AKA how to do the math and science needed for Chemistry Scientific Processes AKA how to do the math and science needed for Chemistry

Scientific Notation In scientific notation a number is written as the product of two numbers: a coefficient or “M” value and 10 raised to a power. M x 10n The coefficient must always be a number greater than or equal to one and less than 10. The power of ten must always be an integer. When writing numbers greater than 1 in scientific notation, the exponent is positive and equals the number of places that the decimal has moved to the left. 6,300,000 = 6.3 x 106 When writing numbers less than 1 in scientific notation, the exponent is negative and equals the number of places the decimal has moved to the right. 0.000008 = 8 x 10-6

Scientific Notation Practice Questions Put the following numbers into scientific notation: 345,000 0.00296 92 0.83 Put the following numbers into standard notation: 5.79 x 103 3.1 x 10-2 7.02 x 106 1.53 x 10-4 Answers: 3.45 x 105 2.96 x 10-3 9.2 x 101 8.3 x 10-1 5,790 0.031 7,020,000 0.000153

Using Scientific Notation When multiplying numbers in scientific notation, do so in two parts. Multiply the “M” values first and get a value Add the exponents on the 10. Adjust the number at the end to put it in proper scientific notation if needed. 6.0 x 108 x 4.0 x 104 =24 x 1012 = 2.4 x 1013 When dividing numbers in scientific notation, do so in two parts. Divide the “M” values first and get a value Subtract the exponents on the 10 4.0 x 1014 = 0.5 x 108 = 5 x 107 8.0 x 106

Scientific Notation Practice Questions Try the following without a calculator: 4 x 103 x 6 x 105 = 2.5 x 103 / 5 x 106 = 3 x 108 x 4 x 10-10 = Try the following with a calculator 4.13 x 1015 x 5.4 x 102 = 1.6 x 104 / 1.39 x 1015 = 4.367 x 104 x 1.96 x 1011 = 24 x 108 = 2.4 x 109 5 x 10-3 12 x 10-2 = 1.2 x 10-1 2.2302 x 1018. 1.151 x 10-11. 8.559 x 1015.

Metric system or SI – based on 10 SI base units of measure Type of measurement Base unit What it measures Length Meters Length of object from one end to the other Mass Grams The quantity of matter an object contains Weight Newtons A force, the pull on a given mass by earth’s gravity Volume Cubic meters or liters Space occupied by matter Temperature Kelvin or Celcius The degree of hotness of an object. This measures the motion of the molecules Energy Joules The energy trapped inside molecular bonds or heat Time seconds The measurement of duration. 9 billion oscillations of the cesium atom Density Grams/Liter Ratio of the mass of an object and its volume

Metric Prefixes and Conversions Giga Mega kilo hecto deca base deci centi milli micro nano G M k h da meter liter d c m µ n 109 106 103 102 101 gram second 10-1 10-2 10-3 10-6 10-9 billion million thousand hundred ten one tenth hundredth thousandth millionth billionth A determine the starting unit and the ending unit Count the number of lines from start to end and notice the direction. For kilo to milli only move one space per line. The two units at each end are exceptions. They move 3 spaces per line! Move the decimal that number of spaces in the same direction that you counted from starting unit to ending unit

Metric conversion practice Convert 600 kg to g. Convert 5000 mL to L Convert 1 dam to mm Convert 500 m to km 600,000 g 5 L 10,000 mm 0.5 km

Metric to English Conversion Determine the unit wanted and the unit known. Find the correct conversion factor Arrange the conversion factor as a fraction like so: Units wanted Units known Multiply the conversion factor with the number you want to convert. The known units will cancel out leaving you with the unit you wanted to convert to. (if they don’t cancel out, you have set up the conversion factor incorrectly)

English to Metric Conversions Convert 16 in to cm Convert 450 km to mi Convert 45 L to gal Convert 345 lbs to kg Convert 75 mL to cm3 40.64 cm 992.07 mi 11.9 gal 156 kg 75 cm3 1 inch = 2.54 centimeter 1 gallon = 3.785 Liter 1 mL = 1 cm3 1 mile = 1.609 kilometer 1 kilogram = 2.2046 poudns

Specific Gravity Specific gravity – is a comparison of the density of a substance to the density of a reference substance, usually at the same temperature. Water at 4 degrees Celsius has a density of 1g/mL. We will use this figure as our reference. Specific Gravity = density of a substance (g/mL) density of water (g/mL) The units cancel, therefore specific gravity has no units. The specific gravity of a liquid can be measured with a hydrometer. Uses – diabetic detection, antifreeze composition, alcohol percentage.

Temperature Scales Celsius 0 degrees = freezing point of water 100 degrees = boiling point of water 37 degrees = normal body temperature Kelvin – degrees are not written on the K scale 273 K = freezing point of water 373 K = boiling point of water 0 K = matter is so cold it stops moving all together Relationship between temperature on the Celsius scale and Kelvin scale K = °C + 273 °C = K – 273

Dimensional Analysis Calculations in Chemistry involve measuring quantities. Each of which have two parts. The numerical portion of the measurement The units in which the measurement was taken. For example 27.4 cm When multiplying the quantities the numbers are multiplied, then the units are multiplied. Example: 1.2 cm x 2.0 cm = 2.4 cm2

Factor – Label Method A conversion factor is a fraction in which the numerator and denominator both represent the same measurement. 100 cm is a conversion factor since both the 1 m numerator and denominator represent the same length (1 meter) The value of all conversion factors must be equal to 1

FLM Conversions How many seconds are there in one week? How many minutes are there in a year? 525600 minutes What is the volume of a 25 g substance that has a density of 4.8 g/mL? 5.2 mL What is the mass of 92 mL of a substance that has a density of 39.1 g/mL? 3597 g

Graphing Graphing is used to show relationships between variables (Quantities) To predict trends Independent variable – the variable that you control or manipulate Independent variable goes on the X – axis Dependent variable – the variable that changes in response to the independent variable Dependent variable goes on the y – axis Choose a good scale: Calculate Range and divide by number of spaces

Scientific measurements Quantitative measurements – give results in a definite form, usually as numbers and units. Example: There are 25 mL of the liquid Qualitative measurements – give results in a descriptive, nonnumeric form. Example: The liquid is blue

Accuracy vs. Precision Accuracy – how close a measurement comes to the true value of whatever is measured. Precision – is concerned with reproducibility of the measurement (how many times you can get the same measurement) Significant figures – deals with the precision with which measurements are taken. The least precise measurement must be used in determining significant digits.

Accuracy vs. Precision

Rules for determining which digits are Significant. Every nonzero digit in a recorded measurement is significant. Zeros appearing between nonzero digits are significant. 206 Zeros appearing in front of all nonzero digits are not significant. They are acting as placeholders. 0.002500 Zeros at the end of a number and to the right of a decimal point are significant. 0.002500 Zeros at the end of a number with no decimal point are not significant. 38,000 Every number in front of the x 10 of scientific notation is significant.

How many sig figs? 35045 0.0025 0.0480 98300 3.800 x 1015 0.006802600 7080900000 5 2 3 4 7

Calculating Using Sig Figs When multiplying and dividing, limit and round your answer to the least number of significant figures in any of the numbers which you are multiplying or dividing. Example: 1.25 cm x .75 cm 0.9375 cm2  0.94 cm2 When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers that are being added or subtracted. Example: 15.25 g + 5.2 g 20.45 g  20.5 g

Calculating Using Sig Figs 23.7 x 3.9 = 45.76 x 0.25 = 6.47 x 64.5 = 1.678 / 0.42 = 28.367 / 3.74 = 92 11 417 4.0 7.58

Calculating Using Sig Figs

Making measurements in the lab There are two kinds of numbers in the world: exact and inexact If I quickly measure the width of a piece of notebook paper, I might get 220 mm (2 sig figs). If I am more precise, I might get 216 mm (3 sig figs). An even more precise measurement would be 215.6 mm (4 sig figs). When doing measurements, add one estimated digit. Example: If the ruler has a marking for every 0.1 mm and you can see the string you are measuring is about halfway between 4.5 mm and 4.6 mm long, then you would estimate the length is 4.55 mm long. In a graduated cylinder, the surface of the liquid is curved. This is called a meniscus. When you read the volume on a graduated cylinder, read it from the very bottom of the meniscus and make sure it’s at eye level.

Making Measurements