2015 AP Chemistry free response 5 | Kinetics | Chemistry | Khan Academy

Blue food coloring can be oxidized by household bleach, which contains hypochlorite. Household bleach would usually consider being sodium hypochlorite to form colorless products, as represented by the equation above. So this is the food coloring reacts with the hypochlorite produces a colorless 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. Since we're talking about blue food coloring, I'm guessing that this is a wavelength of light that is blue, since that's going to be optimally absorbed by blue food coloring in the study. Bleach is present in large excess, so the concentration of hypochlorite is essentially constant throughout the reaction.

All right, the student used data from the study to generate the graphs below. So we're graphing.

On the vertical axis, we have absorbance. You can view absorbance; if we have a high concentration of blue food coloring, then we're going to have a high absorbance, and if we have a low concentration of blue food coloring, we're going to have a low absorbance. So you could view this as a proxy for the concentration of food coloring.

Here they just plotted absorbance relative to time. Here’s the natural log of absorbance relative to time, and here one over absorbance relevant relative to time. Now let’s look at the question here: based on the graphs above, what is the order of the reaction with respect to the blue food coloring?

So let's think of a little super fast primer. 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 concentration of blue food coloring. 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 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 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 plotted absorbance, which is once again the proxy for concentration of food coloring versus time, we would expect to see something more like a line. 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. I'm not going to go into it; it takes a little bit of calculus and even a little bit of basic differential equations to realize it, but this is a giveaway for a first-order reaction.

In a first-order reaction, the rate is proportional to the concentration. Let me just write it as proportional to the concentration since we're saying with respect to the blue food coloring. It is proportional to the concentration of blue food coloring.

I'll just write coloring for short and I'll throw in a little calculus here. You could say the rate of reaction, which is the rate and change of concentration of our coloring with respect to time. If this looks completely unfamiliar to you and you've never taken that class, ignore what I'm about to say for the next 20 seconds. This needs to be proportional to the concentration of coloring.

All right, Co for short. If you solve this, you would see that the natural log of the concentration of coloring with respect to time is going to give you a line. This is a key signature of a first-order reaction. But you can even see it 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 reaction, if you plot one over absorbance versus time or one over the concentration, because 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. If this were a linear plot, then you could say, hey, maybe this is a second order.

But just to answer their question, this is a first-order reaction with respect to blue food coloring.

All right, let's do part B now. The reaction is known to be first order with respect to bleach. All right, 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.

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.

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 going to bump into each other with more energy and more frequently, and so that's just going to get you to colorless even faster. So we can rule that out.

Increasing the concentration of blue food coloring, or that makes sense. Well, they didn't say blue food coloring, but I'm assuming it's blue, whatever. Because if it's getting clear too fast, if you add more food coloring, then it's just 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 a thing that's getting the food is reacting with the food coloring to make it clear. So if you increase this concentration, you're going to 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.

The one that we like is definitely increasing the concentration of the food coloring. And they say circle the one proposed modification. Let me make sure I'm circling it; I guess I'm more rectangular it, but you get the idea that corrects the problem and explains how that modification increases the time for the reaction mixture to reach an absorbance near zero.

So I'll write: more coloring results in higher initial absorbance; higher initial absorbance, and thus more time for the mixture to reach near zero absorbance.

All right, 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 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 pretty good indicator of what order of a 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.

Even if you didn't know that offhand, 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, we would probably want to use a wavelength of light that is optimally absorbed by red.

So, of red wavelength of light, which will be a lower wavelength of light. Change the wavelength of light to be suitable for absorbance by red coloring. You could say the wavelength of light should be in the red part of the spectrum to match the red food coloring. Everything else seems completely reasonable.