1. Measurement Chapter 2

2. Units in Lab In lab we cannot always measure in SI units. In lab we cannot always measure in SI units.Mass Grams (g) Volume Milliliters (mL) Temperature Celsius (C) Length Centimeters (cm) or millimeters (mm)

3. SI Units Quantity Base Unit Time Second (s) Length Meter (m) Volume Liter (L) Mass Gram (g) Temperature Kelvin (K) *Amount of Substance *Mole (mol) * We will study the mole during the 2 nd half of the course

4. Derived Units A combination of base units forms a derived unit A combination of base units forms a derived unit –Ex. Density = mass/volume –Mass = g and volume = L, then the unit for density is g/L

5. Accuracy vs Precision Accuracy is closeness to the true measurement. Accuracy is closeness to the true measurement. Precision is getting same measurement repeatedly. Precision is getting same measurement repeatedly. Think of playing darts... Think of playing darts... –What would be accurate? –What would be precise? –What would be both?

6. Significant Figures Indicate how accurate a measurement is. Indicate how accurate a measurement is. The more significant figures the more accurate. The more significant figures the more accurate. Significant figures come from measurements. Significant figures come from measurements. We need rules if we don’t make the measurements. We need rules if we don’t make the measurements.

7. Significant Figure Rules All non-zero digits are significant. All non-zero digits are significant. Zeroes are significant if: Zeroes are significant if: –Between two significant figures (middle zeroes) –Follow a decimal point AND a significant figure (trailing zeroes) Zeroes before significant figures are NEVER significant (preceding zeros) Zeroes before significant figures are NEVER significant (preceding zeros)

8. How many significant figures do the following have? 1. 250.0 g 2. 500 mL 3. 0.0057 kg 4. 6008 cm 4124

9. Using Significant Figures in Solving Problems (Rounding) When adding or subtracting: When adding or subtracting: –Round to least number of decimal places When multiplying or dividing: When multiplying or dividing: –Round to least number of significant figures

10. Example 1 What is the mass of a marble if the mass of a marble and a beaker together is 77.89g and the mass of the beaker alone is 70.7g? What is the mass of a marble if the mass of a marble and a beaker together is 77.89g and the mass of the beaker alone is 70.7g? 77.89 g -70.7 g 77.89 g -70.7 g 7.19 g, what’s the answer rounded to correct significant figures? 7.19 g, what’s the answer rounded to correct significant figures? 7.2 g 7.2 g

11. Example 2 Calculate the volume of an object that has the following dimensions: 3.4 cm by 30 cm by 0.220 cm. Calculate the volume of an object that has the following dimensions: 3.4 cm by 30 cm by 0.220 cm. 3.4 cm x 30 cm x 0.220 cm = 22.44 cm 3 3.4 cm x 30 cm x 0.220 cm = 22.44 cm 3 What’s the answer rounded to correct significant figures? What’s the answer rounded to correct significant figures? 20 cm 3 20 cm 3

12. Percent Error Tells how far off from the accepted value your value is (experimental) as a percentage. Tells how far off from the accepted value your value is (experimental) as a percentage. Percent error has a positive value if the accepted value is greater than the experimental value. Percent error has a positive value if the accepted value is greater than the experimental value. Percent error has a negative value if the accepted value is less than the experimental value. Percent error has a negative value if the accepted value is less than the experimental value.

13. Example Problem A student measured the volume of a liquid to be 45.5mL, but the actual volume is known to be 48.00mL. What is the student’s percent error? A student measured the volume of a liquid to be 45.5mL, but the actual volume is known to be 48.00mL. What is the student’s percent error? 48.00-45.5 x 100 = 5.21% 48.00-45.5 x 100 = 5.21% 48.00 48.00

14. Numbered Heads Together A student calculates the density of a substance at 1.40 g/mL. The correct, or accepted, value of the density is 1.30 g/mL. What is the percent error of the student’s measurement? A student calculates the density of a substance at 1.40 g/mL. The correct, or accepted, value of the density is 1.30 g/mL. What is the percent error of the student’s measurement?

15. Density Density is mass per unit of volume. Density is mass per unit of volume. A sample of aluminum metal has a mass of 8.4 g. The volume of the sample is 3.1 mL. Calculate the density of aluminum. A sample of aluminum metal has a mass of 8.4 g. The volume of the sample is 3.1 mL. Calculate the density of aluminum. Density=2.7 g/mL Density=2.7 g/mL Note: 1 mL = 1 cm 3 Note: 1 mL = 1 cm 3

16. Numbered Heads Together Density is mass per unit of volume. Density is mass per unit of volume. What is the mass of 5.6 mL of gold which has a density of 19.3g/mL What is the mass of 5.6 mL of gold which has a density of 19.3g/mL D = mass volume D = mass volume 19.3g/mL = x 19.3g/mL = x 5.6 mL 5.6 mL Cross multiply to solve for x. Cross multiply to solve for x. x = 110 g x = 110 g Why not 108g? Why not 108g?

17. How would you find the density? A rectangular cube of metal. A rectangular cube of metal. –Volume: –Mass: A liquid. A liquid. –Volume: –Mass: A rock. A rock. –Volume: –Mass:

18. Temperature We measure temperature in Celsius, but the SI unit for temperature is Kelvin…so there will be instances where we will need to convert. We measure temperature in Celsius, but the SI unit for temperature is Kelvin…so there will be instances where we will need to convert. Kelvin = C + 273 Kelvin = C + 273 Celsius = K - 273 Celsius = K - 273

19. Converting Units (Metric System) 1g = 0.001 kg 1g = 0.001 kg 1 g = 100 cg 1 g = 100 cg 1 g = 1000 mg 1 g = 1000 mg Can switch any unit for grams Can switch any unit for grams Conversion Factor: any 2 quantities that are equal can create a conversion factor. Conversion Factor: any 2 quantities that are equal can create a conversion factor.

20. Example Problem How many milliliters are in 0.50 L? How many milliliters are in 0.50 L? 0.50L x = 0.50L x = This is a conversion factor 1000 mL 1L 500mL

21. Another example How many kilograms are in 750g? How many kilograms are in 750g? 750g x = 750g x = 0.001kg 1g 0.75g

22. Try these 1. How many L are in 1650mL? 2. How many seconds are in 30cs? 3. How many km are in 5.76m? 4. How many mg are in 23g?

23. Let’s try another type of problem using factor label… How many seconds are in 5 days? How many seconds are in 5 days? 5 days x x x = 5 days x x x = 24 h 1 day 60 min 1h 60 s 1 min 432000 s

24. You try this one How many days are in 7400 min? How many days are in 7400 min? 7400 min x _1h__ x 1 day = 5.1 days 60 min 24 h