Problem

In terms of collision theory, to which of the fol…

00:49

Problem 61 Hard Difficulty

An elevated level of the enzyme alkaline phosphatase (ALP) in human serum is an indication of possible liver or bone disorder. The level of serum ALP is so low that it is very difficult to measure directly. However, ALP catalyzes a number of reactions, and its relative concentration can be determined by measuring the rate of one of these reactions under controlled conditions. One such reaction is the conversion of p-nitrophenyl phosphate (PNPP) to p-nitrophenoxide ion (PNP) and phosphate ion. Control of temperature during the test is very important; the rate of the reaction increases 1.47 times if the temperature changes from 30 °C to 37 °C. What is the activation energy for the ALP–catalyzed conversion of PNPP to PNP and phosphate?

Answer

43 $\mathrm{kJ} \mathrm{mol}^{-1}$

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Video Transcript

All right, So this question has a bunch of background information on the reaction that they are asking about. Most of it isn't too important, except for when they talk about, um, that the rate of the reaction increases 1.47 times. If the temperature changes from 30 degrees C 2 37 degrees C me, then ask what is the activation energy for the reaction? Um, and when they say activation energy, I automatically think of the re gnaeus equation J rode out here. And this is the linear form, and we have two different temperatures. So I wrote up that form of the equation, and so one thing to remember is that they give the temperatures in degrees C and the question, But in this equation, the degrees needs to be and Calvin. So I already did the conversion here from degree Celsius to Calvin, and so are 30 degree C becomes 3303 Calvin. And so that is our t one. And our 37 degrees C becomes three tonne. So that is our t. Two of her reaction are for our equation. And I wrote down what the R value is which is the gas constant, which is 8.314 jewels over Calvin Times Moles. Sorry. So, um, going back to this equation, We can use that information to start filling in our variables. Um, let's see. So the natural log of K one over K two. So if you remember from the question, it says that Ah, the reaction increases 1.47 times the temperature increases from 30 degrees to 37 degrees c. And so, for if we make our K one for three degrees one, we can make our K two for 37 degrees. One point, uh, what was it? 1.47? All right. And see, we don't know the activation energy, cause that's what we're solving for. So I'm going to leave that like that and our our value. I grew up on this page 8.3 1/4 five 3145 That was Jules. Over, Calvin Times moles. All right. And then we can just fill in our tea too, and t one So 1/3. Ah, let's see that one should be 3 10 Calvin. And this one is our 303 Kelvin And so I'm just gonna put, um, this one and this one into my calculator and bring right the equation loss of this one. I get negative 0.385 and that equals I'm gonna rewrite this. Her activation energy over eight point 3145 Jules per Calvin Time small. And then for this. When I put that in my calculator, I got negative 7.5 times. 10 to the negative five. Calvin these Calvin's cancel out. And then I'm going to divide both sides by negative seven 0.5 times 10 to the negative size. Let's see, I get, um, my 1001 100 33 points. 33 that cancels out equals R activation energy over our gas constant Jules Perma. And so I'm just gonna multiply both sides by r gas Constant. So that cancels out and then multiply it. This side Jules Permal. Sorry. I'm running out of room here. Um, I'm just gonna put this up at the top here, So when I put that in my calculator, I get that our activation energy equals, Let's see, 4.26 times. 10 to the forth. Um, Jules, per mole. And so that is our answer. Reed. There

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