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.