Mass and Volume

Density

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.

READ FROM

THE BOTTOM

OF THE

MENISCUS

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 the battery

What is heavier, a ten pound puppy or a ten

pound battery

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

What does negligible mean?

Insignificant or a value of zero.

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-----

Which is more dense?

FIGURE 1

A B

A

BFigure 1

Which is more dense? FIGURE 2

A B

C

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

1.

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.

States of Matter

1. Which diagram represents the solid state, the liquid state

and the gas state of matter. Explain your answer.

A B C

Solid - definite

shape & volume.

Liquid - no definite shape but definite volume.

Gas - no definite shape,

no definite volume.