Density Calculati

ons       Density is an important intensive property, which can be used to

help determine the identity of an unknown substance.  While the mass or the volume of a substance will vary from sample to sample, the density will remain the same at a given temperature.  As you know, the density of a substance is a measure of how much mass is present in a given unit of volume.  The formula is shown below:

    In laboratory exercises, it is easy to find the mass and volume of most solids, so it is common to solve for density.  When dealing with gases, however, it is often easy to find the volume, but very hard to find the mass.  By looking up the density of a known gas in a reference table, and using the experimental volume, you can calculate the mass using the equation above.  As in any algebraic expression, we can solve for any of the three variables as long as the other two variables are given or known. 

Solving For Density

   When solving for density, you would use the formula exactly as it appeared above.  Here is an example where density is the unknown, and the steps for solving the problem:

1.  A student determines that a piece of an unknown material has a mass of 5.854 g and a volume of 7.57 cm3.  What is the density of the material, rounded to the correct number of significant digits?

First:  Write the correct formula at the top of your page, and list the knowns and the unknowns.

D = ?M= 5.854 gV = 7.57 cm3

Second: Substitute the known values in the problem

Third:  Calculate your answer, including units

                                                                          D = 0.77331571994 g/cm3  

Fourth:  Round to the correct number of significant figures

                                                                                  D = 0.773 g/cm3   

Solving For Mass

    When solving for mass, we must take the original formula, and isolate the unknown like so:

Multiply both sides by v

  

  

The "v's" cancel out

Isolate for mass

                                                                                     m = v x D

Here is an example where we must solve for mass being the unknown

2.  Iron has a known density of 7.87 g/cm3.  What would be the mass of a 2.5 dm3 piece of iron?  

Notice that the density is given in the units g/cm3, but the volume is given in the units dm3.  Therefore, this problem requires an additional

step.

First:  Change the question so that the volume is given in the same units as the density.

Use the factor label method:      

So:  Iron has a known density of 7.87 g/cm3.  What would be the mass of a 2.5 dm3 piece of iron?

2500 cm3

 Second:  Write the original formula for density, and then isolate the unknown (mass).  List the "knowns" and the "unknown"

Original Formula

         Adjusted Formula

  m = v x D  

D = 7.87 g/cm3   m = ? 

v = 2500 cm3

   Third:  Substitute the known values in the problem

m = 2500 cm3 x 7.87 g/cm3

Fourth:  Calculate the answer including units

     m = 2500 cm3 x 7.87 g/cm3

m = 19675 g

Fifth:  Round to the correct number of significant figures

m = 2.0 x 104 g

Note - we use scientific notation to express the correct number of significant digits.

Solving For Volume

When solving for volume, we must take the original formula, and isolate the unknown like so:

Original Formula

Multiply both sides by volume

  m = v x D 

Divide both sides by density

Adjusted formula

Now, here is an example of a density problem where volume is the unknown

3.  Mercury has a density of 13.5 g/cm3.  How much space would

50.0 g of mercury occupy?

    First:  Write the original formula for density, and then isolate the unknown (Volume).  List the "knowns" and the "unknown".

Original Formula

Multiply both sides by volume

  m = v x D 

Divide both sides by density

Adjusted formula

D = 13.5 g/cm3   M = 50.0 g  

V = ?

Second: Substitute the known values in the problem

Third:  Calculate your answer, including units

 v = 3.70370370. . . cm3  

 

Fourth:  Round to the correct number of significant figures

v = 3.70  cm3

Density Problemsby Arthur Keeney

1 If a material has a mass of 77.6g and a volume of 11.5cm3, what is its density? 

6.75g/cm3

76.6g/cm3

67.6g/cm3

7.6g/cm3

2A sample has a volume of 10.2cm3 and a mass of 15.6g. What is the density of the gold? 

110.3g/cm3

1.53g/cm3

5.1g/cm3

15.0g/cm3

3What is the density of a material when the mass is 20.4g and the volume is 18.6cm3? 

381.5g/cm3

1.10g/cm3

38.5g/cm3

.97g/cm3

4What is the density of a substance if its mass is 36.7g and its volume is 1.57cm3? 

55.5g/cm3

23.4g/cm3

15.5g/cm3

0g/cm3

5A sample has a mass of 1.02g and a volume of 1.35cm3, what is the density of the nickel? 

46.7g/cm3

.756g/cm3

75.0g/cm3

3.02g/cm3

6A sample has a mass of 1.2g and a volume of 1.1cm3, what is its density? 

1.1g/cm3

11.2g/cm3

2.2g.cm3

11.1g/cm3

7What is the density of a sample if its mass is 44.3g and its volume is 22.1cm3? 

.56g/cm3

56.3g/cm3

88.3g/cm3

2.00g/cm3

8What is the density a substance that has a mass of 87.6g and a volume of 8.09cm3? 

11.7g/cm3

.09g/cm3

10.0g/cm3

10.8g/cm3

9A piece of metal has a mass of 32.4g and has a volume of 24.9cm3, what's its density? 

806.8g/cm3

1.30g/cm3

.77g/cm3

7.5g/cm3

10

If a sample that has a volume of 5.25cm3 and a mass of 97.4g its density would be... 

185g/cm3

18.6g/cm3

.053g/cm3

1.8gcm3

11

What is the density of a substance when its volume is 51.6cm3 and its mass is 134.5g? 

2.61g/cm3

.823g/cm3

.38g/cm3

6.23g/cm3

12

A substance has a mass of 61.9g and its volume is 5.46cm3, what is this density?  

11.3g/cm3

333.06g/cm3

3.11g/cm3

33.1g/cm3

13

What's the density of a sample that has a mass of 75.4g and a volume of 5.24cm3? 

76.8g/cm3

13.4g/cm3

14.4g/cm3

15.6g/cm3

14

What is the density of a substance that has a mass of 54.2g and a volume of 3.06cm3? 

7.17g/cm3

1g/cm3

1,77g/cm3

17.7g/cm3

15

What is the density of a material if its mass 2.02g and its volume is .500cm3? 

3.04g/cm3

1.02g/cm3

5.02g/cm3

4.04g/cm3

1How many significants digits are in the number 760? 

1

0

2

3

2How many significants digits are in the number 407? 

1

2

3

0

3How many significants digits are in the number 780? 

5

2

4

1

4How many significants digits are in the number 0.560? 

2

4

3

1

5How many significants digits are in the number 6.02 X 103? 

4

3

5

2

6How many significants digits are in the number 7.0 X 102? 

1

3

4

2

7How many significant digits are in the number 269? 

1

2

4

3

8How many significants digits are in the number 700? 

4

3

2

1

9How many significants digits are in the number 3.07? 

2

3

1

0

10

How many significants digits are in the number 0.0030? 

1

4

2

5

Name__________________________

Section____________________________

Hit the print command and show all work in the spaces provided.   Use the 5-step method and be sure to include units where appropriate.  Round your answers to the correct number of significant digits.

                                                  Mass                           m                                    Density = --------------     or    D = -------                                                 Volume                         v

Use the density formula to solve the following problems:

1.  Calculate the density of a material that has a mass of 52.457 g and a volume of 13.5 cm3.

 

 

2.  A student finds a rock on the way to school.  In the laboratory he determines that the volume of the rock is 22.7 cm3, and the mass in 39.943 g.   What is the density of the rock?

 

 

3.  If 30.943 g of a liquid occupy a space of 35.0 ml, what is the density of the liquid in g/cm3?

 

 Answers     1)    3.89 g/cm3                            2)      1.76 g/cm3                             3)      0.884 g/cm3

Name__________________________ Section____________________________

Hit the print command and show all work in the spaces provided.   Use the 5-step method and be sure to include units where appropriate.  Round your answers to the correct number of significant digits.

                                                  Mass                           m                                    Density = --------------     or    D = -------                                                 Volume                         v

Adjust the density formula and solve the problems below:

              m                                                                                 D = -------    Original Formula          -    Adjust the formula for the unknown     m =                v

1.  The density of silver is 10.49 g/cm3.  If a sample of pure silver has a volume of 12.993 cm3, what would the mass?

 

 

2.  How many grams of tin would occupy 5.5 L, if it has a density of 7.265 g/cm3?

 

 

3.  What is the mass of a 350 cm3 sample of pure silicon with a density of 2.336 g/cm3?

 

 

 Answers            1)      136.3g                                 2)      4.0 x 104 g                                 3)      820 g

Name__________________________ Section____________________________

Hit the print command and show all work in the spaces provided.   Use the 5-step method and be sure to include units where appropriate.  Round your answers to the correct number of significant digits.

                                                  Mass                           m                                    Density = --------------     or    D = -------                                                 Volume                         v

Adjust the density formula and solve the problems below:

               m                                                                                 D = -------    Original Formula          -    Adjust the formula for the unknown     v =                v

1.  Pure gold has a density of 19.32 g/cm3.  How large would a piece of gold be if it had a mass of 318.97 g?

 

 

2.  How many cm3 would a 55.932 g sample of copper occupy if it has a density of 8.92 g/cm3?

 

 

3.  The density of lead is 11.342 g/cm3.  What would be the volume of a 200.0 g sample of this metal?

 

 

 Answers            1)     16.51 cm3                                2)      6.270 cm3                               3)      17.63 cm3 

Answer the following questions. Remember to include units and significant figures in your answer.

1. Calculate the density of each of the following:

a. 252 mL of a solution with a mass of 500. g

b. 252 mL of a solution with a mass of 500 g

c. A 6.75 g solid with a volume of 5.35 cm3

d. 50.0 mg of a gas which occupies a volume of 0.0064 L

e. A substance with a mass of 7.55 x 104 kg and a volume of 9.50 x 103 L

2. Calculate the volume of each of the following:

a. 26.5 g of a solution with a density of 7.48 g/mL

b. A 3.400 kg solid with a density of 10.74 g/mL

3. Calculate the mass of each of the following:

a. A solid with a volume of 1.68 ft3 and a density of 9.2 g/mL

b. An 80 mL aliquot of a solution with a density of 5.80 g/cm3

c. A solid with a density of 2.65 g/mL and dimensions of 2.5 cm x 2.5 cm x 2.5 cm

4. The mass of an empty flask is 49.74 g. What is the mass of the flask filled with acetone (d = 0.792

g/mL) if the same flask weighs 75.2 g when filled with water?

5. An empty flask has a mass of 123.4 g. When the flask is filled with water, the mass is 211.6 g. If

10.0 g of zinc (d = 7.14 g/cm3) are added to the flask filled with water (and the sides of the flask

are dried from the displaced water) what is the new mass of the flask?

DENSITY QUESTIONS WORKSHEET1) A substance is cut into several pieces. As compared to the density ofthe original sample, the density of each piece will beA) Greater B) Less C) The Same2) As the temperature of water changes from 4 degrees Celsius To 0degrees Celsius. The volume of the water willA) Increase B) Decrease C) Remain the same3) If a sphere is heated to a temperature below it’s melting point,which of the following is most likely to occur?A)The volume of the sphere will increase but its density will decrease.B)The volume of the sphere will decrease but its density will increase.C)Both the volume and the density of the sphere will increase.D)Both the volume and the density of the sphere will decrease.4) An empty 250 milliliter beaker has a mass of 60 grams. When 100milliliters of oil is added to the beaker, the total mass is140 grams. What is the density of the oil?A) 1.4 g/ml B) 0.8 g/ml C) 0.6 g/ml D) 1.7 g/ml5) Which characteristic of an object will always change as the objecttravels from the Earth to the moon?A) Volume B) Density C) Weight D) Mass6) Four solid cubes have equal mass. Which occupies the greatest volume?A)Aluminum (density = 2.7 g/cm3) C) Tin (density 7.3 g/cm3)B)Glass (density 3.6 g/cm3) D) Lead (density = 11.4 g/cm3)7) What is the density of a rock, which has a mass of 35 grams and avolume of 7.0 cubic centimeters?A) 28 g/cm3 B) 42 g/cm3 C) 5 g/cm3 D) 0.20 g/cm38) A prediction of next winter’s weather is an example ofA) a measurement B) an inference C) an observation9) A person measures the length of a piece of wood and finds that it is41 centimeters. If the actual length is 40 centimeters, what is thepercent deviation (percent of error from the actual length)?A) 1.0% B) 2.5% C) 5.0% D) 9.8%10) Which factor can be predicted most accurately from day to day?

A) Chance of precipitation B) Altitude of the Sun at noon.C) Time of an earthquake occurring D) Direction of the wind.11) A student measures the depth of a lake as 7.00 meters. What is thepercent deviation if the correct measurement is 8.00 meters?A) 1.0% B) —12.5% C) 16.7% 0) 28.6%12) A 5.00 milliliter sample of a substance has a mass of 12.5 grams.What is the mass of a 100 milliliter sample of the same substance?

A) 40.0 g B)125 g C)400 g D)250 g

In a well-known tale, Archimedes was given the task of determining whether King Hiero's goldsmith was embezzling gold during the manufacture of a wreath dedicated to the gods and replacing it with another, cheaper alloy.[1]

Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily and compared with the mass; but the king did not approve of this.

Baffled, Archimedes took a relaxing immersion bath and observed from the rise of the warm water upon entering that he could calculate the volume of the gold crown through the displacement of the water. Allegedly, upon this discovery, he went running naked through the streets shouting, "Eureka! Eureka!" (Εύρηκα! Greek "I found it"). As a result, the term "eureka" entered common parlance and is used today to indicate a moment of enlightenment.

The story first appeared in written form in Vitruvius' books of architecture, two centuries after it supposedly took place.[2] Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time. [3][4]