Basic Mathematical Skills in Chemistry

Mr. DoerksenChemistry 20

In chemistry, we have to do a lot of math.

None of the math is super complicated, but it is important that you learn some basic rules that we will use for the next two Semester in chemistry courses.

There are also some conventions and important notation that we have to get used to.

Chemistry is Math!

The International System of Units (or Systeme Internationale) is basically an international language used by scientists to communicate quantities and measurements.

When you write a number, you need to get used to one, simple fact.

A NUMBER IS MEANINGLESS WITHOUT UNITS

For instance, let’s say I walk up to you and say this: “Hey, I have 500 of water.”

What does that mean?!?!?

NOTHING

Units are CRITICALLY IMPORTANT

Although there are more SI units than this, these 4 will the most important to us:

Four Important SI Units:

FOUR IMPORTANT SI UNITS IN CHEMISTRY:

Quantity SI Base Unit English Equivalent

Length Meter (m) 1 m = 39.36 in

Mass Kilograms (kg) 1 kg = 2.2 lbs

Time Seconds (s)

Temperature Degrees Kelvin (K) °F = 1.8(oC)+32K = °C + 273.15

Note: many people screw up the SI unit for mass. The SI unit for mass is kg, which means 1000 g. Lots of people think this means the SI unit for mass is grams; ITS NOT.

Write the following numbers with the proper units:

1. One thousand seconds2. Three hundred degrees Kelvin3. Two decimal five four grams4. Thirty two metres

Quick Practice

Scientists often make use of a special way of expressing large and small numbers. The numbers are expressed in terms of powers, or exponents, of 10. Only one real number is allowed to be placed to the left of the decimal place when a number is expressed in scientific notation.

1. Convert these numbers, which are written in exponential notation, to ordinary expanded notation.

a. 1 x 102_______________________ b. 4.56 x 10-3___________________ c. 9.65 x 106____________________ d. 6.45 x 1012___________________

e. 8.56 x 10-4____________________ f. 6.60 x 100____________________

Scientific Notation

2. Convert the following numbers into exponential notation.

a. 0.01________________________ b. 10 000 ______________________

c. 0.000 000 0001 _______________ d. 100 _________________________

e. 0.000 2 _____________________ f. 1 ___________________________

3. Re-write the following numbers in correct scientific notation form:

a. 856.3 x 10-3__________________ b. 0.005 x 102____________________

c. 44.32 x 105__________________ d. 99 x 101_______________________

Scientific Notation Continued...

There is an old school way to convert between units, and a big kid way that we are going to learn in this class. Here is old school:

Unit Conversions

From top to bottom, the metric ladder goes in the following order:Mega (106)Kilo (103)Hecto (102)Deca (101)Base (100)Deci (10-1)Centi (10-2)Milli (10-3)Micro (10-6)

1. 470 ml = _______ L 2. 2000 L = _______ kL 3. 83 g = _______ kg

4. 41300 L = _______ kL 5. 5340 mg = _______ g 6. 2000 m = _______ km

7. 13200 kg = _______ g 8. 1000000 g = _______ kg 9. 320 ml = _______ L

10. 12 L = _______ ml 11. 800 L = _______ kL 12. 250 cm = _______ m

Use the Old-School Method to Convert These Units:

Conversion factors are the most important and useful way to convert between different units.

A conversion factor shows the relationship between two units. For instance, 1km = 1000m, so the conversion factor is:

1000 m OR 1 km 1 km 1000 m

Conversion Factors: The Big Kid Way

When you use a conversion factor, you always arrange it like this:

RequiredGiven

For example, if you want to find how many metres there are in 5 km, you need to use this conversion factor:

1000 m1 km

Conversion Factors Continued...

13. 20 ml = _______ kL 14. 7000 ml = _______ L 15. 72 cm = _______ mm

16. 900 L = _______ ml 17. 65 m = _______ mm 18. 100 cm = _______ m

19. 117 km = _______ m 20. 42 mg = _______ kg 21. 32 m = _______ mm

Convert These Using the Big Kid Conversion Factors:

A man has 17284 logs of wood. He knows that he can bundle 4 logs together to make a complete bundle. How many complete bundles can he make? Use a conversion factor.

The density of water is 1 g/mL. If you have 2.68 kg of water, how many mL do you have? Use conversion factors.

Those Others Were Too Easy...

SCIENTIFIC ARITHMETIC

Can you add, subtract, multiply and divide? We’ll see...

When you add and subtract numbers with units associated with them, the units never change.

Ex: 2 kg + 3 kg = 5 kg

It seems fairly obvious. However, you also need to know that in order to add two numbers together, they must have the same units as a result.

Ex: we can’t add 2 m to 3 km unless we make the units the same.

Adding and Subtracting with Units ( + - )

When we multiply and divide with units, it gets a little more complicated because the units also multiply and divide.

Ex: 2 m x 2 m = 4 m2

As a result, sometimes the units will cancel each other out, and we have to understand this:

Ex: 4 s x 2 m = 8 m s

Multiplying and Dividing with Units ( x / )

For example: 3 x 4.5 x 10 = ?

If you get 140, you broke the golden rule.

If you get 135, you can stay in this class.

And Finally, The Golden Rule:

NEVER, EVER, ROUND YOUR ANSWER IN THE MIDDLE OF A CALCULATION