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a
b c
d
e.
Sample
Mass of
Sample,
(g)
Initial
Volume,
(mL)
Final
Volume,
(mL)
Volume
of
sample,
(mL)
Mass/ volume of the sample (g/ mL) (a ÷ d)
Red 1 Red 2 Red 3
AVERAGE XXX XXXXX XXXXX XXX Silver 1 Silver 2 Silver 3
AVERAGE XXX XXXXX XXXXX XXX
Mass & Volume Lab
IV is mass, DV is volume, mass/ volume ratio (density) is the calculated quantity.
Reading a Graduated Cylinder
major
divisions: numbers
minor divisions:
Marks without numbers
Scale read up and in
some cylinders, down
also
Mass and Volume Lab Graduated Cylinders
Red metal
• Use 10 mL cylinder with exactly 5 mL water
added.
Silver Metal
• Use 25 mL cylinder with exactly 14 mL water
added.
Major and Minor Marks on the Graduated Cylinder
1. Define major & minor marks Major mark has a number, minor mark is just a line.
a. What is the value of each minor mark?
b. What is the uncertainty (the
estimation)?
c. What is the measurement?
Subtract two subsequent numbers &
divide by the number of lines in-between.
𝟒𝟎−𝟑𝟎
𝟏𝟎 𝒍𝒊𝒏𝒆𝒔 = 1 mL
Estimation or uncertainty is ½ the minor mark, which is 𝟏.𝟎 𝒎𝑳
𝟐 = 0.5 mL
38.5 mL
Record object’s volume consistent with a graduated cylinder’s limit of precision.
13.0 mL
How many significant
figures?
three
The major marks
are ____ mL 5
The minor marks
are ____ mL 1
Estimation is ½ the
minor mark, which
is 0.5 mL
The measurement is
What is the measurement shown
in cm3?
Reading a Graduated Cylinder Determine the value of
each minor mark
𝟏𝟎−𝟗
𝟏𝟎 𝒍𝒊𝒏𝒆𝒔 = 0.1 mL
What is the uncertainty?
Estimation is ½ the minor
mark, which is
𝟎.𝟏 𝒎𝑳
𝟐 = 0.05 mL
8.85 cm3
The measurement has ___ significant
figures 3
10
9
8
Draw the section of the cylinder in the red
box:
Water Displacement
To the right is a graduated cylinder
containing water.
An object with a mass of 21g and a volume
of 15 mL is lowered into the water.
a. What is the value of each minor
mark?
b. What is the initial volume in the
graduated cylinder?
c. What is the final volume after the object
is placed in the cylinder?
d. What is the water displacement?
Water Displacement a. minor mark =
b. initial volume =
c. final volume =
d. Volume change = water displacement
39.0 mL – 26.0 mL = 13 mL 39
or 13 mL
26.0 mL
50-40/5 = 2mL
39.0 mL
Volume of the
object = the
volume of the
water displaced
Water Displacement
The object place in the water caused the water to rise 15mL. This is the water displacement.
The volume of the object = the water displacement. 39
13 mL or
13 cm3
Volume of
the object
39.0 mL – 26.0 mL = 13 mL
1 mL = 1 cm3
Need 3 Mass Samples of Each Metal Red metal: need 3 samples, each with a different mass.
– Smallest sample >= 4.00g – Largest sample ≈<= 15.00 g
Silver Metal: need 3 samples, each with a different mass
– Smallest sample >= 4.00 g – Largest sample ≈ <= 11.00 g
In multiples of ≈5 g
sample 1 2 3
Approximately: 4.00g – 5.00 g 9.00g – 10.00g 14.00g – 15.00g
Example 1 4.17 g 9.33 g 14.24g
Example 2 4.35 9.65 14.87
Example 3 5.07 10.22 15.11
In multiples of ≈3 g
sample 1 2 3 Approximately: 3.00 g – 5.00 g 6.00 g – 8.00 g 9.00 g – 11.00 g
Example 1 3.17 g 6.33 g 9.24g
Example 2 4.35 7.65 10.87
Example 3 5.07 8.22 11.11
Mass and Volume Lab Graduated Cylinders
Red metal
• Use 10 mL cylinder with exactly 5 mL water
added.
Silver Metal
• Use 25 mL cylinder with exactly 14 mL water
added.
a
b c
d
e.
Sample
Mass of
Sample,
(g)
Initial
Volume,
(mL)
Final
Volume,
(mL)
Volume
of
sample,
(mL)
Mass/ volume of the sample (g/ mL) (a ÷ d)
Red 1 Red 2 Red 3
AVERAGE XXX XXXXX XXXXX XXX Silver 1 Silver 2 Silver 3
AVERAGE XXX XXXXX XXXXX XXX
Mass & Volume Lab
IV is mass, DV is volume, mass/ volume ratio (density) is the calculated quantity.
a b c d e
Sample
Mass of
Sample,
(g)
Initial
Volume,
(mL)
Final
Volume,
(mL)
Volume of
sample, (mL)
(c -b)
𝒎𝒂𝒔𝒔
𝒗𝒐𝒍𝒖𝒎𝒆
(a ÷ d)
Density
1
6.82 10.1 11.2 1.1 6.2 2
8.74 11.2 12.4 1.2 7.3 3
9.8 12.3 13.7 1.4 7.0
AVERAGE: 6.8
Average Experimental
Value of Density
Metal: Magnesi
um
Aluminum Barium Titanium Zinc Copper Lead Hafnium
Density
(g/mL)
1.55 2.70 3.50 4.51 7.14 8.96 11.3 13.10
Accepted Density Values
Use the above accepted values of density to determine the
probable identity of your metal by comparing these accepted
values (shown above) with your experimental density
values for each metal.
Write in your lab book:
According to my experimental density values the red
metal is _________ and the silver metal is __________.
a b c d e
Sample
Mass of
Sample,
(g)
Initial
Volume,
(mL)
Final
Volume,
(mL)
Volume of
sample, (mL)
(c -b)
𝒎𝒂𝒔𝒔
𝒗𝒐𝒍𝒖𝒎𝒆
(a ÷ d)
Density
1
6.82 10.1 11.2 1.1 6.2 2
8.74 11.2 12.4 1.2 7.3 3
9.8 12.3 13.7 1.4 7.0
AVERAGE: 6.8
| exp |% experimental error 100
accepted value erimental valuex
accepted value
Percent experimental error calculation
From your data table, your average density for the your
metal is 6.80 grams/ mL.
This is the experimental value.
The closest value to 6.80 g/mL is zinc.
The accepted value of density of zinc is 7.14 g/ml
% 𝑒𝑟𝑟𝑜𝑟 =| 7.14 −6.80|
7.14 x 100 = 4.76%
Consider your results accurate if the percent error is
equal or less than 10%. Write in your lab book:
Our results are/ are not accurate because _______.
Are Your Results Accurate? • Write one of the following in your lab book
depending on the outcome of your % error
calculation: • Our results are accurate because our % error is
= < 10%.
• Our results are not accurate because our
% error is > 10%.
Use This Calculation to see if Your Data Is
Precise Example:
– Value 1 = 6.2g/cm3,
– value 2 = 7.0g/cm3,
– value 3 = 7.3 g/cm3
highest value - lowest value
% range = -------------------------------- x 100
lowest value
Consider your values precise if the range is less than or equal
to 20%.
% 𝑟𝑎𝑛𝑔𝑒 = 7.3 − 6.2
6.2𝑥 100 = 17.7%
Is Your Data Precise? • Write one of the following in your lab book
depending on the outcome of your % range
calculation: • Our data is precise because our % range is = <
10 %.
• Our data is not precise because our %
range is > 10%.
What is bigger, the pillow or the battery?
What is heavier, the pillow or battery?
How can the battery have less volume than the
pillow but have more mass?
There are more particles in the battery and/ or the
particles of the battery are heavier than the pillow.
The battery is
more dense
than the pillow.
3. List some important properties of the particle model that help explain the different densities of different substances.
a) matter is comprised of particles that have mass and take up space.
Mass is a measure of the number of particles present.
Volume is a measure of the space the particles take up.
b) The particles cannot be divided.
c) Some particles have more mass than others particles,
1 mass unit 5 mass unit
d) and some particles take up more space.
𝑫𝒆𝒏𝒔𝒊𝒕𝒚 = 𝒎𝒂𝒔𝒔
𝒗𝒐𝒍𝒖𝒎𝒆
Density is the amount of mass that 1 mL or
1 cm3 contains.
• Mass is the amount of particles that
make up a particular sample of matter.
• Density is the mass of the particles that
occupies one unit of volume.
Examples: 1 g of water occupies 1 cm3
The density is 1 g per cm3 and is written
1 𝒈
𝒄𝒎𝟑 or 1 𝒈
𝒎𝑳
or 1 g/cm3 or 1 g/mL
1 mL = 1cm3
Silver y = 2.6984x - 0.2182
Red y = 7.8947x + 0.4211
0
3
6
9
12
15
0 3 6M
as
s
(g)
Volume (mL)
Mass vs. Volume, Red Metal
x,volume y, mass
0.7 6.00
0.85 7.00
0.95 8.00
Silver
x,volume y, mass
2.2 5.78
3 7.78
4.3 11.69
When y = mass & x = volume, the slope of the line = density because:
𝑺𝒍𝒐𝒑𝒆 =𝒓𝒊𝒔𝒆
𝒓𝒖𝒏=
𝒚
𝒙=
𝒎𝒂𝒔𝒔
𝒗𝒐𝒍𝒖𝒎𝒆= 𝒅𝒆𝒏𝒔𝒊𝒕𝒚
The slope of a mass and volume graph is density
Slope Write the linear equation (equation of a straight line). Define
the variables:
y = mx + b
x & y are data points you measured
m = the slope (𝒓𝒊𝒔𝒆
𝒓𝒖𝒏=
∆𝒚
∆𝒙) b = the y-intercept
Explain these this equation: y = 4.75x + 0.465
The equation is a linear equation because it has the form of y
= mx +b.
4.75 is
0.465 is
y is x is
the slope (m)
where the line crosses the y axis (the y-intercept) (b)
a y coordinate on the line, an x coordinate on the line,
y = 2.66 x + 1.06
0
2
4
6
8
10
-1 0 1 2 3 4
Mas
s (
g)
Volume (mL)
Mass vs. Volume
mass = (2.66 g/mL) ● volume + 1 .06g
y = m x + b
y-intercept
• m and b are constants because a straight line only has one slope and one y-intercept (b). Constants have values & units.
• Substitute the values and units for m & b: m=2.66 g/mL, b= 1.06 g • “b” is on the y axis so it has the units of the y axis, grams. • mass = (2.66 g/mL) ● volume + 1 .06g
Mathematical Models in the form of y= mx + b • X and y are
variables.
• Name the variables by substituting the labels found on the x & y axis ( just the names, no units).
• y = mass, x= volume
y = 2.66 x + 1.06
0
2
4
6
8
10
-1 0 1 2 3 4
Mas
s (
g)
Volume (mL)
Mass vs. Volume
mass = (2.66 g/mL) volume + 1.06g
The y-intercept should be zero because 0 mL of metal has a mass of zero grams. Because of uncertainty in measurement, we do not end up with a perfect y-intercept of zero.
What does the y-intercept mean? • Y-intercept
shows the value of y when x =0.
• For this graph the y-intercept means that the mass = 1.26 g when the volume = 0 mL
• Does that make sense?
y = m x + b
y-intercept
y = 2.66 x + 1.06
0
2
4
6
8
10
-1 0 1 2 3 4
Mas
s (
g)
Volume (mL)
Mass vs. Volume
mass = (2.66 g/mL) volume + 1.06g
y = m x + b
For this experiment we will say if the y-intercept is approximately between -1.0 - 1.0 we will assume that this error is caused by uncertainty in measurement is small and we can assume this y-intercept is negligible. That means the real y-intercept is zero.
What does the negligible mean?
• Negligible means insignificant.
• If a value is negligible it can be ignored or set equal to zero.
y-intercept
Density , 2013
Density is how much mass an object has for
each cubic centimeter of its volume .
massDensity
Volume
mD
V
D = density
m = mass
v = volume
𝑫𝑽 = 𝒎
Slope = density
Each substance has its own
unique density.
• Density is a characteristic
property.
Characteristic Properties • Properties that are unique to the identity of the
substance can be used to i.d. a substance:
• Density – amount of mass per unit volume
• Boling Point – temp that the stuff boils
• Melting/ Freezing Point- temp that the stuff melts/ freezes
• Electrical conductivity- amount electricity conducted
• Heat conductivity- amount heat conducted
• Reflection or absorption of light – amount of light reflected or refracted
• Absorption/ emission if light - amount of light absorbed or emitted
• ----More-----
volume
massDensity
What is the density of a substance that occupies a
volume of 2 cubic centimeters and has a mass of 6.4
grams?
• Mass = 6.4g
• Volume = 2 cm3
Density
3
3/2.3
2
4.6cmg
cm
g
V
mD
1. Find the density of a material, given that a
7.75 g sample occupies 2.25 mL.
Round answer to two decimal places.
V
mD
m = 7.75 g
V = 2.25 mL
D = ?
252
g 7.75
mL.D
D = 3.44 g/mL
2. What is the mass of a sample of material that has a
volume of 55.1 cm3 and a density of 6.72 g/cm3?
Round answer to the nearest whole number.
V
mD
m = ?
V = 55.1 cm3
D = 6.72 g/ cm3
3
3
cm 55.1
m
1
726
cm/g.
cm 55.1
m cm g/ 6.72
3
3
mcm/g. 1cm 55.172633
m = 370.272 g = 370 g
m = 370.272 g
= 370 g
2.
V
mD
m = ?
V = 55.1 cm3
D = 6.72 g/ cm3
3
3
cm 55.1
m
1
726
cm/g.
cm 55.1
m cm g/ 6.72
3
3
mcm/g. 1cm 55.172633
m = 370.272 g = 370 g
3. The density of gold is 19.3 g/cm3. What is
the volume, in cubic centimeters, of a
sample of gold that has a mass of 715 g?
ROUND YOUR ANSWER TO ONE
DECIMAL PLACE
3. D = 19.3 g/cm3
V = ?, cm3
m = 715 g?
V
mD
V
g 715 g/cm 19.3
3
V
g 715
1
g/cm 19.33
37.046 cm3 37.0 cm3
Densities of Solids , Liquids, & Gases 1. What is the density of the CO2 gas from Mr. B’s demo?
0.0018 – 0.0020 g/ mL
2. Liquids CO2 has a density of 1.10 g/mL? How does the
density of the gas compare to the liquid?
3. How does the density of the gas compare to solid CO2
(density = 1.56 g/mL), dry ice?
4. Using what you know about density, draw a picture of a
solid, a liquid, and a gas using particle drawings in a box.
A lot smaller? 500 x smaller
A lot smaller? ≈ 800 x smaller
Densities of Solids , Liquids, & Gases What do we know about how our particles arrange themselves in solids, liquids & gasses ? What is this property called?
• The solid particles are very close together (very dense).
• The liquid particles are not as dense as a solid but are
still close together,
• The gas particles are very spread out.
This property is called density.
Solid Liquid Gas
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Resources Chapter menu
Water in Three States Chapter 1
•Gas particles are well separated with no regular arrangement.
•liquid particles are close together with no regular arrangement.
•Solid particles are tightly packed, usually in a regular pattern.
•Solid water (ice) is an exception. •When liquid water becomes a solid (ice) the particle arrangement expands.