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Chapter 2 Section 3 Using Scientific Measurements

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Objectives Distinguish between accuracy and precision Determine the number of significant figures Perform mathematical operations involving significant figures Convert measurements into scientific notation Distinguish between inversely and directly proportional relationships

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Accuracy and Precision (i) Accuracy: refers to how close an answer is to the “true” value Generally, don’t know “true” value Accuracy is related to systematic error (ii) Precision: refers to how the results of a single measurement compares from one trial to the next Reproducibility Precision is related to random error Low accuracy, low precision Low accuracy, high precision High accuracy, low precision High accuracy, high precision

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Significant Figures Non-zero numbers are always significant. For example, 352 g has 3 significant figures. Zeros between non-zero numbers are always significant. For example, 4023 mL has 4 significant figures. Zeros before the first non-zero digit are not significant. For example, 0.000206 L has 3 significant figures. Zeros at the end of the number after a decimal place are significant. For example, 2.200 g has 4 significant figures. Zeros at the end of a number before a decimal place are ambiguous (e.g. 10,300 g).

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Multiplying & Dividing Least # of sig figs in value Example: 4.870 x 3.21 15.6

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Adding & Subtracting Least precise number--usually determined by Least # of decimal places Examples: 2.345 2500. + 0.1__ + 27.3 2.4 2527.

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Rounding Rules If the first digit to be removed is 5 or greater, round UP, 4 or lower, round DOWN. Example: 2.453 rounded to 2 sig figs is 2.5 5.532 rounded to 3 sig figs is 5.53

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Percent Error Percent Error: Measures the accuracy of an experiment Can have + or – value

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Example Measured density from lab experiment is 1.40 g/mL. The correct density is 1.36 g/mL. Find the percent error.

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Used to characterize substances (a measure of “compactness”) and is an intensive property. Defined as mass divided by volume: Units: g/cm 3. Sometimes this is written as g cm –3. NOTE: cm 3 = mL Frequently used as a conversion factor (mass to volume) Density Mass and volume are extensive properties, they are dependant on the amount of substance.

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Bromine is one of two elements that is a liquid at room temperature (mercury is the other). The density of bromine at room temperature is 3.12 g/mL. What volume of bromine is required if a chemist needs 36 g for an experiment? Solution: 11.53 mL Sig fig 12 mL

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What volume is occupied by 461 g of mercury when it’s density is 13.6 g/ mL? Volume from Mass and Density Solution Here we can express the inverse of density as a ratio, 1.00 mL/13.6 g, and use it as a conversion factor. V = 461 g x ––––– = 3.9 mL 1 mL 13.6 g

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A metal ball was found to have a mass of 0.085 kg and a volume of 3.1 mL. Calculate the density of the metal ball in units of g/mL.

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The density of liquid mercury is 13.55 g/cm 3. A mercury thermometer contains exactly 0.800 mL of liquid mercury. Calculate the mass of the liquid mercury contained in the thermometer.

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A glass container weighs 48.462 g. A sample of 4.00 mL of antifreeze solution is added, and the container plus the antifreeze weigh 54.51 g. Calculate the density of the antifreeze solution.

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