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blue food coloring can be oxidized by household bleach which contains hypochlorite ion or ocl - to form colorless products as represented by the equation above so we have this equation this equation where we have blue food coloring which has this chemical formula and it's reacting with bleach or hypochlorite and it's making colorless products so we're getting this color change from blue to colorless a student used a spectrophotometer set at a wavelength of 625 nanometers to study the absorbance of the food coloring over time during the bleaching process in the study bleach is present in large excess and I will underline that because that's important it's a present in large excess so that the concentration of hypochlorite is essentially constant throughout the reaction the student used data from the study to generate the graphs below so we'd like to answer part 8 and Part A based on the graphs above what is the order of the reaction with respect to the blue food coloring so we have a lot of information here you have these three graphs here we have if we write absorbance as a we're looking at the concentration of a over time we're looking at the Ln of eight over time the natural log and we are also lastly looking at one over the concentration eight over time so we would like to know what is the order of the reaction with respect to our blue my first instinct when I see this problem is actually to be a little bit panicky because hey we have we have a lot of information here so how do we deal with it we also have a little bit more information for this problem we also have the equation sheet so this is a part of the equation sheet that's relevant for this problem so it's all of the equations that have to do with kinetics which is looking at reaction rates so that is what we're looking at here so we have three possible things that might be helpful for this problem maybe not right so we have this first equation which gives us the first order integrated rate law we have the second equation which gives us the second order integrated rate law and we have this third equation which is actually an equation for the half-life so it's saying half-life is 0.693 divided by K and that is a half-life for a first-order reaction and the important thing to remember here which will come up again in a second is that this is a constant because K is a constant so our half-life is also a constant for a first-order reaction so that's the information we have let's look back at our graphs we're gonna start by looking at just the first graph it turns out we can get a lot of information just by looking at the concentration of a over time so if we look at this first graph and we look at the concentration of our blue stuff going down over time we can see immediately that this is not linear so the fact that it's not linear immediately tells us it's not zero order if it was zero order we would expect to see a straight line which I will draw with a dotted line because that's not actually what we're seeing so it's not zero order we can also get some more information by looking at this one graph we know it's not zero order can we tell from this first graph if it's first-order and the answer is we actually can if you remember from looking at the equations sheet we said that first-order reactions so for first-order reactions we would you know and I'd say this is maybe one of the first the most important things about first-order reactions is that half-life is constant so that means that the Khans the time it takes for the concentration to go down to half of what it was is the same no matter what your initial concentration is no matter what point in your class in your reaction you're you're at so that's something we can actually investigate just by looking at this first graph we can see how much time it takes to get to half the concentration and see if that's something that changes over time so for example if we start with 0.8 right here half of 0.8 is 0.4 so we can see how much time it takes to get from a point eight two point four which is right here and if we let go down we can see it takes 20 seconds to go from to go to have the concentration from point eight starting at point eight absorbance units we can look at the half-life now to go from point four two point two so if we go from point four to point 2 and I will change colors so going from 0.4 to 0.2 takes another 20 seconds and so we can do this again and again we could go for point two two point one we'll just see the continuation of a pattern here which is that we can see that it always takes twenty seconds to have the concentration and so the fact that half-life is constant based on graph one immediately tells us that our reaction is first-order because or half-life is constant we don't even have to look at any of the other graphs there is another way you could do this problem you might remember based on the equations that we have or based on just equations you know off the top of your head so one reason we know and one reason we could say this is first orders because P 1/2 is constant the other reason why we know this is first-order is when a reaction is first-order in your reactant you know that graphing Ln of your reaction versus time gives you a straight line and we can see from graph two that this is the case so we have these two pieces of evidence from graph one and graph two that tell us that this particular reaction is actually first order with respect to the blue food coloring

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