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Basic Mathematical Skills in Chemistry Mr. Chapman Chemistry 20 Chemistry is Math! 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 years in chemistry courses. There are also some conventions and important notation that we have to get used to. The International System of Units (or Systeme Internationale) is basically an international language used by scientists to communicate quantities and measurements. Units are CRITICALLY IMPORTANT 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 Four Important SI Units: Although there are more SI units than this, these 4 will the most important to us: 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)+32 K = °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. Quick Practice 1. 2. 3. 4. Write the following numbers with the proper units: One thousand seconds Three hundred degrees Kelvin Two decimal five four grams Thirty two metres Scientific Notation 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 Continued... 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_______________________ Unit Conversions 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: 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) Use the Old-School Method to Convert These Units: 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 Conversion Factors: The Big Kid Way 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 1 km OR 1 km 1000 m Conversion Factors Continued... When you use a conversion factor, you always arrange it like this: Required Given For example, if you want to find how many metres there are in 5 km, you need to use this conversion factor: 1000 m 1 km Convert These Using the Big Kid Conversion Factors: 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 Those Others Were Too Easy... 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. Can you add, subtract, multiply and divide? We’ll see... SCIENTIFIC ARITHMETIC Adding and Subtracting with Units ( + - ) 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. Multiplying and Dividing with Units ( x / ) 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 And Finally, The Golden Rule: 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.