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.

Density & Percent Error

Unit 1B

DensityAt the conclusion of our time together, you should be able to:

1.1. Define densityDefine density2.2. Calculate the density of a given object if Calculate the density of a given object if

given the volume and massgiven the volume and mass3.3. Calculate the volume or mass if the density Calculate the volume or mass if the density

is given with the volume or massis 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)

DENSITYDENSITY - an important and - an important and useful (qualitative) intensive physical useful (qualitative) intensive physical propertyproperty

Density mass (g)volume (cm3)

Density mass (g)volume (cm3)

Mercury

13.6 g/cm13.6 g/cm33 21.5 g/cm21.5 g/cm33

Aluminum

2.7 g/cm2.7 g/cm33

Platinum

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” featuresVolume, mL

Mass, g

0.0 0.002.0 5.405.0 12.5010.0 27.3015.0 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

ProblemProblem A piece of copper has a mass of A piece of copper has a mass of 57.54 g. It is 9.36 cm long, 7.23 cm 57.54 g. It is 9.36 cm long, 7.23 cm wide, and 0.95 mm thick. Calculate wide, and 0.95 mm thick. Calculate density (g/cmdensity (g/cm33).).

Density mass (g)volume (cm3)

Density mass (g)volume (cm3)

M

D V

StrategyStrategy

1. Get dimensions in 1. Get dimensions in commoncommon units. units.

2.2. Calculate Calculate volumevolume in cubic in cubic centimeters.centimeters.

3. Calculate the 3. Calculate the densitydensity..

SOLUTIONSOLUTION

1. Get dimensions in common units.1. Get dimensions in common units.

2.2. Calculate volume in cubic centimeters. Calculate volume in cubic centimeters.

3. Calculate the density.3. Calculate the density.

0.95 mm • 1cm

10 mm = 0.095 cm

57.54 g

6.4 cm3 = 9.0 g / cm3

(9.36 cm)(7.23 cm)(0.095 cm) = 6.4 cm(9.36 cm)(7.23 cm)(0.095 cm) = 6.4 cm33

Note only 2 significant figures in the answer!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?

PROBLEM:

Mercury (Hg) has a density of 13.6 g/cm3. What is the mass of 95 mL of Hg in grams? In pounds?

1.1. Use density to calculate mass (g) from Use density to calculate mass (g) from volume.volume.

2.2. Convert mass (g) to mass (lb)Convert mass (g) to mass (lb)

Need to know conversion factorNeed to know conversion factor

= 454 g / 1 lb= 454 g / 1 lb

First, note that 1 cmFirst, note that 1 cm33 = 1 = 1 mLmL

StrategyStrategy

1.1. Convert volume to Convert volume to massmass

95 cm3 • 13.6 g

cm3 = 1.3 x 103 g

1.3 x 103 g • 1 lb

454 g = 2.8 lb

2. Convert mass (g) to mass (2. Convert mass (g) to mass (lblb))

StrategyStrategy

Learning CheckLearning Check

Osmium is a very dense metal. What is its Osmium is a very dense metal. What is its

density in g/cmdensity in g/cm3 3 if 50.00 g of the metal occupiesif 50.00 g of the metal occupies

a volume of 2.22 cma volume of 2.22 cm33??

1) 2.25 g/cm1) 2.25 g/cm33

2)2) 22.5 g/cm22.5 g/cm33

3)3) 111 g/cm111 g/cm33

Solution

2) Placing the mass and volume of the osmium 2) Placing the mass and volume of the osmium metal into the density setup, we obtainmetal into the density setup, we obtain

D = D = massmass = = 50.00 g 50.00 g = = volumevolume 2.22 cm2.22 cm33

= = 22.522522 g/cm22.522522 g/cm3 3 = 22.5 g/cm= 22.5 g/cm33

Learning CheckLearning Check

Osmium is a very dense metal. What is its Osmium is a very dense metal. What is its

density in g/cmdensity in g/cm3 3 if 50.00 g of the metal occupiesif 50.00 g of the metal occupies

a volume of 2.22 cma volume of 2.22 cm33??

1) 2.25 g/cm1) 2.25 g/cm33

2)2) 22.5 g/cm22.5 g/cm33

3)3) 111 g/cm111 g/cm33

Volume DisplacementVolume Displacement

A solid displaces a matching volume of water A solid displaces a matching volume of water when the solid is placed in water.when the solid is placed in water.

33 mL33 mL

25 mL 25 mL

Learning CheckLearning Check

What is the density (g/cmWhat is the density (g/cm33) of 48 g of a metal if the ) of 48 g of a metal if the metal raises the level of water in a graduated metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? cylinder from 25 mL to 33 mL?

1) 0.2 g/ cm1) 0.2 g/ cm33 2) 6 g/m 2) 6 g/m33 3) 252 g/cm3) 252 g/cm33

33 mL33 mL

25 mL25 mL

Percent Error

Percent ErrorAt 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

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.

DensityLet’s see if you can:

1.1. Define densityDefine density2.2. Calculate the density of a given object if Calculate the density of a given object if

given the volume and massgiven the volume and mass3.3. Calculate the volume or mass if the density Calculate the volume or mass if the density

is given with the volume or massis given with the volume or mass

Learning CheckLearning Check

Which diagram represents the liquid layers in Which diagram represents the liquid layers in the cylinder?the cylinder?

(K) Karo syrup (1.4 g/mL), (V) vegetable oil (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL)(0.91 g/mL,) (W) water (1.0 g/mL)

1)1) 2) 2) 3) 3)

K

K

W

W

W

V

V

V

K

Learning CheckLearning Check

The density of octane, a component of The density of octane, a component of gasoline, is 0.702 g/mL. What is the mass, gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane?in kg, of 875 mL of octane?

1) 0.614 kg1) 0.614 kg

2) 614 kg2) 614 kg

3) 1.25 kg3) 1.25 kg

Learning CheckLearning Check

If blood has a density of 1.05 g/mL, how many If blood has a density of 1.05 g/mL, how many liters of blood are donated if 575 g of blood are liters of blood are donated if 575 g of blood are given?given?

1) 0.548 L1) 0.548 L

2) 1.25 L2) 1.25 L

3) 1.83 L3) 1.83 L

4) 548 L4) 548 L

Learning CheckLearning Check

A group of students collected 125 empty A group of students collected 125 empty aluminum cans to take to the recycling center. If aluminum cans to take to the recycling center. If 21 cans make 1.0 pound of aluminum, how many 21 cans make 1.0 pound of aluminum, how many liters of aluminum (D = 2.70 g/cmliters of aluminum (D = 2.70 g/cm33) are obtained ) are obtained from the cans? (1 kilogram = 2.2 pounds)from the cans? (1 kilogram = 2.2 pounds)

1) 1.00 L1) 1.00 L 2) 2.00 L2) 2.00 L 3) 4.00 L 3) 4.00 L

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.

►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