The chemist in Example 1.14 did some further experiments. She found that the pipet used to measu

The chemist in Example 1.14 did some further experiments....

Key Concepts

Measurement Precision

Measurement precision refers to the degree to which repeated measurements under unchanged conditions show the same results. In experimental science, understanding the precision of instruments helps determine if small differences in physical properties can be reliably detected.

Uncertainty Analysis

Uncertainty analysis involves assessing and quantifying the possible errors in measured data. This analysis is critical in deciding whether the experimental uncertainties are small enough to allow a conclusive distinction between similar substances.

Instrument Accuracy

Instrument accuracy is the measure of how close a measurement is to the true or accepted value. High accuracy in instruments such as mass balances and volumetric pipets ensures that experimental measurements can be trusted to differentiate between substances with similar characteristics.

Error Propagation

Error propagation is a technique used to evaluate how uncertainties in individual measurements combine to affect the uncertainty in a calculated result. This concept is essential in experimental design to ensure that the overall precision is sufficient to discern between substances.

Transcript

00:01 Okay, so this question in that had a textbook revisits the interactive example 1 .14 on page 27 of the textbook.

00:12 And the chemist was trying to identify an unknown liquid, so she weighed out a volume, and she has a mass of the substance, and by calculating the density, she was able to conclude that the substance was isopropanol.

00:26 That was as far as the example in the textbook went.

00:29 This problem is telling us, okay, now we have these new uncertainties.

00:34 So she knows now the scientists that the volume error in her pipette is 0 .03 centimeters cubed, and the error in her balance, i'm guessing, is 0 .002 grams.

00:52 So now knowing the error of her system and of her pipettes and her balances and whatever, can we still be certain that the unknown substance is isopropinol? is the error enough to throw in that potentially we might have ethanol instead? you'll notice that the density of ethanol and the density of isopropanol are only different by 0 .004 grams per centimetri cubed.

01:18 They're very, very close together.

01:22 So because ethanol has a greater density, not by a lot, but it's still a greater density, based on the uncertainties here, it will be the upper limit that we're concerned with, right? so is the random error, let's say, the one that's causing the higher limit of uncertainty, is that enough to surpass the density of 0 .789? we could get a range, right? we could take density, take the least dense possibility, and the most dense possibility, calculate those and see the range, but we don't necessarily have to do that.

02:00 So let's get started, right? so i'm talking about the most dense possibility, so the higher range of the densities that we're now having to take into account knowing the error, right? so if we want the density, so i'll call it d high, it's going to have the largest mass and the smallest volume because we want d to be the greatest, right? so within the error, 25.

02:30 0 .03.

02:31 Let's add the error.

02:33 So this is the maximum mass that can be calculated from the sample, right? no, sorry, that's the volume.

02:40 I apologize.

02:42 The highest mass is 19 .627 grams.

02:47 So we're adding 0 .002 to 19 .625 and then the lowest volume is going to be 24 .97 center meters cubed.

02:58 Right.

02:59 So if the error in the balance forces the mass to be the greatest it could possibly be given the uncertainty, the volume is going to be the lowest it could possibly be given the uncertainty, then the density should be the highest...

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