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Chapter 1: Problem 39

Three students \((A, B,\) and \(C)\) are asked to determine the volume of a sample of ethanol. Each student measures the volume three times with a graduated cylinder. The results in milliliters are: \(\mathrm{A}(87.1,88.2,\) 87.6)\(; \mathrm{B}(86.9,87.1,87.2) ; \mathrm{C}(87.6,87.8,87.9) .\) The true volume is \(87.0 \mathrm{~mL}\). Comment on the precision and the accuracy of each student's results.

Short Answer

Expert verified
Student B's measurements are the most accurate as their average is closest to the true value, and both students B and C are the most precise as their measurements have the smallest range.

Step by step solution

01

Calculate the Average for Each Student

Calculate the average of each students' measurements. For student A, it's \((87.1+88.2+87.6) / 3 = 87.63\) mL. For student B, it's \((86.9+87.1+87.2) / 3 = 87.07\) mL. For student C, it's \((87.6+87.8+87.9) / 3 = 87.77\) mL.
02

Evaluate the Accuracy

Now compare each average to the true value. The closer the average is to the true value, the more accurate the measurements are. Student A's average is 0.63 mL above the true value, student B's average is 0.07 mL above the true value, and student C's average is 0.77 mL above the true value. Student B's measurements are the most accurate as the difference is least.
03

Evaluate the Precision

Precision involves looking at how close the measurements are to each other. Measure the range (difference between the highest and the lowest measurement) for each student. For student A, it's \(88.2-87.1=1.1\) mL. For student B, it's \(87.2-86.9=0.3\) mL. For student C, it's \(87.9-87.6=0.3\) mL. Both students B and C are the most precise as the range is smallest.

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Most popular questions from this chapter

The men's world record for running a mile outdoors (as of 1999 ) is 3 min 43.13 s. At this rate, how long would it take to run a \(1500-\mathrm{m}\) race? \((1 \mathrm{mi}\) \(=1609 \mathrm{~m} .)\)

The unit "troy ounce" is often used for precious metals such as gold (Au) and platinum ( \(\mathrm{Pt}\) ). ( 1 troy ounce \(=31.103\) g.) (a) A gold coin weighs 2.41 troy ounces. Calculate its mass in grams. (b) Is a troy ounce heavier or lighter than an ounce? ( \(1 \mathrm{lb}=\) \(160 z ; 1 \mathrm{lb}=453.6 \mathrm{~g} .)\)

You are given a liquid. Briefly describe steps you would take to show whether it is a pure substance or a homogeneous mixture.

Carry out the following operations as if they were calculations of experimental results, and express each answer in the correct units with the correct number of significant figures: (a) \(5.6792 \mathrm{~m}+0.6 \mathrm{~m}+4.33 \mathrm{~m}\) (b) \(3.70 \mathrm{~g}-2.9133 \mathrm{~g}\) (c) \(4.51 \mathrm{~cm} \times 3.6666 \mathrm{~cm}\) (d) \(\left(3 \times 10^{4} \mathrm{~g}+6.827 \mathrm{~g}\right) /\left(0.043 \mathrm{~cm}^{3}-0.021 \mathrm{~cm}^{3}\right)\)

A pycnometer is a device for measuring the density of liquids. It is a glass flask with a close-fitting ground glass stopper having a capillary hole through it. (a) The volume of the pycnometer is determined by using distilled water at \(20^{\circ} \mathrm{C}\) with a known density of \(0.99820 \mathrm{~g} / \mathrm{mL}\). First, the water is filled to the rim. With the stopper in place, the fine hole allows the excess liquid to escape. The pycnometer is then carefully dried with filter paper. Given that the masses of the empty pycnometer and the same one filled with water are \(32.0764 \mathrm{~g}\) and \(43.1195 \mathrm{~g},\) respectively, calculate the volume of the pycnometer. (b) If the mass of the pycnometer filled with ethanol at \(20^{\circ} \mathrm{C}\) is \(40.8051 \mathrm{~g},\) calculate the density of ethanol. (c) Pycnometers can also be used to measure the density of solids. First, small zinc granules weighing \(22.8476 \mathrm{~g}\) are placed in the pycnometer, which is then filled with water. If the combined mass of the pycnometer plus the zinc granules and water is \(62.7728 \mathrm{~g}\). what is the density of zinc?
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