11.1 - density

what is density?

• the mass of a substance per unit volume

• ρ = m / v

ρ = m / v

density

what is the symbol for density?

ρ (rho)

what is the unit for density?

kg m^-3

how can we compare the density of two substances?

by measuring the mass per equal volumes and using ρ = m / v

which is denser - gases or liquids?

gases

why are gases less dense than liquids?

because the average separation between molecules in a gas is much greater than in a liquid or solid

what is the density of air?

1.2 kg m^-3

what is the density of aluminium?

2700 kg m^-3

what is the density of copper?

8900 kg m^-3

what is the density of gold?

19300 kg m^-3

what is the density of hydrogen?

0.083 kg m^-3

what is the density of iron?

7900 kg m^-3

what is the density of lead?

11300 kg m^-3

what is the density of oxygen?

1.3 kg m^-3

what is the density of silver?

10500 kg m^-3

what is the density of water?

1000 kg m^-3

how can we identify an unknown substance using density?

by measuring the density and comparing it with the density of known substances

what are the three ‘object types’ regarding to finding density?

• regular solid

• liquid

• irregular solid

how do we find the density of a regular solid?

1. measure its mass using a top pan balance

2. measure its dimensions using a vernier caliper or micrometre

3. calculate its volume using the appropriate equation

4. ρ = m / v

what are these volume equations (dimensions-wise)?

• cube

• rectangular prism

• triangular prism

• cylinder

• pyramid

• cone

• sphere

• cube , a³

• rectangular prism , l x w x h

• triangular prism , base area x height

• cylinder , π r² h

• pyramid , 1/3 x base area x height

• cone , 1/3 π r² h

• sphere , 4/3 π r³

what’s the volume of a cube?

a³

here

a³

volume of a cube

what’s the volume of a rectangular prism?

l x w x h

here

l x w x h

volume of a rectangular prism

what’s the volume of a triangular prism?

area of base x height

here

area of base x height

volume of triangular prism

what’s the volume of a cylinder?

π r² h

here

π r² h

volume of a cylinder

what’s the volume of a pyramid?

1/3 x base area x height

here

1/3 x base area x height

volume of a pyramid

what’s the volume of a cone?

1/3 π r² h

here

1/3 π r² h

volume of a cone

what’s the volume of a sphere?

4/3 π r²

here

4/3 π r²

volume of a sphere

the density of which object is found by measuring mass and dimensions?

regular solid

how do we find the volume of a regular solid?

• measure dimensions using a vernier caliper / micrometer

• find mass using a top pan balance

• calculate volume using the appropriate equation

how to use a vernier caliper

how to use micrometer

how do you find the mass of a regular solid?

using a top pan balance

how do you find the dimensions of a regular solid?

using a vernier caliper / micrometer

how do you find the density of a liquid?

1. measure mass of empty measuring cylinder

2. pour some liquid into the measuring cylinder

3. volume can be measured directly (from the measuring cylinder)

4. measure the mass of the cylinder full of liquid

5. liquid mass = mass of cylinder with liquid - empty cylinder mass

6. ρ = m / v

when finding the density of a liquid, should you use a lot or a little liquid?

a lot

why should you use a lot of liquid when finding its density?

to reduce percentage error

how do you find the volume of a liquid?

it can be measured directly from the measuring cylinder

how do you find the mass of a liquid?

1. measure the mass of an empty cylinder

2. measure the mass of the cylinder full of liquid

3. liquid mass = mass of cylinder with liquid - empty cylinder mass

how do we reduce the percentage error in our measurement for liquid density?

• use as much liquid as possible

• read the volume measurement at eye level to avoid parallax error

• read at the bottom of the meniscus

how do we avoid parallax error when measuring a liquid’s volume?

by reading the measurement from the measuring cylinder at eye level

why should we read a liquid’s volume measurement at eye level to the measuring cylinder?

to avoid parallax error

how do we find the density of an irregular solid?

1. measure mass of object using a top pan balance

2. immerse the object on a thread in liquid in a measuring cylinder, or eureka can with a predetermined volume of liquid. displace liquid / increase in liquid level is volume

3. ρ = m / v

how do we find the mass of an irregular solid?

using a top pan balance

how do we find the volume of an irregular object?

• using a measuring cylinder

• using a eureka can

how do we find the volume of an irregular object using a measuring cylinder?

1. immerse the object on a thread in liquid in a measuring cylinder

2. observe the increase of liquid level

3. this increase is the object volume

how do we find the volume of an irregular object using a eureka can?

1. fully fill a eureka can with liquid

2. position a measuring cylinder under the spout

3. when the object is immersed, the water displaced into the measuring cylinder is the object volume

what is the meniscus?

the curve in the upper surface of a liquid close to the surface of a container, produced by surface tension

here

when reading volume from a measuring cylinder, should we read at the top or bottom of the meniscus?

the bottom, i.e., the part that isn’t curving up

what is an alloy?

a solid mixture of two or more metals

what is brass?

a copper and zinc alloy that has a good resistance to corrosion and wear

what is brass an alloy of?

copper and zinc

what is a copper - zinc alloy?

brass

what is good about brass?

it has a good resistance to corrosion and wear

what is the density of an alloy when mass isn’t given?

ρ = (ρ_A v_A + ρ_B v_B) / v

ρ = (ρ_A v_A + ρ_B v_B) / v

density of an alloy, for when mass isn’t given

derive ρ = (ρ_A v_A + ρ_B v_B) / v

• ρ = m / v

• rearranging gives m = ρ v

• m_A = ρ_A v_A

  m_B = ρ_B v_B

• therefore ρ = (ρ_A v_A + ρ_B v_B) / v

1 m³ = ? cm³

1 m³ = 10⁶ cm³

10⁶ cm³ = ? m³

10⁶ cm³ = 1 m³

1000 kg m^-3 = ? cm^-3

1000 kg m^-3 = 10⁶ g / 10⁶ cm³ = 1 g cm^-3

1 g cm^-3 = ? kg m^-3

1 g cm^-3 = 10⁶ g / 10⁶ cm³ = 1000 kg m^-3