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blue food coloring can be oxidized by household bleach which contains hypochlorite household bleach we usually consume 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 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 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 through the reaction all right the student used data from the study to generate the graphs below so we're graphing see the vertical axis we have absorbance and you could view absorbance if we're 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 color we'd have a low absorbance so you could view this as a 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're the natural log of absorbance relative to time here one over absorbance relevant a 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 respect to the food blue food coloring so let's think let's up them a little as 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 pendant of the concentration I'll just say of the coloring concentration of the coloring is that the case here 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 stoped the slope gets less and less steep as 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 Natura 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 going to go into it takes a little bit of calculus and even a little bit of basic differential equations to to realize it but this is a giveaway for a first order for a first order reaction so in a first order 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 it's 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 and change of concentration of our coloring with respect to time and if this looks completely unfamiliar to you you've never taken a calculus class ignore what I'm about to say for the next twenty seconds this needs to be proportional to the concentration of coloring coloring all right Co L dot for short and if you solve 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 the second-order if you plot 1 over absorbance versus time or 1 over the concentration because as we said absorbance is a is a proxy for the concentration of our food coloring well then this would be a linear plot but as you can see it is not but this is a linear plot then you could say 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 the 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 all right when the solutions are combined the student observes that the reaction mixture reaches an absorbance near zero to 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 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 temperatures just going to make the reaction happen even faster though the molecules are going to bump into each other with more energy and more land and more frequently and so that's that's just going to make that's going to get you to colorless even faster so that's that's going to go in the opposite direction so we can rule that out increasing the concentration of blue food coloring or well that that makes sense well they did say blue food growing but I'm assuming it's blue whatever because well if it's getting clear too fast well if you had if you had more food coloring well then it's just going to it's it's going to 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 that's getting the is reacting with the food coloring to make it clear so if you increase this concentration you're going to get clearer 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 and they say circle the one proposed modifications let me make sure I'm circling it I guess I'm more rectangle in it but you get the idea that correct the problem and explain how that modification increases the time for the reaction mixture to reach and absorb it's in absorbance near zero so I'll write more coloring more coloring results in higher initial absorbs absorbance higher initial initial Abbe sorbents and and thus and thus more time more time for mixture to reach to reach near zero absorbance Abbas or Vince number that I really have trouble saying all right Part C and 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 is as we saw a pretty a very good indicator of what order of a reaction we were talking about but at the very beginning of this question we talked a little bit about this wavelength of light this is blue light and if you didn't know that offhand you would be able so while we're studying blue food coloring they probably picked a wavelength of light that gift 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 a or by red so of red wavelength of light which will be a lower wavelength of light so change change the wavelength of light change the wavelength to be suitable suitable for absorbance EPS or or absorption by red colouring red colouring or you could say you could lower the wavelength lower the wavelength the light should be in the red part of the spectrum to match the red food coloring everything else seems completely reasonable
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