Density Practice Problems

Summary

This educational video script introduces the concept of density, defined as mass per unit volume. It guides viewers through three examples: calculating the density of a granite rock, determining the mass of a gold bar using its density, and finding the volume of isopropyl alcohol given its mass and density. The script emphasizes the importance of significant figures and unit consistency, highlighting the conversion between grams and cubic centimeters, and the interchangeable use of milliliters for liquids. The examples are practical, illustrating how density is used to solve real-world problems, and the script concludes with a teaser for upcoming videos on more complex density problems, including unit conversions and identifying unknown metals.

Takeaways

• 📚 Density is defined as mass per unit volume.
• 📏 The formula for calculating density is Density = Mass / Volume.
• 📉 When calculating density, units must be consistent, such as grams and cubic centimeters.
• 🔢 Significant figures in both mass and volume should be considered when determining the final answer.
• 📌 The units of density will be the units of mass divided by the units of volume, e.g., grams per cubic centimeter.
• 📐 Density can be used as a conversion factor to find mass from volume or vice versa.
• 📊 To find the mass of an object with given volume and density, multiply the volume by the density.
• 🔍 To find the volume of a substance with given mass and density, divide the mass by the density.
• 💡 Gold has a high density of 19.3 grams per cubic centimeter, indicating its heaviness.
• 🍾 Isopropyl alcohol, a liquid, has a density of 0.785 grams per cubic centimeter, which can be used to calculate its volume given its mass.
• 🥤 The volume of liquids is often measured in milliliters, which is equivalent to cubic centimeters.

Q & A

What is the definition of density?

Density is defined as mass per unit volume, mathematically expressed as Density = Mass / Volume.

What is the mass and volume of the granite rock mentioned in the script?

The granite rock has a mass of 15.5 grams and a volume of 6.01 cubic centimeters.

How is the density of the granite rock calculated in the script?

The density of the granite rock is calculated by dividing its mass (15.5 grams) by its volume (6.01 cubic centimeters), resulting in approximately 2.58 grams per cubic centimeter.

What is the significance of significant figures in the calculation of density in the script?

Significant figures are important to ensure the precision of the result. In the script, the density is rounded to three significant figures, which is 2.58 grams per cubic centimeter.

What are the units for the density of the granite rock as calculated in the script?

The units for the density of the granite rock are grams per cubic centimeter (g/cm³).

What is the density of gold given in the script?

The density of gold is given as 19.3 grams per cubic centimeter.

How is the mass of the gold bar calculated using its density and volume?

The mass of the gold bar is calculated by multiplying its volume (44.9 cubic centimeters) by the density of gold (19.3 g/cm³), resulting in approximately 867 grams.

What is the density of isopropyl alcohol, and how is it used to find its volume when given a mass?

The density of isopropyl alcohol is 0.785 grams per cubic centimeter. It is used as a conversion factor to find the volume when the mass is given, by dividing the mass (50.0 grams) by the density (0.785 g/cm³), resulting in approximately 63.7 cubic centimeters or milliliters.

Why might one choose to express the volume of a liquid in milliliters instead of cubic centimeters?

While cubic centimeters and milliliters are equivalent in volume, milliliters are commonly used to express the volume of liquids for convenience and convention.

What is the concept of a conversion factor in the context of density calculations?

A conversion factor in density calculations is a ratio that allows the conversion between two related quantities, such as mass and volume. It helps to cancel out units and isolate the desired unit in the calculation.

What are the next topics to be covered in the series on density problems according to the script?

The next topics to be covered include unit conversions, determining the volume of an object by measurement or displacement in water, and identifying unknown metals by measuring their density.

Outlines

00:00

📚 Calculating Density and Mass from Volume

This paragraph explains the concept of density, defined as mass per unit volume, using the formula Density = Mass / Volume. It demonstrates the calculation of the density of a granite rock with a mass of 15.5 grams and a volume of 6.01 cubic centimeters, resulting in a density of 2.58 grams per cubic centimeter. The explanation includes the significance of rounding to three significant figures and the importance of units in the calculation. It also covers a problem involving the mass of a gold bar given its volume and density, illustrating the use of density as a conversion factor to find mass.

05:03

🧪 Determining Volume from Mass Using Density

The second paragraph delves into using density to calculate the volume of a substance when its mass is known. It uses the example of isopropyl alcohol with a density of 0.785 grams per cubic centimeter and a mass of 50.0 grams to find the volume. The explanation highlights the selection of the appropriate conversion factor to cancel out the mass units and leave the volume in cubic centimeters. The result is rounded to three significant figures, yielding a volume of 63.7 cubic centimeters, which is also equivalent to milliliters due to the 1:1 relationship between the two units for liquids.

Keywords

💡Density

Density is a fundamental concept in physics, defined as the mass of an object divided by its volume. In the video, density is used to calculate the mass of a granite rock given its mass and volume, and to determine the volume of isopropyl alcohol when its mass is known. It is central to understanding the relationships between the mass and volume of substances, as exemplified by the script's step-by-step calculations.

💡Granite Rock

Granite Rock is a type of igneous rock used in the script to illustrate the calculation of density. The video uses the mass and volume of a granite rock to demonstrate how to find its density, which is a measure of how compact the rock is. The granite rock's density calculation serves as the first example in the video, setting the stage for further discussions on density.

💡Significant Figures

Significant figures are the digits in a number that carry meaningful information about its precision. The video explains how to determine the number of significant figures in a calculated result, such as the density of the granite rock, by looking at the digits and rounding accordingly. This concept is crucial for scientific accuracy and is demonstrated in the rounding of the calculated density to 2.58.

💡Gold

Gold is used in the script as an example of a material with a high density, which is 19.3 grams per cubic centimeter. The video explains how to use this density value to calculate the mass of a gold bar given its volume. Gold's high density is a key point in the video's discussion on the heaviness of the metal and its practical applications.

💡Conversion Factor

A conversion factor is a ratio that allows for the conversion of one unit to another. In the context of the video, density serves as a conversion factor to move between mass and volume. The script demonstrates how to manipulate these factors to solve for unknown quantities, such as converting the volume of a gold bar into its mass.

💡Isopropyl Alcohol

Isopropyl alcohol, also known as rubbing alcohol, is a liquid with a density of 0.785 grams per cubic centimeter. The video uses this density to calculate the volume that 50.0 grams of isopropyl alcohol would occupy. The example illustrates the application of density in liquids and the conversion between mass and volume.

💡Cubic Centimeter

A cubic centimeter is a unit of volume equal to a cube with 1 cm sides. The script frequently references cubic centimeters when discussing the volume of substances, such as the granite rock and isopropyl alcohol. It is the standard unit for volume in the examples provided, showing its importance in density calculations.

💡Milliliter

A milliliter is a unit of volume equivalent to a cubic centimeter, commonly used for liquids. The video mentions that the volume of isopropyl alcohol can be expressed in milliliters, reflecting the interchangeable use of these units in different contexts. The script suggests that while the units are the same, the choice between them can depend on the substance's state (solid or liquid).

💡Unit Conversion

Unit conversion is the process of changing a quantity from one unit of measure to another. The video script discusses the importance of unit conversion in density calculations, particularly when dealing with different units for the same physical quantity, such as cubic centimeters and milliliters.

💡Graduated Cylinder

A graduated cylinder is a piece of laboratory equipment used to measure the volume of liquids. Although not explicitly used in the calculations within the script, the video mentions it as a tool for measuring volume in more complex problems, such as determining the volume of an object by water displacement.

💡Unknown Metal

The script alludes to a future discussion on identifying unknown metals by measuring their density. This concept is introduced as an advanced application of density, where the unique density of a metal can be used to determine its type, showcasing the practical use of density in material science.

Highlights

A granite rock with a mass of 15.5 grams and a volume of 6.01 cubic centimeters has a density of 2.58 grams per cubic centimeter.

Density is calculated by dividing mass by volume.

Significant figures are important in scientific calculations, and the result should match the number of significant figures in the original data.

The units of density are determined by the units of mass and volume and should be reported as such.

Gold has a high density of 19.3 grams per cubic centimeter, indicating its heaviness.

A gold bar with a volume of 44.9 cubic centimeters has a mass of 867 grams, calculated using the density as a conversion factor.

Density can be used as a conversion factor to move between mass and volume.

Choosing the correct conversion factor is crucial for canceling out the correct units to obtain the desired result.

Isopropyl alcohol has a density of 0.785 grams per cubic centimeter, which is lower than that of gold.

50.0 grams of isopropyl alcohol occupies a volume of 63.7 cubic centimeters, calculated using the density as a conversion factor.

The volume of liquids is often measured in milliliters, which is equivalent to cubic centimeters.

The concept of density is fundamental in understanding the mass and volume relationship of substances.

Practical applications of density include identifying unknown metals by measuring their density.

Density problems can involve unit conversions and measuring volumes by submersion in a graduated cylinder.

The video introduces more complex density problems in the next installment.

Transcripts

a piece of granite rock has a mass of

15.5 G and a volume of

6.01 cubic cm what is its density so

density is defined as mass ID volume in

this problem I have a mass in GRS and I

have a volume in cubic centimet so all I

got to do is take this Mass

15.5 G and divide it here by the volume

which which is

6.01 cm cubed or cubic cenm and that

gives me 2.5 7

903 what do I round this to well I have

three significant figures in the top

three significant figures in the bottom

so I'm going to keep this keep this and

keep this and look to the nine to see

whether I keep the seven the same or if

I round up it's higher than five so I'll

round up and I'll get two

2.58 for my rounded answer now what are

the units here what are the units for

density in this division problem here I

haven't canceled out any units I have my

gr and my cubic centim and nothing's

happened to them they're still both

there so that means that the units of my

answer have to have both these in them

so I'll report this as

G

divided cubic cm just like this

and this is my final answer for the

density of the rock let's do another one

gold has a density of

19.3 G per cubic centimeter that's

really high gold is very heavy if you

have a gold bar with a volume of 44.9

cubic cm what is its mass okay so in

this example all we have is a volume and

we have to take the density to figure

out what the mass is going to be so

let's start out with this volume here

okay

44.9 cubic

cm now how are we going to get from

cubic cenm to GRS which is the

mass I like to think of density here as

a conversion factor that lets me move

between mass like how much something

weighs and lets me convert between that

and volume how much space something

takes up

so the density here I can write this as

a conversion factor I can kind of expand

this gr per cubic cenm like this okay

it's like

19.3 G is the top and then we have the

slash here and on the bottom I have one

cubic cm right I have this cm cubed but

if there's no number in front of it it

can always be one okay so I can take

this number here the density I can turn

it into a conversion factor kind of

pulling this this cubic cenm down and

putting it on the bottom of the fraction

putting a one in front of it as you know

anything that you can write as a

conversion factor you can also flip so I

could write density like this or I could

flip it and put one cubic cm on the top

and put

19.3 G on the bottom either way this

conversion factor lets me go between

mass and volume the question is which of

these do I want to use

I want to use the conversion factor

that's going to let me cancel out the

units of cubic cm and will leave me with

units in grams which is mass so what I'm

going to want to choose is the

conversion factor here that has centimet

Cubed on the bottom so that it will

cancel out and has grams on the top so

I'm going to choose this one I'm going

to write it in here and you'll see why

19.3 G up here on the top 1 cubic cm on

the bottom and now now I have cubic

centimet up here and I have cubic

centimet down here and I'm left with GRS

as my unit okay so I chose the right

version of the conversion factor okay

now I'm going to do

44.9 *

19.3 and I'm going get

86657 three sigfigs here three sigfigs

here and we have one which is a counting

number it's a definite number so we

don't worry about the significant figure

here so I'm going to round this number

to three significant figures I'm going

to keep the eight six look there to five

so that six is going to go up it's going

to be 8 6 7 and what are my units units

right here units are in grams

867 g is how much this piece of gold

would weigh one more isopropyl alcohol

is a liquid with a density of

0.785 G per Cub cm how much volume would

be taken out by 50.0 G of isopropyl

alcohol so here is our definition of

density and in this problem I get a

density I get this and I get a mass in

grams I'm going to have to use the

density to figure out what the volume is

so I'll start with

50.0 G and as I said I have to go

between mass and volume so I can use the

density as a conversion factor to do

that so let's write the density as a

conversion factor as I showed in the

previous example we're going to take

this centim cubed we're going to grab it

and we're going to pull it under the

fraction so we're going to get one

conversion factor that looks like this

0.785 G divided by 1 cm Cub that is one

of the conversion factors the other

valid conversion factor is to take this

and flip it so I'll do one cubic cm

divided by

0.785 G which of these do I want to use

I want to use the one that's going to

cancel out GRS from here and leave me

with cubic cenm so since GRS is going to

be on the top here I want to choose the

version that has grams on the bottom so

it's going to be this version of the

conversion factor that I'm going to use

so 50.0 G times this

1 cm cubed / 0

785 G Gams up here grams down there so

they cancel out so I know that I use the

right conversion factor I'm going to be

left with centime cubed and the mathod

I'll do is 50.0 * 1 the answer to that I

mean that's just going to be 50 but so

I'm 50 * 1 ided

0.785 and I get

63.

6943 three sigfigs here three sigfigs

here this is a counting number so it

doesn't matter so rounding the answer to

1 2 three significant figures look to

the nine SE the six goes up to 7even so

I get

63.7 the units are cubic cm now

isopropyl alcohol also known as rubbing

alcohol is a liquid and so for volume of

liquid we often measure it in

milliliters instead of cubic centimeters

now millimet milliliters and cubic cenm

are the same thing it's just that we

often use cubic centimet to talk about

the volume of like a solid object and we

often use milliliters to talk about the

volume of a liquid so if we wanted to be

super picky we might choose to say that

the volume of isopropyl alcohol because

it's a liquid is

63.7 ml milliliters and also because

isopropyl alcohol as a liquid if we

wanted to be super super picky we could

say that it had a density of

0.785 G per milliliter but it's the same

thing remember that 1 cubic cm equals 1

milliliter and you know if your teacher

is really picky or something and you're

talking about liquid you might want to

use milliliters instead of cubic

centimet but it's the exact same thing

anyway that finishes our introduction to

density in the next video we're going to

look at more difficult problems where

we've got to do unit conversions where

we've got to figure out what the volume

of something is by measuring it or by

dunking it into a graduated cylinder and

watching how much the water rises and

finally we'll look at problems where we

have to identify an unknown metal figure

out what kind of metal It Is by

measuring its density so that's all in

the next video on density problems