2015 AP Chemistry free response 5

- [Voiceover] Blue food coloring can be oxidized by household bleach, which contains hypochlorite, household bleach will usually use sodium hypochlorite, to form colorless products, as represented by the equation above. So this is the food coloring, reacts with the hypochlorite, produces colorless a product. A student uses a spectrophotometer set at a wavelength of 635 nanometers to study the absorbance of the food coloring over time during the bleaching process. So since we're talking about blue food coloring, I'm guessing this is a wavelength of light that is blue, since that's gonna be optimally absorbed by blue food coloring. In the study, bleach is present in large excess so the concentration of hypochlorite is essentially constant through the reaction. Alright. The student used data from the study to generate the graphs below. So we're graphing, see the vertical access we have absorbents and you can view absorbents, if we have a high concentration of blue food coloring, then we're gonna have a high absorbance, and if we have a low concentration of blue food coloring, we're gonna have a low absorbance. So you can view this as a, as a proxy for concentration of food coloring, food coloring, food coloring concentration. And so, here they just plotted absorbance relative to time, here they have the natural log of absorbance relative to time. Here, one over absorbance relative to time. And so let's look at the questions here. Based on the graphs above, what is the order of the reaction with respect to the blue food coloring? With the respect to the blue food blue coloring. So let's think of, I'll do a little super fast primer, so if we're talking about a zero, if we're talking about a zero order reaction that means that the rate of reaction is constant. Rate, constant. And it's independent of, the independent of the concentration of blue food coloring. Independent of the concentration, I'll just say of the coloring. Concentration of the coloring. Is that the case here? Well no, the rate isn't constant, if we look at just absorbance, which is just once again, a proxy for our concentration of food coloring, up here our rate is pretty fast, we have a steep slope over here and then the slope gets less and less steep as more as our concentration of food coloring goes down, as the reaction proceeds. So this is definitely not a zero order reaction, if this was a zero order reaction when we just plot absorbance, which is once again the proxy for concentration of food coloring versus time, we would expect to see something more of a line. So, if you saw something like that, then you would say "okay, "that looks like a zero order reaction." Now when we took the natural log of absorbance, which is once again a proxy for the natural log of the concentration of food coloring, here we get a clear line, here we actually do get a clear line. And I'm not gonna go into it, it takes a little bit of calculus and a little bit of basic differential equations to realize it, but this is a give away for a first order, for a first order reaction. So in a first order of reaction, in first order, the rate, the rate is proportional, proportional, is proportional to the concentration, concentration, let me just write it, is proportional to the concentration since we're saying with respect to the blue food coloring, is proportional to the concentration of blue food coloring. I'll just write coloring, coloring for short. And I'll throw a little calculus here, you could say the rate of reaction, which is the rate in change of concentration of our coloring, with respect to time, and if this looks completely unfamiliar to you and you've never taken a calculus class ignore what I'm about to say for the next 20 seconds. This needs to be proportional to the concentration of coloring. Coloring, alright, COL dot for short. And if you saw this, you would see that the natural log of the concentration of coloring with respect to, if you plot that versus time, is you're going to get a line. So this is a key, this is a key signature of a first order, first order reaction. But you can even see it here, up here when the concentration of our coloring is high, our rate is high, we have a steep slope and then when our concentration becomes lower, we also have our slope being lower. So you actually don't even need calculus, you could look at this one and see that something very similar to that is happening. So this is a first order reaction. If you're thinking about second order, why do they even show us this? Well a second order if you plot one over absorbance versus time, or one over the concentration, cause' as we said absorbance is a proxy for the concentration of our food coloring, well then this would be a linear plot, but as we can see it is not. But if this linear plot, then you could say "hey maybe this is a second order," but just to answer the question, this is a first order reaction with respect to blue food coloring. Alright, let's do part B now. The reaction is known to be first order with respect to bleach. Alright, so now we're talking about the reaction order with respect to bleach, not the food coloring. In a second experiment, the student prepares solutions of food coloring and bleach with concentrations that differ from those used in the first experiment. Alright. When the solutions are combined, the student observes that the reaction mixture reaches an absorbance near zero too rapidly. So it's getting to no color too fast. In order to correct the problem, the student proposes the following three possible modifications to the experiment. So the solution doesn't want, the student does not want the solution to become colorless that fast, so what should they do? Should they increase the temperature? Well increasing the temperature is just going to make the reaction happen even faster, the molecules are gonna bump into each other with more energy and more frequently, and so, that's just gonna make, that's gonna get you to colorless even faster. So that's gonna go in the opposite direction, so we can rule that out. Increasing the concentration of blue food coloring. Well, that makes sense, well they say blue food coloring but I'm assuming it's blue, whatever. Because, well if it's getting clear too fast, well, if you add more food coloring well then it's just gonna, it's going to have a higher absorbance and it's going to take longer to get to clear. So, this one seems interesting. Now what about this, increasing the concentration of bleach? Well once again the bleach is the thing that's getting the food, is reacting with the food coloring to make it clear, so if you increase its concentration, you're gonna get clear even faster which is not what the student wants, this is the opposite of what the student wants. So once again we would cross that one out. And the one that we like is definitely increasing the concentration of the food coloring. They say circle the one proposed modification, so let me make sure I'm circling it, I guess I'm more rectangling it, but you get the idea. Correct the problem and explain how that modification increases the time for the reaction mixture to reach an absorbance near zero. So I'll write, more coloring, more coloring, results in higher initial absorbance, higher initial, initial absorbance, and thus, and thus, more time, more time, for mixture to reach, to reach near zero absorbance. Absorbance, the word that I really have trouble saying. Alright, part C. In another experiment, a student wishes to study the oxidation of red food coloring, just in the spirit of that one I'll underline it with red, of red food coloring with bleach. How would the student need to modify the original experiment procedure, experimental procedure, to determine the order of the reaction with respect to the red food coloring? Well overall, this is a pretty good experiment, they plotted it in three different ways, which was, as we saw, a very good indicator of what order of reaction we were talking about. But at the very beginning of this question, I talked a little bit about this wavelength of light, this is blue light, and even if you didn't know that off hand, you would be able to say "well we're studying "blue food coloring, they probably picked "a wavelength of light that gets absorbed by blue." But if we now care about red, well we would probably want to use a wavelength of light that is optimally absorbed by red, so a red wavelength of light, which will be a lower wavelength of light. So, change the wavelength of light, change the wavelength to be suitable, suitable for absorbance, or absorption by red coloring, red coloring. Or you could say you could lower the wavelength of light or the wavelength of light should be red part of the spectrum to match the red food coloring. Everything else seems completely reasonable.