The Interdependence of math and science• The Interdependence of Math and Science: You really can't learn one

without the other.• Unfortunately, science is often presented to high school students without

the math that students need to truly understand the subject. • You see, Mathematics and Science are Inseparable. Math has no point

unless it is describing aspects of nature or economics, and science cannot study nature without using the concept of scale and mathematical descriptions of natural phenomena.

• Any attempt to take the math out of the natural sciences so that biology, chemistry and physics will be easier

for students, is like taking the food away from lunch so that the meal is easier to swallow. It just doesn't make sense, and ultimately such a strategy

cheats students out of their education.

What does interdependent mean?Why are math and science interdependent?

Slide by: J. Levasseur ©

Understanding Some Fundamentals of Math

0 1 2 3 4 5

1

2

3

4

That

5

This

• There are a few essential math skills that you must master in order to learn high school chemistry.

• Those Skills are:

1. Multiplying and Dividing Fractions

2. Direct Proportions The #1 most important math

skill there is.

3. Indirect Proportions

This

This per That That

Fractions Direct Proportion Indirect Proportion

A Very Significant Problem:How many students per room?

Here it is; if you can solve this problem you can solve just about any chemistry problem you will ever see in this buildingThere will be 25 students PER room

• There are in fact 2200 students at Springfield Central High School.

• There are 88 classrooms at Central.

• If the students are evenly disbursed to all the classrooms, what is the number of students per room?

Mass (measured in Grams or Kilograms) How heavy is an egg?Volume (measured in m3, cm3 or Liters) How much space does an egg occupy?Density (measured in kg/m3 , g/cm3) Does an egg size piece of steel or

wood have the same mass?Pressure (measured in torr, atm, mm Hg) How hard is it to crush an egg by squeezing evenly from all sides?Amount (measured in dozens, or in chemistry Moles) How many eggs come in a standard carton of eggs?Temperature (measure in ˚Fahrenheit, ˚Celsius or Kelvin) At what temperature will an egg cook?

MeasurementsComparing matter and energy against clear standards of measurements,

we can communicate more effectively in answering simple questions.

Question:How Do We Use the Concept of Scale to Understand Matter and Matter’s Changes?

The size (or volume) does not tell us how much matter there is.

Mass

• Mass (measured in Grams or Kilograms)

• How heavy is an egg?• Mass is technically a measure

of how much matter is present• But on Earth Mass is essentially

weight, weight technically is the force of gravity on matter

1 gram1,000 grams

Mass of a single peanut

The gram is a unit of mass

Mass of a 1-L bottle

of water

Volume

You can measure the volume of a liquid using a graduated cylinder.

75 mL1 mL = 1 cm3

You can measure the volume of a liquid using a graduated cylinder.

Volume indicates an amount of space.The milliliter (mL) is a unit of volume.

1cm3 = 1mL

• Volume (measured in m3, cm3 or Liters)

• How much space does an egg occupy?

• Volume measure 3-dimensional space

Density Tutorial

1 cm3 1 cm3 1 cm3

Which of these three cube has the most volume? Which of these three cubes has the most mass? What is the density of each cube?

3 blocks of equal volume

3 different mass values

plastic glass iron

Titanium has a known density of 4.5 g/cm3. If 45 g of titanium are added to a graduated cylinder containing 50 mL of water, what will the cylinder read after the titanium has been added?

Looks like “This per That” to

me!!!

density: a property of a substance that describes how much matter the substance contains per unit volume; typical units are grams per cubic centimeter (g/cm3).

• Density (measured in kg/m3, g/cm3)

• Does an egg size piece of steel or wood have the same mass?

Pressure

force: an action, such as a push or a pull, that has the ability to change the motion of an object, such as to start it moving, stop it, or turn it.

pressure: force per unit area with units of Pa (N/m2) or psi (lb/in2) or atm; acts equally in all directions within a liquid or a gas.

F

P A

• Pressure (measured in torr, atm, mm Hg)• How hard is it to crush an egg by squeezing evenly from all sides?• Pressure is a force per unit area, or P= F/A

Amount• Amount (measured in

dozens, or in chemistry Moles)

• How many eggs come in a standard carton of eggs?

• Mole is a count word with a value of 6.02 x 1023

• We often measure amounts in groups like:– Pair of shoes (2 shoes)– Dozen eggs (12 eggs)– Ream of Paper (500 Sheets)

• In chemistry the key amount that we count by is the mole.– Mole of Atoms (6.02 x 1023

atoms)– Moles allow us the measure and

count things that are too small to be counted (atoms and molecules)

Matter and energy are closely associated:

E=mc2 says matter is energy, (but you need a nuclear reaction to get that energy)Chemical compounds also hold

energy in the chemical bonds; you break those bonds in a chemical reaction to release the energy.

This is how fuel and food give energy.

http://www.answers.com/topic/joule Prentice Hall ChemGuide Essentials of Chemistry 2002

• Energy is the ability to do work.– Work is the ability to move objects.

• Energy is measured in units called joules.• A joule is the SI (international measuring

system) unit of electrical, mechanical, and thermal energy.– A joule is a unit of electrical energy equal

to the work done when a current of one ampere is passed through a resistance of one ohm for one second.

– A joule is likewise a unit of energy equal to the work done when a force of one Newton acts through a distance of one meter.

– 1 calorie = 4.184 joules• Calorie is a common unit of measuring

energy• A calorie is the energy, (heat) required

to raise 1 gram of water 1 degree Celsius

How Energy is Measured

Temperature: a measure of hot/cold but also a measure of loss/gain of Energy

Prentice Hall ChemGuide Essentials of Chemistry 2002

Study Cards

Temperature (measure in ˚Fahrenheit, ˚Celsius or Kelvin)

At what temperature will an egg cook?

• Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold.

• However, Temperature is a measure of kinetic energy or rapidness of molecular movement

• Temperature is officially measured with Kelvin in the SI system– Temperature is usually measured in Celsius or,

(in the USA) by Fahrenheit.– You will need to convert all temperature

measurements to Kelvin for gas problems• The temperature of gases effects the volume

and pressure of gases

Converting Between Temperature Units• To convert a temperature from Fahrenheit

to Celsius use the following formula: °C = 5/9 X (°F – 32)

• To convert a temperature from Celsius to Fahrenheit use the following formula: ° F = 9/5 °C + 32

• A change in temperature of 1 °F represents only 5/9 as much as a change in temperature of 1 °C.– A degree Celsius is 9/5 “larger” than a

Fahrenheit degree.– A Kelvin and Celsius degree are the

same size, just 0 is represents different amounts of energy.

• To convert a degree Celsius to Kelvin use: K = ° C + 273

• To convert Kelvin to degrees Celsius use: ° C = K - 273 Prentice Hall ChemGuide Essentials of Chemistry 2002

To Solve Gas Law Problems

You need to know how to convert TO Kelvin:• If given Celsius:

• Add 273• K = ° C + 273

• If given Fahrenheit:• Convert to Celsius

then add 273• °C = 5/9 X (°F – 32)• K = ° C + 273