From a plot of the concentration–time data in Worked Example 14.9, estimate: (a) the instantaneous rate of decomposition of NO₂ at t = 100 s.

Video transcript

Hey everyone today, we're being given the data for the purification of acetic acid with ethanol and were given the specifically concentration of acetic acid. As time progresses. Given this data, we're asked to plot a graph and calculate the instantaneous rate of the reaction at times 10,000 seconds. And when time is at 25,000 seconds. Now, I've gone ahead and brought in the plotted values. And a very important thing to note is that to find the instantaneous rate of reaction, especially when given a curve like this, we need to find the slope of the tangent line at that specific point on the curve. So let's go ahead and draw the tension line for the 10,000 seconds first. And this isn't exact but it'll look something like this. No. Now, while that's not perfect, I'd say that's pretty close to what we need but to find the slope, since we don't really have a Y intercept and we're dealing with a curve, not a linear line. In this case, we can actually use a variation of the point slope form in order to find the slope X 2 -11. And we'll go ahead and label our smaller values as one in like X one and Y one and our larger ones at X two and Y two. And you'll see what I mean in just a second. So right here why one is equal to 0. and why to Which will be right about here, let's say why two will be equal to 0.6. Similarly, X one will be 5000 And X two will equal 10, plugging this into the formula. Right over here we get that 0.6 -0. divided by 10, -5000. Once simplified Gives us a final value of 4. times 10 to the negative 5th Mueller per second. So this is the instantaneous rate of the reaction. When time is 10,000 seconds we can use a similar process for When time is at 25,000 seconds. Let me go ahead and draw out the tangent line at that point and we'll draw this in red for a little variation. I'd say that's pretty close. So anyways, using the same conventions we can go ahead and find D X one, Y one and X two and Y two for these values. So let's say why one is equal to 0.1 here and why two is about 0.14. Uh X one is equal to 20,000 And X two. musical to 25,000. Plugging this back into the formula will get that M is equal to excuse me, M is equal to 0.14 -0.1 divided by 25, -20000 Which gives us a final answer of 8.0 times 10 to the - Mueller per second. And that is the instantaneous rate of the reaction at time Is equal to 25, seconds and this is Ed T is equal to 10,000 seconds. I hope this helps, and I look forward to seeing you all in the next one.