1. Density & Percent Error Unit 1B

2. Density At the conclusion of our time together, you should be able to: 1.Define density 2.Calculate the density of a given object if given the volume and mass 3.Calculate the volume or mass if the density is given with the volume or mass

3. Density Density = mass volume Mass = the amount of matter in an object Volume = the amount of space the object takes up Units = g/mL (liquid) OR g/cm 3 (solid)

4. DENSITY - an important and useful (qualitative) intensive physical property Mercury 13.6 g/cm 3 21.5 g/cm 3 Aluminum 2.7 g/cm 3 Platinum

5. Density Calculations M DV Cover up whatever unit you are solving for, the two units remaining will show you how to solve the problem.

6. Density Pre-Lab (Page 35) 1. Graph the following data on a sheet of graph paper. What variable goes on the x-axis? __________ What variable goes on the y-axis? __________ 2. Make sure to include all “ graph ” features Volume, mLMass, g 0.00.00 2.05.40 5.012.50 10.027.30 15.040.50

7. Density Pre-Lab(Page 35) 3. Determine the slope of your line – use (0,0) as one of your data points. Please show all of your work below: 4. How are the slope of the line from the graph and density related? Explain.

8. Density Calculations Regularly Shaped Solid : mass = balance volume = measure (l x w x h) Irregularly Shaped Solid: mass = balance volume = water displacement

9. Density Calculations Liquid: volume = read graduated cylinder mass = tare graduated cylinder, mass liquid

10. Problem A piece of copper has a mass of 57.54 g. It is 9.36 cm long, 7.23 cm wide, and 0.95 mm thick. Calculate density (g/cm 3 ). M DV

11. Strategy 1. Get dimensions in common units. 2. Calculate volume in cubic centimeters. 3. Calculate the density.

12. SOLUTION 1. Get dimensions in common units. 2. Calculate volume in cubic centimeters. 3. Calculate the density. (9.36 cm)(7.23 cm)(0.095 cm) = 6.4 cm 3 Note only 2 significant figures in the answer!

13. DENSITYDENSITY Density is a (qualitative) intensive property of matter.  does NOT depend on quantity of matter.  like temperature Contrast with (quantitative) extensive property  depends on quantity of matter.  like mass and volume. StyrofoamBrick

14. PROBLEM: Mercury (Hg) has a density of 13.6 g/cm 3. What is the mass of 95 mL of Hg in grams? In pounds?

15. 1.Use density to calculate mass (g) from volume. 2.Convert mass (g) to mass (lb) Need to know conversion factor = 454 g / 1 lb First, note that 1 cm 3 = 1 mL Strategy

16. 1.Convert volume to mass 2. Convert mass (g) to mass (lb) Strategy

17. Learning Check Osmium is a very dense metal. What is its density in g/cm 3 if 50.00 g of the metal occupies a volume of 2.22 cm 3 ? 1) 2.25 g/cm 3 2)22.5 g/cm 3 3)111 g/cm 3

18. Solution 2) Placing the mass and volume of the osmium metal into the density setup, we obtain D = mass = 50.00 g = volume2.22 cm 3 volume2.22 cm 3 = 22.522522 g/cm 3 = 22.5 g/cm 3 = 22.522522 g/cm 3 = 22.5 g/cm 3

19. Learning Check Osmium is a very dense metal. What is its density in g/cm 3 if 50.00 g of the metal occupies a volume of 2.22 cm 3 ? 1) 2.25 g/cm 3 2)22.5 g/cm 3 3)111 g/cm 3

20. Volume Displacement A solid displaces a matching volume of water when the solid is placed in water. 33 mL 25 mL

21. Learning Check What is the density (g/cm 3 ) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? 1) 0.2 g/ cm 3 2) 6 g/m 3 3) 252 g/cm 3 33 mL 25 mL

22. Percent Error

23. Percent Error At the conclusion of our time together, you should be able to: 1.Define experimental error, relative error and percent error 2. Determine percent error for an experiment

24. How to Determine Experimental Error Error = experimental – accepted value

25. Percent Error % Error = (experimental – accepted) x 100 accepted value

26. Example of Percent Error Your instructor has just massed a penny using 3 different balances. One balance measured 2.3 g, another measured 2.55 g and a third measured 2.49865 g. Determine the average mass of the penny. 2.3 g + 2.55 g + 2.49865 g = 7.34865 g ? 7.3 g /3 = 2.4333333 g ? 2.4 g

27. Example of Percent Error Ex. Err. = 2.4 g – 2.520 g = -0.12 g Rel. Err. = -0.12 g 2.520 g = -0.047619 = -0.048 % Err. = -0.048 x 100 = -4.8 % error If the standard mass of a United States penny is 2.520 g, determine the experimental error, relative error and percentage error in the measurements.

28. Density Let’s see if you can: 1.Define density 2.Calculate the density of a given object if given the volume and mass 3.Calculate the volume or mass if the density is given with the volume or mass

29. Learning Check Which diagram represents the liquid layers in the cylinder? (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL) 1) 2) 3) K K W W W V V V K

30. Learning Check The density of octane, a component of gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane? 1) 0.614 kg 2) 614 kg 3) 1.25 kg

31. Learning Check If blood has a density of 1.05 g/mL, how many liters of blood are donated if 575 g of blood are given? 1) 0.548 L 2) 1.25 L 3) 1.83 L 4) 548 L 4) 548 L

32. Learning Check A group of students collected 125 empty aluminum cans to take to the recycling center. If 21 cans make 1.0 pound of aluminum, how many liters of aluminum (D = 2.70 g/cm 3 ) are obtained from the cans? (1 kilogram = 2.2 pounds) 1) 1.00 L2) 2.00 L 3) 4.00 L

33. Which is heavier, a quart of water or a quart of mercury? If we have equal volumes of two different substances, then the one with the greater density will have the greater mass. Water has a density of 1.0 g/ml and mercury (Hg) has a density of 13.6 g/ml.

34. ► Which is heavier, a ton of feathers or a ton of bricks? ► Which is larger? ► If two objects have the same mass, the one with the higher density will be smaller. Neither Feathers