Here it states 2 students wish to prepare a stock solution for their lab experiment. Student A uses an uncalibrated pipette that delivers 50.00 ± 0.02 ml to deliver 200 ml to a container. Student B uses a calibrated pipette that delivers 40 ± 0.01 ml to deliver 200 ml to a container. So, we're asked to calculate the absolute uncertainty in each of their deliveries. Alright. So the big thing here is one is using a pipette that is uncalibrated while the other one is using one that is calibrated. This difference means that we're going to have to take different approaches to get to our answer. So, we have Student A here, and then we'll have Student B here. Alright, so if we're looking, it says Student A needs to get to 200 ml's. So that is our goal. And we’re doing it in multiples of 50. So we say to ourselves, okay, I would have to do it 4 times in order to get to 200 ml's. So that's 50 ± 0.02 ml's and you add that 4 times. Okay, so then we add that 4 times. Put this in. So adding that 4 times will get us to the 200 that we want plus last one. Alright. So we know that if we're adding the measurements that comes out to 200, and when it's uncalibrated, we don't do what we normally would to figure out the absolute uncertainty at the end. Because it's uncalibrated, that means my uncertainties are additive. That means I can just add them together. So we're just gonna do ± 0.02 and add it to one another. So at the end, that's gonna give me ± 0.08 ml's. So remember, when it's uncalibrated, we're gonna just add them together. In Student B though, it's a calibrated pipette, so we're going to have to do what we are normally going to do when adding up uncertainties with one another. Here we're doing it in multiples of 40. Again, our goal is to get to 200. So we do 40 each time, that means we'd have to do it a total of 5 times in order to get to 200 mls. So it's 40 ± 0.01, and actually here, for this answer, following the real rule, it’d actually be 200.00 because there are 2 decimal places here. Alright. So then we're adding all of these together. We have to do it 5 times. So adding it 5 times. Okay. So we have that. So we added that 5 times. Now, we know that in terms of the overall volume at the end, we know it's going to add up to 200 ml's, but then we have to determine what our overall absolute uncertainty will be. Remember, when we're adding or subtracting to figure out our new absolute uncertainty, We're going to take the square root, take each one of these absolute uncertainties, square them and then add them all together. Okay. So adding them all up together gives me 5.0×10-4 which just comes down to 0.022361 as my new overall absolute uncertainty. And here, it reduces down to 0.02. So because this has 2 decimal places in it, that means my final volume of 200 also has to have 2 decimal places in it. So here would be 200.00 ± 0.02 ml. So what these two answers are showing us is that by calibrating your pipette, you decrease your absolute uncertainty, which means that you're going to get a final volume that is closer to your desired amount of 200 ml's. When it's uncalibrated, there's a much bigger variation in the final amount that you're going to get. In that case, it would be ± 0.08. So it's 4 times, of a difference in terms of your final volume. So again, out of these 2 students, Student B would be the more correct student because they're using a calibrated pipette, which helps us to get a final answer that's closer to our true value of 200 ml's. Now that we've seen this, attempt to do the practice question that's left on the bottom. We've determined the volume of our 2 students, but now we're asked to figure out the molarity. Remember, molarity is just simply moles over liters. Knowing that is the key to answering this question correctly. Also, one more thing. Since it's liters and these are in milliliters, you'd have to change these values into liters. Remember, that means you divide them by 1000. Both the measurement and the absolute uncertainty will be divided by 1000 so that this becomes liters at the end. Put all those numbers together. Find out what the final answer will be. If you're stuck, don't worry. Just come back and see how I approach this practice question.
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- 2. Tools of the Trade1h 17m
- 3. Experimental Error1h 52m
- 4 & 5. Statistics, Quality Assurance and Calibration Methods1h 57m
- 6. Chemical Equilibrium3h 41m
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- 9. Polyprotic Acid-Base Equilibria2h 17m
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3. Experimental Error
Uncertainty
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