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Chapter 2 Section 3 Using Scientific Measurements.

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1 Chapter 2 Section 3 Using Scientific Measurements

2 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

3 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

4 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).

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

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

7 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

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

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

10 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.

11 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

12 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

13 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.

14 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.

15 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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