, with activation energy, calculate t2.
This is typically a fairly straightforward type of problem, if we assume activation energy and pre-exponential factors are temperature independent. I would approach it by leaving it in terms of rates at first and then calculating t2 afterwards. But the problem is, unless you left it out, you never specify the time for the reference condition (t1). This isn't listed anywhere in the problem? If not, I must be missing something else that's obvious, because it seems you have too many unknowns.
(My suspicion of a missing piece of information is brought about by the first sentence "An egg boils at the sea level at a temperature of 373K and pressure of 101,3 kPa". This doesn't say anything about how long the process takes, which would seem to be a crucial piece of information. It can't be determined independently from the temperature or pressure, because, as mentioned above, one egg isn't a real unit - eggs come in different sizes.)
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Topic: Arrhenius equation (Read 8313 times)