The Numerical Side of Chemistry Chapter 2 Types of measurement Quantitative- use numbers to describe –4 feet –100 ْF Qualitative- use description without

The Numerical Side of Chemistry Chapter 2

Types of measurement Quantitative- use numbers to describe 4 feet 100 F Qualitative- use description without numbers extra large Hot

Scientists prefer Quantitative- easy check Easy to agree upon, no personal bias The measuring instrument limits how good the measurement is

How good are the measurements? Scientists use two word to describe how good the measurements are Accuracy- how close the measurement is to the actual value Precision- how well can the measurement be repeated

Differences Accuracy can be true of an individual measurement or the average of several Precision requires several measurements before anything can be said about it examples

Lets use a golf analogy

Accurate? Precise?

In terms of measurement Three students measure the room to be 10.2 m, 10.3 m and 10.4 m across. Were they precise? Were they accurate?

Summary of Precision Vs. Accuracy Precision Grouping of measurements Need to have several measurements Repeatability Can have precision without accuracy Accuracy How close to true value Can use one measurement or many Can have accuracy without precision

Significant Figures

Significant figures (sig figs) How many numbers mean anything When we measure something, we can (and do) always estimate between the smallest marks. 21345

Significant figures (sig figs) The better marks, the better we can estimate. Scientist always understand that the last number measured is actually an estimate 21345

Sig Figs What is the smallest mark on the ruler that measures 142.15 cm? 142 cm? 140 cm? Here theres a problem does the zero count or not? They needed a set of rules to decide which zeroes count. All other numbers count

Which zeros count? Those at the end of a number before the decimal point dont count 1000 1000000000 12400 If the number is smaller than one, zeroes before the first number dont count 0.045 0.123 0.00006

Which zeros count? Zeros between other sig figs COUNT. 1002 1000000003 zeroes at the end of a number after the decimal point COUNT 45.8300 56.230000 If they are holding places, they dont. If they are measured (or estimated) they do

Sig Figs Only measurements have sig figs. Counted numbers are exact A dozen is exactly 12 A a piece of paper is measured 11 inches tall. Being able to locate, and count significant figures is an important skill. YOU MUST KNOW ALL THE SIG FIG RULES !!!!

Summary of Significant Figures A number is not significant if it is: A zero at the beginning of a decimal number ex. 0.0004lb, 0.075m A zero used as a placeholder in a number without a decimal point ex. 992,000,or 450,000,000 A number is a S.F. if it is: Any real number ( 1 thru 9) A zero between nonzero digits ex. 2002g or 1.809g A zero at the end of a number or decimal point ex. 602.00ml or 0.0400g

Learning Check 2 How many sig figs in the following measurements? 458 g_____ 4085 g_____ 4850 g______ 0.0485 g_____ 0.004085 g_____ 40.004085 g______

Learning Check 2 Cont 405.0 g______ 4050 g_______ 0.450 g_______ 4050.05 g______ 0.0500060 g______

Scientific Notation

Problems 50 is only 1 significant figure if it really has two, how can I write it? A zero at the end only counts after the decimal place Scientific notation 5.0 x 10 1 now the zero counts.

Purposes of Scientific Notation Express very small and very large numbers in a compact notation. 2.0 x 10 8 instead of 200,000,000 3.5 x 10 -7 instead of 0.00000035 Express numbers in a notation that also indicates the precision of the number. What is meant if two cities are said to be separated by a distance of 3,000 miles?

What Do We Mean by 3,000 miles? A distance between 2,999 and 3,001 miles? A distance between 2,990 and 3,010 miles? A distance between 2,900 and 3,100 miles? A distance between 2,000 and 4,000 miles?

What Do We Mean by 3,000 miles? Without a context, we dont know what is meant. In each case above, the colored digit is the largest one that is uncertain. As you ascend from bottom to top, the uncertainty decreases and the numbers become increasingly precise. Scientific notation will allow us to express these quantities (all are three thousand) with the precision or uncertainty being explicit.

First Things First Power-of-ten exponential notation is central to scientific notation. To start, you should review powers of ten and make sure that you understand the exponential notation and can covert it to standard notation.

How to Handle Significant Figs and Scientific Notation When Doing Math

Adding and subtracting with sig figs The last sig fig in a measurement is an estimate. Your answer when you add or subtract can not be better than your worst estimate. You have to round it to the least place of the measurement in the problem

For example 27.936.4+ l First line up the decimal places 27.93 6.4+ Then do the adding 34.33 Find the estimated numbers in the problem. 27.93 6.4 This answer must be rounded to the tenths place

What About Rounding? look at the number behind the one youre rounding. If it is 0 to 4 dont change it If it is 5 to 9 make it one bigger round 45.462 to four sig figs to three sig figs to two sig figs to one sig fig

Practice 4.8 + 6.8765 520 + 94.98 0.0045 + 2.113 6.0 x 10 2 - 3.8 x 10 3 5.4 - 3.28 6.7 -.542 500 -126 6.0 x 10 -2 - 3.8 x 10 -3

Multiplication and Division Rule is simpler Same number of sig figs in the answer as the least in the question 3.6 x 653 2350.8 3.6 has 2 s.f. 653 has 3 s.f. answer can only have 2 s.f. 2400

Multiplication and Division Same rules for division practice 4.5 / 6.245 4.5 x 6.245 9.8764 x.043 3.876 / 1983 16547 / 714

The Metric System An easy way to measure

Measuring The numbers are only half of a measurement It is 10 long 10 what. Numbers without units are meaningless.

The Metric System Easier to use because it is a decimal system Every conversion is by some power of 10. A metric unit has two parts A prefix and a base unit. prefix tells you how many times to divide or multiply by 10.

The SI System The SI system has seven base units from which all others are derived. Five of them are showed here Physical Quantities Name of UnitAbbreviation MassKilogramkg LengthMeterm TimeSeconds TemperatureKelvinK Amount of Substance Molemol

SI Units (Cont) These prefixes indicate decimal fractions or multiples of various units PrefixAbbreviationMeaning Mega-M10 6 Kilo-k10 3 Deci-d10 -1 Centi-c10 -2 Milli-m10 -3 Micro- 10 -6 Nano-n10 -9 Pico-p10 -12 Femto-f10 -15

Derived Units

SI units are used to derive the units of other quantities. Some of these units express speed, velocity, area and volume. They are either base units squared or cubed, or they define different base units

Volume calculated by multiplying L x W x H (for a square) x r 2 x H (for a cylinder) (for a sphere) Basic SI unit of volume is the cubic meter (m 3 ). Smaller units are sometimes employed ex. cm 3, dm 3 . Volume is more commonly defined by liter (L).

Mass weight is a force, is the amount of matter. 1gram is defined as the mass of 1 cm 3 of water at 4 C. 1000 g = 1000 cm 3 of water 1 kg = 1 L of water

Converting khDdcm how far you have to move on this chart, tells you how far, and which direction to move the decimal place. The box is the base unit, meters, Liters, grams, etc.

Conversions Change 5.6 m to millimeters khDdcm l starts at the base unit and move three to the right. l move the decimal point three to the right 5600

Conversions convert 25 mg to grams convert 0.45 km to mm convert 35 mL to liters It works because the math works, we are dividing or multiplying by 10 the correct number of times khDdcm

Temperature Scales

Measuring Temperature Celsius scale. water freezes at 0C water boils at 100C body temperature 37C room temperature 20 - 25C 0C

Measuring Temperature Kelvin starts at absolute zero (-273 C) degrees are the same size C = K -273.15 K = C + 273.15 Kelvin is always bigger. Kelvin can never be negative. 273 K

Temperature Conversions At home you like to keep the thermostat at 72 F. While traveling in Canada, you find the room thermostat calibrated in degrees Celsius. To what Celsius temperature would you need to set the thermostat to get the same temperature you enjoy at home ? C = 5/9 ( F-32) F = 9/5 (C ) +32 K = C + 273.15

Which is heavier? it depends

Density how heavy something is for its size the ratio of mass to volume for a substance D = M / V Independent of how much of it you have gold - high density air low density.

Calculating The formula tells you how units will be g/mL or g/cm 3 A piece of wood has a mass of 11.2 g and a volume of 23 mL what is the density? A piece of wood has a density of 0.93 g/mL and a volume of 23 mL what is the mass?

Calculating A piece of wood has a density of 0.93 g/mL and a mass of 23 g what is the volume? The units must always work out. Algebra 1 Get the thing you want by itself, on the top. What ever you do to onside, do to the other

Floating Lower density floats on higher density. Ice is less dense than water. Most wood is less dense than water Helium is less dense than air. A ship is less dense than water

Density of water 1 g of water is 1 mL of water. density of water is 1 g/mL at 4C otherwise it is less

Problem Solving

Word Problems The laboratory does not give you numbers already plugged into a formula. You have to decide how to get the answer. Like word problems in math. The chemistry book gives you word problems.

Problem solving Identify the unknown. Both in words and what units it will be measured in. May need to read the question several times. Identify what is given Write it down if necessary. Unnecessary information may also be given

Problem solving Plan a solution The heart of problem solving Break it down into steps. Look up needed information. Tables Formulas Constants Equations

Problem solving Do the calculations algebra Finish up Sig Figs Units Check your work Reread the question, did you answer it Is it reasonable? Estimate

Conversion factors A ratio of equivalent measurements. Start with two things that are the same. One meter is one hundred centimeters Write it as an equation. 1 m = 100 cm Can divide by each side to come up with two ways of writing the number 1.

Conversion factors A unique way of writing the number 1. In the same system they are defined quantities so they have unlimited significant figures. Equivalence statements always have this relationship. 1000 mm = 1 m

Write the conversion factors for the following kilograms to grams feet to inches 1.096 qt. = 1.00 L

What are they good for? We can multiply by one creatively to change the units. 13 inches is how many yards? 36 inches = 1 yard. 1 yard = 1 36 inches 13 inches x 1 yard = 36 inches

What are they good for? n We can multiply by one creatively to change the units. n 13 inches is how many yards? n 36 inches = 1 yard. n 1 yard = 1 36 inches n 13 inches x 1 yard = 36 inches

Dimensional Analysis Dimension = unit Analyze = solve Using the units to solve the problems. If the units of your answer are right, chances are you did the math right.

Dimensional Analysis A ruler is 12.0 inches long. How long is it in cm? ( 1 inch is 2.54 cm) in meters? A race is 10.0 km long. How far is this in miles? 1 mile = 1760 yds 1 meter = 1.094 yds Pikes peak is 14,110 ft above sea level. What is this in meters?

Multiple units The speed limit is 65 mi/hr. What is this in m/s? 1 mile = 1760 yds 1 meter = 1.094 yds 65 mi hr 1760 yd 1 mi1.094 yd 1 m1 hr 60 min 1 min 60 s

Units to a Power How many m 3 is 1500 cm 3 ? 3 1500 cm 3 1 m 100 cm 1 m 100 cm 1 m 100 cm 3 1500 cm 3 1 m 100 cm 3

Dimensional Analysis Another measuring system has different units of measure. 6 ft = 1 fathom 100 fathoms = 1 cable length 10 cable lengths = 1 nautical mile 3 nautical miles = 1 league Jules Verne wrote a book 20,000 leagues under the sea. How far is this in feet?

Quantifying Energy

Recall Energy Capacity to do work Work causes an object to move (F x d) Potential Energy: Energy due to position Kinetic Energy: Energy due to the motion of the object

Energy Kinetic Energy energy of motion KE = m v 2 Potential Energy stored energy Batteries (chemical potential energy) Spring in a watch (mechanical potential energy) Water trapped above a dam (gravitational potential energy) massvelocity (speed) B A C

The Joule The unit of heat used in modern thermochemistry is the Joule Non SI unit calorie 1Cal=1000cal 4.184J =1cal or 4.184kJ=Cal

Calorimetry The amount of heat absorbed or released during a physical or chemical change can be measured usually by the change in temperature of a known quantity of water 1 calorie is the heat required to raise the temperature of 1 gram of water by 1 C

Coffee Cup CalorimeterBomb Calorimeter

Specific heat Amount of heat energy needed to warm 1 g of that substance by 1 o C Units are J/g o C or cal/g o C

Specific heats of some common substances Substance Water Iron Aluminum Ethanol (cal/g C) (J/g C) 1.000 4.184 0.1070.449 0.2150.901 0.5812.43

Calculations Involving Specific Heat s = Specific Heat Capacity q = Heat lost or gained T = Temperature change (T final -T inital )

Example Calculate the energy required to raise the temperature of a 387.0g bar of iron metal from 25 o C to 40 o C. The specific heat of iron is 0.449 J/g o C

Documents

The Numerical Side of Chemistry Chapter 2 Types of measurement Quantitative- use numbers to describe –4 feet –100 ْF Qualitative- use description without