Density & Percent Error Unit 1B 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 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/cm3 (solid) DENSITY - an important and useful (qualitative) intensive physical property Density Mercury mass (g) volume (cm3) Platinum Aluminum 13.6 g/cm3 21.5 g/cm3 2.7 g/cm3 Density Calculations M D V Cover up whatever unit you are solving for, the two units remaining will show you how to solve the problem. 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, mL 0.0 2.0 5.0 10.0 15.0 Mass, g 0.00 5.40 12.50 27.30 40.50 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. Density Calculations Regularly Shaped Solid : mass = balance volume = measure (l x w x h) Irregularly Shaped Solid: mass = balance volume = water displacement Density Calculations Liquid: volume = read graduated cylinder mass = tare graduated cylinder, mass liquid 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/cm3). mass (g) Density volume (cm3) M D V Strategy 1. Get dimensions in common units. 2. Calculate volume in cubic centimeters. 3. Calculate the density. SOLUTION 1. Get dimensions in common units. 1cm 0.95 mm • = 0.095 cm 10 mm 2. Calculate volume in cubic centimeters. (9.36 cm)(7.23 cm)(0.095 cm) = 6.4 cm3 3. Calculate the density. 57.54 g 3 = 9.0 g / cm 6.4 cm3 Note only 2 significant figures in the answer! PROBLEM: Mercury (Hg) has a density of 13.6 g/cm3. What is the mass of 95 mL of Hg in grams? In pounds? Strategy First, note that 1 cm3 = 1 mL 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 Strategy 1. Convert volume to mass 13.6 g 3 3 95 cm • = 1.3 x 10 g 3 cm 2. Convert mass (g) to mass (lb) 1.3 x 103 g • 1 lb = 2.8 lb 454 g Learning Check Osmium is a very dense metal. What is its density in g/cm3 if 50.00 g of the metal occupies a volume of 2.22 cm3? 1) 2.25 g/cm3 2) 22.5 g/cm3 3) 111 g/cm3 Solution 2) Placing the mass and volume of the osmium metal into the density setup, we obtain D = mass = 50.00 g = volume 2.22 cm3 = 22.522522 g/cm3 = 22.5 g/cm3 Learning Check Osmium is a very dense metal. What is its density in g/cm3 if 50.00 g of the metal occupies a volume of 2.22 cm3? 1) 2.25 g/cm3 2) 22.5 g/cm3 3) 111 g/cm3 Volume Displacement A solid displaces a matching volume of water when the solid is placed in water. 33 mL 25 mL Learning Check What is the density (g/cm3) 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/ cm3 2) 6 g/m3 3) 252 g/cm3 33 mL 25 mL Percent Error 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 How to Determine Experimental Error Error = experimental – accepted value Percent Error % Error = (experimental – accepted) x 100 accepted value 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 Example of Percent 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. Ex. Err. Rel. Err. % Err. = 2.4 g – 2.520 g = -0.12 g = -0.12 g 2.520 g = -0.047619 = -0.048 = -0.048 x 100 = -4.8 % error 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 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) V W 2) W K K V 3) K V W 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 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) 2) 3) 4) 0.548 L 1.25 L 1.83 L 548 L 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/cm3) are obtained from the cans? (1 kilogram = 2.2 pounds) 1) 1.00 L 2) 2.00 L 3) 4.00 L Water has a density of 1.0 g/ml and mercury (Hg) has a density of 13.6 g/ml. 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. ►Which is heavier, a ton of feathers or a ton of bricks? Neither ►Which is larger? Feathers ►If two objects have the same mass, the one with the higher density will be smaller.