NAME_____________________________________ DATE__________ DUE________
CHS INTRO CHEM Density HW3
Table of Densities of
Some Common
Substances
EXAMPLES WHERE DENSITY AND MASS ARE GIVEN AND YOU ARE
CALCULATING volume
EXAMPLE: A piece of copper has a mass of 178 kg. What is its volume?
Start by listing the values
you know and need to find:
Volume = V = ?
Mass = 178 kg
Density of copper =
8,890 kg/m3
(from table)
Algebraic Solution
Numerical Solution.
Write Algebraic Equation
you are starting with:
Plug your numbers with units into the
equation you created for volume:
𝜌=
𝑚
𝑉
𝑉=
Solve this equation for the
desired variable:
𝑚
𝑉=
𝜌
.
𝑚
178𝑘𝑔
=
=
𝜌 8890𝑘𝑔/𝑚3
020 m3
EXAMPLES FOR YOU TO WORK OUT
1. The roofs of large classic building are often made of lead. If the mass of lead used for a roof is 100,000 kg
how many cubic meters are necessary (8.85 m3)
Start by listing the values
you know and need to find:
Volume = V = ?
Mass = 100,000 kg
Density of Lead =
11,300 kg/m3
Algebraic Solution
Write Algebraic Equation
you are starting with:
𝜌=
𝑚
𝑉
Numerical Solution.
Plug your numbers with units into the
equation you created for volume:
𝑉=
Solve this equation for the
desired variable:
𝑚
𝑉=
𝜌
𝑚
100,000𝑘𝑔
=
=
𝜌 11,300 𝑘𝑔/𝑚3
8.85 m3
If 1 kg = 2.2 pounds, how many pounds of lead are needed for the roof? (Show the equation to calculate the answer)
(220,000 pounds) (These structures must be very strong>
𝟏𝟎𝟎, 𝟎𝟎𝟎 𝒌𝒈 𝟐. 𝟐 𝒑𝒐𝒖𝒏𝒅𝒔
×
=
𝟏
𝟏 𝒌𝒈
2. The Eiffel Tower has a mass 7,300,000 kg of steel. Calculate the volume of steel. (about 928 m3)
Start by listing the values
you know and need to find:
Volume = V = ?
Mass = 7,300,00 kg
Density of Steel =
7,860 kg/m3
Algebraic Solution
Write Algebraic Equation
you are starting with:
𝜌=
𝑚
𝑉
Solve this equation for the
desired variable:
𝑚
𝑉=
𝜌
Numerical Solution.
Plug your numbers with units into the
equation you created for volume:
𝑽=
𝒎 𝟕, 𝟑𝟎𝟎, 𝟎𝟎𝟎 𝒌𝒈
=
=
𝝆
𝟕, 𝟖𝟔𝟎 𝐤𝐠/𝐦𝟑
928 m3
EXAMPLE WHERE DENSITY AND MASS ARE GIVEN AND YOU ARE CALCULATING A VARIABLE
THAT IS PART OF THE VOLUME
This is the same as calculating the thickness of the aluminum foil for the aluminum foil lab.
1. Copper rectangular prism is 4 cm wide and 4cm meters long. It has a mass of .5 g. How thick is the
rectangle.
a. What is the density of Aluminum? 2.7 g/cm3
Remember that you need to convert the units if you have kg/m3,
From the table on the front the density of Aluminum is 2,700 kg/m3
𝟐𝟕𝟎𝟎 𝒌𝒈
𝟏 𝒎𝟑
𝟏, 𝟎𝟎𝟎 𝒈
𝒈
×
×
= 𝟐. 𝟕
𝟑
𝟑
𝒎
𝟏, 𝟎𝟎𝟎, 𝟎𝟎𝟎 𝒄𝒎
𝟏 𝒌𝒈
𝒄𝒎𝟑
b. State the values for the dimensions you know: length 4 cm width 4 cm height =h
c. State the Equation for density
𝜌=
𝑚
𝑉
a. State the Equation for volume
Volume = V = L x W x H
where V= volume (m3) , L = length (m)
W = width (m) and H = Height (m)
b. Substitute the Equation for volume into the equation for density.
c. Algebraically solve the equation for the unknown (H).
Mulitply both sides by H
𝐻
𝑚
𝐻
(1) 𝜌 = 𝐿 𝑥 𝑊 𝑥 𝐻 (1)
Simplifying gives
𝐻𝜌 =
𝑚
𝐿𝑥𝑊
Now Divide both sides by density (ρ)
1
𝑚
1
( ) 𝐻𝜌 =
( )
𝜌
𝐿𝑥𝑊 𝜌
Simplifying this gives and equation for H
𝐻=
𝑚
𝐿 𝑥 𝑊𝑥𝜌
d. Plug in the values you know with the appropriate units.
𝑚
𝐻 = 𝐿 𝑥 𝑊𝑥𝜌 =
.5 𝑔
4 𝑐𝑚 𝑥 4 𝑐𝑚 𝑥 2.7
𝑔 =
𝑐𝑚3
e. Calculate the answer and state the answer.
About .01 cm.