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Problem(Set(03(–(Measurements! Chem!105! 1. (a) Define precision and accuracy (1 sentence each). Precision: The degree to which a measurement can be repeated and give consistent results. Accuracy: How close a measured result is to the real value. (b) To test the precision and accuracy of a weight scale in the laboratory, you take a small metal block that is known to be exactly 1.000 g and weigh it three times on the scale. Three measurements are reported as follows: 0.843 g, 0.842 g, and 0.843 g. Is this scale precise, accurate, both, or neither? Explain your choice in 1 sentence. The scale is precise because the measurements are close in value, but it is not accurate since the values are not close (within 1%) to the real value. 2. If the real weight of an object is 100 grams, state whether the following measurements are precise, accurate, both, or neither. Precision is the degree to which a measurement can be repeated and give consistent results. Accuracy is how close a measured result is to the real value. For this class, if the average value of a measurement is within 1% of the actual value, it can be considered accurate. a. 112 g, 118 g, 106 g neither precise nor accurate i. These measurements are too far away from the real value to be accurate. The measurements are not consistent either, therefore they are not precise. b. 99.7 g, 100.1 g, 100.2 g precise and accurate i. The values are accurate because all measurements (and their average value) is close to the real value of 100 g, and precise because all three measurements are similar. c. 110 g, 111 g, 110.5 g precise, not accurate i. The measurements are precise because all three values are close together. They are not accurate because they (and their average) are all far from the real value. d. 105 g, 93 g, 102 g accurate because the average value (likely the number that would be reported) is 100g. However, not precise because they are not close together. e. 105 ± 2 g neither i. The reported/average value is 1% away from the actual value, so by the standards of this class mentioned above it’s not very accurate. An uncertainty of ± 2 means the individual measurements were not close together (if there were 2 measurements, they could have been 99 and 103 g.) f. 100.5 ± 0.2 g precise and accurate i. The reported/average value is within 1% of the actual value, and the uncertainty is less than 0.5% of the actual value. 3. How many sig figs are in the following number? 0.0509200 6 4. Perform the following calculations for measured numbers. Give your answers in scientific notation with the correct units and number of significant figures. a. 124 mg + 316 mg 4.40´102 mg. In addition and subtraction, the answer is significant to the same decimal place shared by every term in the calculation. Since both numbers are significant to the ‘ones’ place, the answer will be significant to the ones place.

b. 613 µL + 582 µL 1.195´103 µL. Even though the two numbers being added have only three significant figures, the answer has four. With addition and subtraction, we are only concerned with the last decimal place shared by all terms in the calculation. c. 4´10–3 mL – 2´10–5 mL 4´10-3 mL. Because 4´10–3 is only significant to the thousandths place (0.004), the answer is limited to this place. It may seem strange that our answer is the same as the original number. This is because 2´10–5 is much smaller compared to 4´10–3, and will not affect its value when subtracted. d. 85 ng ´ 34 ng 2.9´103!ng2.!In!multiplication!and!division,!the!answer!has!the!same! number!of!significant!digits!as!the!value!with!the!fewest.!!Since!thirty-four!has!only!two! significant!figures,!our!answer!can!only!have!two. e. 6.31´104 pm!´ 3.536 ´105 pm 2.23´1010!pm2.!Because!6.31´104!only!has!three!significant! figures,!so!must!the!answer.! f. 25.34 cm ÷ 1.55´10–4 cm 1.63´105. The 1.55´10–4 limits our answer to three sig. figures. 5. Perform the following calculations for measured numbers. Convert your answers to the base unit for that quantity (m, kg, m3, kg/m3). Give your answers with the correct number of significant figures. a. 77.3 g + 41.7 g = 119.0 g = .1190 kg or 1.190´10-1 kg b. 123.4 Gm – 68.93 Gm = 54.5 Gm = 5.45´1010 m c. 21.7 cm ´ 9300 cm2 = 200000 cm3 = 0.20 m3 or 2.0´10-1 m3 d. (2.76´103)(7.4´102) nL = 2.0´106 nL = 2.0´10-3 L e. 8.1´10–1 µm – 3.7´10–8 µm = 8.1´10–1 µm = 8.1´10–7 m f. 387 pg ÷ 2´10–2!mL!=!19350!pg/mL!=!1.935´10-11!kg/mL!=!2´10-5!kg/m3 6. Comfortable room temperature is about 72°F. Body temperature is about 98°F. Water freezes at 32°F and boils at 212°F. The lowest temperature ever recorded at sea level (by a human) was −128.6 °F at the Soviet Vostok Station in Antarctica, on July 21, 1983. Convert these temperatures to °C and K. *** MAKE SURE IT’S 273.15 K*************** 5 𝑇 ˚𝐶 = [𝑇 ˚𝐹 − 32] 9 -

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𝑇 ˚𝐶 = [ 72 − 32] → 𝑇 ˚𝐶 = . [40] → 𝑇 ˚𝐶 = 22 → 22˚𝐶 + 273 = 295𝐾 . 𝑇 ˚𝐶 = [ 98 − 32] → 𝑇 ˚𝐶 = . [66] → 𝑇 ˚𝐶 = 37 → 37˚𝐶 + 273 = 310𝐾 . 5 5 𝑇 ˚𝐶 = [ 32 − 32] → 𝑇 ˚𝐶 = [0] → 𝑇 ˚𝐶 = 0 → 0˚𝐶 + 273 = 273𝐾 9 9 5 5 𝑇 ˚𝐶 = [ 212 − 32] → 𝑇 ˚𝐶 = [180] → 𝑇 ˚𝐶 = 100 → 100˚𝐶 + 273 = 373𝐾 9 9 5 5 𝑇 ˚𝐶 = −128.6 − 32 → 𝑇 ˚𝐶 = −160.6 → 𝑇 ˚𝐶 = −89.22 → −89.22˚𝐶 + 273 9 9 = 184𝐾 7. The diameter of a US dime is 17.9 mm, and the diameter of a silver atom is 2.88 Å. How many silver atoms could be arranged side-by-side across the diameter of a dime? (10 Å = 1 nm). 1𝑚 1𝑛𝑚 10Å 1:𝐴𝑔:𝑎𝑡𝑜𝑚 17.9𝑚𝑚:×: :× × × = 6.22×10D :𝐴𝑔:𝑎𝑡𝑜𝑚𝑠 =. 1000𝑚𝑚 1×10 𝑚 1𝑛𝑚 2.88:Å

8. Which of the following represents the largest amount of matter? Convert them all to the same unit (g) and then compare a. 3.0 ´ 10–1 Mg b. 4.5 ´ 102 mg c. 1.0 ´ 107 µg d. 2.0 ´ 108 ng e. 2.5 ´ 1013 fg 9. Lead metal (11.3 x 109 ng/ml), tungsten (0.019 kg/ml), and liquid mercury (13.5 g/cm3) are all very dense. If chunks of lead and tungsten are placed in liquid mercury, will they sink or float? Does it matter what size the chunks are? Why or why not? First convert all of the densities to a density with common units. If the substance is more dense than mercury, it will sink regardless of the size of the chunks. Also, remember that 1 mL is equal to 1 cm3. 1×10=. 𝑔 11.3𝑔 Lead:::11.3:x:10. :ng:× = 11.3:𝑔 → 𝐷 = 𝑚𝐿 1:𝑛𝑔 → 𝑇ℎ𝑖𝑠:𝑖𝑠:𝑙𝑒𝑠𝑠:𝑑𝑒𝑛𝑠𝑒:𝑡ℎ𝑎𝑛:𝑚𝑒𝑟𝑐𝑢𝑟𝑦, 𝑠𝑜:𝑖𝑡:𝑤𝑖𝑙𝑙:𝑓𝑙𝑜𝑎𝑡 1000:𝑔 19:𝑔 Tungsten:::.019:kg:× = 19:𝑔 → 𝐷 = 𝑚𝐿 1:𝑘𝑔 → 𝑇ℎ𝑖𝑠:𝑖𝑠:𝑚𝑜𝑟𝑒:𝑑𝑒𝑛𝑠𝑒:𝑡ℎ𝑎𝑛:𝑚𝑒𝑟𝑐𝑢𝑟𝑦, 𝑠𝑜:𝑖𝑡:𝑤𝑖𝑙𝑙:𝑠𝑖𝑛𝑘 10. The price of gold in May was $1,228.40 per ounce (1 ounce = 28.35 g). A typical gold bar such as those shown here has a mass of 12.4 kg. a. How much would one of these bars of gold cost? 1000𝑔 1:𝑜𝑧. $1,228.40 = $537,000 12.4:𝑘𝑔:𝐴𝑢 :×: × × 1:𝑜𝑧. 1:𝑘𝑔 28.35:𝑔 b. The density of gold is 19.3 g/cm3. Suppose a certain gold wedding ring displaced 0.55 mL of liquid when dropped in a glass of sparkling cider. How much did this wedding ring cost? (assuming you paid the market price of gold) 𝑚 19.3𝑔 𝑚 1:𝑜𝑧. $1,228.40 𝐷= → = → 𝑚 = 10.6𝑔 → 10.6𝑔:× × = $459:𝑜𝑟:$460 𝑉 𝑚𝐿 . 55𝑚𝐿 28.35𝑔 1:𝑜𝑧. Note: For problems concerning money, you do not need to round, since you have an exact value of $....