Hydrogen cyanide, HCN, is a poisonous gas. The lethal dose is approximately 300 mg HCN per kilogram of air when inhaled. (c) HCN forms when synthetic fibers containing Orlon® or Acrilan ® burn. Acrilan® has an empirical formula of CH2CHCN, so HCN is 50.9% of the formula by mass. A rug measures 3.5 * 4.5 m and contains 850 g of Acrilan® fibers per square yard of carpet. If the rug burns, will a lethal dose of HCN be generated in the room? Assume that the yield of HCN from the fibers is 20% and that the carpet is 50% consumed.

Video transcript

Hello everyone in this video we're going to be doing dimension analysis and a slightly longer and more complicated problem. But not to worry, we can always break this down to get in baby steps. So first I want to go ahead and write out the information I'm given just to make sure that I'm using all the material that the problem provides. And also it could definitely guide us on doing our dimensional analysis. So first I want to write out what is given by the problem. So first here I can see we have The 12% of our burnt material. And next piece of information will be the one metric ton of waste. This is how much waste we are starting with. So one the metric ton of waste and this is our starting Next piece of information. We have the 35% yield of Dioxin. Again this is our yield. Okay, last piece of information we're given is for every one g of plastic it produces AIDS micrograms of dioxin. Alright. And the whole purpose or goal and what we're trying to find from this problem is going to be how much dioxin produced. So how much dioxin or in other words, how much is the mass of a toxin that's produced? So mass of dioxin. So I smile to go ahead and like I said right out whatever given that we're trying to find this scan of will make a better road map for us to do these types of problems, especially the longer and more complicated ones. So first like I said I'm going to start off with my one metric ton of waste here, I'm going to go ahead and scroll down to give us a little bit more writing group. Starting off the dimensional analysis, we have one metric ton of waste. So first things first, I want to go ahead and actually use my first given information. So I want to point out that whenever we're giving a percentage, You should know that that's also going to be it could be also written as a fraction. So 12% just means 12 over 100. Right? In our case of unit wise, it's going to be 12 or 12 metric tons of plastic on top. So metric ton of plastic, which is not as bad as P. And then for the denominator it's going to be metric ton of W for waste. All right. So we can see that if we use this right here, we can go ahead and actually cancel out the metric tons of waste. Okay, So let's go ahead and plug that in then. So to cancel the metric ton of waste, we want to put that denominator as our denominator for the analysis as well. So, 100 metric ton of waste, which is w let's extend this fraction. Bar I want to multiply on top will be our metric ton of plastic, abbreviated as P. So again, you see that the metric kind of waste can be canceled out nicely continuing on argument analysis. We can then convert our metric tons of plastic into kilograms of plastic. So for everyone, metric ton of plastic There's going to be 1000 kilograms of plastic. And you see here metric tons of plastic can be very nicely continuing on. I'm going to go ahead and convert the kilograms of plastic into grams of plastic. I'll tell you guys buy soup. So again, we have one kg p. for plastic for every one kg we have 10 to the third grams of plastic. All right. I try very smaller for the next version and then we'll continue down below. Alright, so the reason why I want to go ahead and convert the kilograms into grams is that as you can see right here, we have this conversion of one g of plastic for every eight micrograms of dioxin. So, if we go ahead and use this, we be able to cancel out the grams of plastic and continue on with our dimension analysis. So, I like to think of dementia analysis as like a puzzle piece. You're essentially kind of just mixing and matching the conversions and canceling each other out. So, that's what I'm kind of thinking about when doing this type of problem. So now that we have converted our kilograms of plastic into grams of plastic, we can use this bit of information and use it as our conversion factor. So on the bottom we have our one gram of P. For plastic. And then on top we have our eight micrograms of dioxin. What does abbreviate the dioxin two D. And you see for our grounds of plastic it can be canceled out. So now um continuing on in the next row So we have our micrograms dioxin and now I'm gonna go ahead and convert the micrograms in two mg. So everyone Milica We have our 10 to the third of the micrograms. And can see here obviously the micrograms can we cancel out very nicely in the last bit of our Given information? We see that we have the 35% of dioxin. Let's go ahead and actually just multiply this by 35%. This is our last bit of information that we're given. So once we have put all of this into the calculator you can see that we will end up with milligrams of our dioxin. They should also have the dioxin and this is going to be our final value. And the answer for this problem, thank you so much for watching