Unit 0: Scientists’ Tools

Unit 0: Scientists’ Tools

Chemistry is an Experimental Science
This unit will introduce the following tools that scientists use to “do chemistry” Section 1: Observations & Measurements Section 2: Accuracy, Precision & Significant Figures Section 3: Rounding & Calculating with Significant Digits Section 4: Density Section 5:Metric System & Converting Units Section 6: Scientific Notation

Section 1—Observations & Measurements

Collecting Data by Making Observations
Qualitative Data Descriptive Words Can be observed but not measured Examples: quantity, texture, smell, taste, appearance Quantitative Data Numbers Can be measured Examples: length, volume, time, temperature, taste, appearance

Qualitative Data: Common Mistake: Clear vs Colorless
Colorless does not describe transparency Words to describe transparency Clear Cloudy Opaque See-through Parts are see-through with solid “cloud” in it Cannot be seen through at all You can be clear & colored You can be cloudy & colored

Clear versus Colorless
Cherry Kool-Aid Example: Describe the following in terms of transparency words & colors Whole Milk Water

Clear versus Colorless
Cherry Kool-Aid Clear & red Example: Describe using the terms of transparency & color Whole Milk Opaque & white Water Clear & Colorless

Types of Quantitative Data
Quantity Most Common Unit Instrument used Mass (how much stuff is there) gram (g) Balance Volume (how much space it takes up) Liters (L) Graduated cylinder Temperature (how fast the particles are moving) Kelvin (K) or Celsius (°C) Thermometer Length Meters (m) Meter stick Time Seconds (sec) stopwatch Energy Joules (J) (Measured indirectly)

Uncertainty in Making Measurements
Each measuring instrument has different calibrations. The more lines, the more precise the instrument better measurement. Beaker A: 10 ml calibrations Volume = 28 mL Graduated Cylinder B: 1 ml calibrations Volume = 28.3 mL Buret C: 0.1 calibrations Volume = mL

Every Measurement has a Degree of Uncertainty
Record ALL numbers you definitely can read off the instrument, plus an estimated digit when measuring. The last decimal you write down is an estimate Write down a “5” if it’s in-between lines Write down a “0” if it’s on the line 5 mL 10 15 20 25 mL 5 mL 10 15 20 25 mL Remember: Always read liquid levels from the bottom of the meniscus Example: Read the measurements

Keep it SIMPLE! REMEMBER, the last decimal you write down is an estimate Write down a “5” if it’s in-between lines Write down a “0” if it’s on the line 5 mL 10 15 20 25 mL 5 mL 10 15 20 25 mL Example: Read the measurements It’s in-between the 10 & 11 line 10.5 mL It’s on the 12 line 12.0 mL

YOU TRY! Read the volume of the liquid in the graduated cylinder
 36.5 ml

HINT:Uncertainty in Measurement
Choose the right instrument If you need to measure out 5 mL, don’t choose the graduated cylinder that can hold 100 mL. Use the 10 or 25 mL cylinder The smaller the measurement, the more an error matters—use extra caution with small quantities If you’re measuring 5 mL & you’re off by 1 mL, that’s a 20% error If you’re measuring 100 mL & you’re off by 1 mL, that’s only a 1% error

Measuring Length of the Ruler

Extra Practice: Measurement Tool for Length
1.5 cm 1.95 cm

You Try! Uncertainty in Measurement
Example: Read the measurements 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

Uncertainty in Measurement
Example: Read the measurements It’s right on the 6.9 line 6.90 1 2 3 4 5 6 7 8 It’s between the 3.8 & 3.9 line 3.85 1 2 3 4 5 6 7 8

Practice!

Measurement Tool for Temperature

You Try: Measure the temperature of thermometer B

Measuring Mass with an Electronic Balance
Always read exactly what you see on the balance. There is no need to estimate the last digit.

Section 2—Accuracy, Precision & Significant Digits

Describe each group’s data as not precise, precise or accurate
Gathering Data Multiple trials help ensure that you’re results weren’t a one-time fluke! Accurate—getting the “correct” or “accepted” answer consistently Precise—getting consistent data (close to one another) Example: Describe each group’s data as not precise, precise or accurate Correct value

Precise & Accurate Data
Precise, but not accurate Correct value Example: Describe each group’s data as not precise, precise or accurate Precise & Accurate Correct value Not precise Correct value

Can you be accurate without precise?
This group had one value that was almost right on…but can we say they were accurate? Correct value No…they weren’t consistently correct. It was by random chance that they had a result close to the correct answer.

Can you be accurate without precise?
This group had one value that was almost right on…but can we say they were accurate? Correct value

You Try! Accepted Value = bulls-eye
*not accurate but precise *accurate & precise *not precise nor accurate

Example: Below is a data table produced by three groups of students who were measuring the mass of a paper clip which had a known mass of g. Group 1 Group 2 Group 3 Group 4 1.01 g g g 2.05 g 1.03 g g g 0.23 g 0.99 g g g 0.75 g Average g Group 1 has the most precise (all 3 measurements are consistent with each other) & accurate (the average value of the 3 trials are closest to the accepted value of g) data.

Percent Error A calculation designed to determine accuracy
% Error = |Accepted - Experimental| x 100 |Accepted|

You Try! A student measured an unknown metal to be 1.50 grams. The accepted value is 1.87 grams. What is the percent error? % Error = |1.87 –1.50|x 100 1.87 = 20% error

Significant Digits A significant digit is all the digits in a measurement known with certainty plus one final digit, which is uncertain or is estimated The real purpose of “significant digits” is to know how many places to record in an answer from a calculation.

Example explaining why SIG FIGS are important
3.0 mL = g/mL If the actual measurements were only taken to 2 or 3 decimal places… how can the answer be known to and infinite number of decimal places? It can’t!

Significant Digit Rules
1 All non-zero numbers & middle zeroes are significant Example: and 2 Leading zeros are never significant Example: 3 Trailing zeros are significant if there’s a decimal place in the value Example: 4 Trailing zeros are not significant if there is no decimal place Example: and

All the fuss about zeros
Middle zeros are important…we know that’s a zero (as opposed to being 112.5)…it was measured to be a zero 102.5 g The convention is that if there are ending zeros with a decimal place, the zeros were measured and it’s indicating how precise the measurement was. 125.0 mL 125.0 is between and 125.1 125 is between 124 and 126 The leading zeros will dissapear if the units are changed without affecting the physical meaning or precision…therefore they are not significant m m is the same as 127 mm

Sum it up into 2 Rules: Oversimplification Rule
The 4 earlier rules can be summed up into 2 general rules If there is no decimal point in the number, count from the first non-zero number to the last non-zero number 1 If there is a decimal point (anywhere in the number), count from the first non-zero number to the very end 2

Examples of Summary Rule 1
If there is no decimal point in the number, count from the first non-zero number to the last non-zero number 1 124 20570 200 150 Example: Count the number of significant figures in each number

If there is no decimal point in the number, count from the first non-zero number to the last non-zero number 1 124 20570 200 150 3 significant digits Example: Count the number of significant figures in each number 4 significant digits 1 significant digit 2 significant digits

If there is a decimal point (anywhere in the number), count from the first non-zero number to the very end 2 240. 370.0 Example: Count the number of significant figures in each number

If there is a decimal point (anywhere in the number), count from the first non-zero number to the very end 2 240. 370.0 3 significant digits Example: Count the number of significant figures in each number 3 significant digits 4 significant digits 4 significant digits

Importance of Trailing Zeros
Just because the zero isn’t “significant” doesn’t mean it’s not important and you don’t have to write it! “250 m” is not the same thing as “25 m” just because the zero isn’t significant The zero not being significant just tells us that it’s a broader range…the real value of “250 m” is between 240 m & 260 m. “250. m” with the zero being significant tells us the range is from 249 m to 251 m

Count the number of significant figures in each number
SELF CHECK 7007 m g m 250 mL 250. g x 104 Example: Count the number of significant figures in each number

Count the number of significant figures in each number
Let’s Practice 7007 m g m 250 mL 250. g 4 significant digits Example: Count the number of significant figures in each number 3 significant digits 5 significant digits 2 significant digits 3 significant digits x 104 5 significant digits

Section 3—Rounding & Calculating with Significant Digits

Rounding & Calculating with Sig Figs
Rules to Rounding! 1 What place are you rounding to? Circle it! What is the neighbor #? Underline it! 2 3 Look at the neighbor # & remember: 5 or more, raise the score Less than 5, let it lie 4 After rounding the place, all neighbors to the right are dropped to the right of the decimal point; if a whole number, all neighbors to the right become zeroes

SELF CHECK: Round each to the number of sig figs in the parentheses
(3) 5.05 (2) 6578 (3) (3) 5.1 6580 1.20 x 105

Performing Calculations with Sig Figs
When recording a calculated answer, you can only be as precise as your least precise measurement Addition & Subtraction: Answer has least number of decimal places as appears in the problem 1 Multiplication & Division: Answer has least number of significant figures as appears in the problem 2 Always complete the calculations first, and then round at the end!

Compute & write the answer with the correct number of sig digs
Addition Example #1 Addition & Subtraction: Answer has least number of decimal places as appears in the problem 1 Example: Compute & write the answer with the correct number of sig digs 1.457 g g g

Addition Example #1 Addition & Subtraction: Answer has least number of decimal places as appears in the problem 1 Example: Compute & write the answer with the correct number of sig digs 1.457 3 decimal places Lowest is “1” 1 decimal places g Answer is rounded to 1 decimal place 84.7 g

Subtraction Example #2 Addition & Subtraction: Answer has least number of decimal places as appears in the problem 1 Example: Compute & write the answer with the correct number of sig digs mL mL mL

Subtraction Example #2 Addition & Subtraction: Answer has least number of decimal places as appears in the problem 1 Example: Compute & write the answer with the correct number of sig digs mL mL 4 decimal places Lowest is “4” 6 decimal places mL Answer is rounded to 4 decimal places .0324 mL

Multiplication Example #1
Multiplication & Division: Answer has least number of significant figures as appears in the problem 2 Example: Compute & write the answer with the correct number of sig digs 1.704 g/mL  2.75 mL 4.686 g

Multiplication Example #1
Multiplication & Division: Answer has least number of significant figures as appears in the problem 2 Example: Compute & write the answer with the correct number of sig digs 1.704 g/mL  2.75 mL 4 significant dig Lowest is “3” 3 significant dig 4.686 g Answer is rounded to 3 significant digits 4.69 g

Division Example #2 Multiplication & Division: Answer has least number of significant figures as appears in the problem 2 Example: Compute & write the answer with the correct number of sig digs g mL = g/mL

Division Example #2 Multiplication & Division: Answer has least number of significant figures as appears in the problem 2 Example: Compute & write the answer with the correct number of sig digs 5 significant digits Lowest is “3” g mL = g/mL Answer is rounded to 3 sig digs 3 significant digits 535 g/mL

SELF CHECK #1 Example: Compute & write the answer with the correct number of sig digs 0.045 g g

Let’s Practice #1 Example: Compute & write the answer with the correct number of sig digs 0.045 g g 3 decimal places Lowest is “1” 1 decimal place 1.245 g Answer is rounded to 1 decimal place 1.2 g Addition & Subtraction use number of decimal places!

Let’s Practice #2 Example: Compute & write the answer with the correct number of sig digs 2.5 g/mL  23.5 mL

Compute & write the answer with the correct number of sig figs
Let’s Practice #2 Example: Compute & write the answer with the correct number of sig figs 2.5 g/mL  23.5 mL 2 significant fig Lowest is “2” 3 significant fig 58.75 g Answer is rounded to 2 significant digits 59 g Multiplication & Division use number of significant digits!

Let’s Practice #3 Example: Compute & write the answer with the correct number of sig figs 1.000 g 2.34 mL

Let’s Practice #3 Example: Compute & write the answer with the correct number of sig figs 4 significant digits Lowest is “3” 1.000 g 2.34 mL = g/mL Answer is rounded to 3 sig digs 3 significant digits 0.427 g/mL Multiplication & Division use number of significant digits!

Let’s Practice #4 Example: Compute & write the answer with the correct number of sig figs 6.732 m m

Let’s Practice #4 Example: Compute & write the answer with the correct number of sig figs 6.732 m m 3 decimal places Lowest is “2” 2 decimal places 6.502 m Answer is rounded to 2 decimal places 6.50 m Addition & Subtraction: use number of decimal places

Multi Step Calculations
Always complete the calculations first. Then round at the end! 6.68 x 1.2/ 14.8 =  .54 EXCEPTION: When adding/subtracting & then multiplying/dividing, follow the rules for addition/subtraction first. Then apply that number of sig figs to the multiplication/division. ( ) / 2.0 = _______ / = 3 s.f. / 2 s.f. = .17

You Try! ( )/ =

Section 4

Density the ratio of mass to volume of a sample
How heavy is it for its size? Lead = high density…small size & is very heavy Air = low density…large sample & very little mass

Density Mass Density m D = V Volume
In grams (g) Density In g/L or g/mL D = m V Volume In liters (L) or mL Don’t try to cancel out the units…density has “2 units” – a mass unit over a volume unit!

Floating Substances float when they are less dense than the substance they are in! Is vegatable oil more or less dense than water? Fewer particles in the same space = less dense More particles in the same space = More dense

Density Values: the larger the value, the more dense

Density Varies with Temperature
WHY? Most substances will expand when heated, increasing the volume & decreasing the density. Water is an exception: As water is cooled, it expands, increasing the volume & decreasing the density. Thus, ICE is less dense than WATER!

Calculating Volume using Water Displacement
The volume is the difference between the final volume and the initial volume of water. What is the volume of the dinosaur? ______________

Example 1—Solving for Density
What is the density of a sample with a mass of 2.50 g and a volume of 1.7 mL?

Example 1—Solving for Density
m = 2.50 g V = 1.7 mL Example: What is the density of a sample with a mass of 2.50 g and a volume of 1.7 mL?

Example 2—Solving for Mass
What is the mass of a 2.34 mL sample with a density of 2.78 g/mL?

Example 2—Solving for Mass
V = 2.34 mL D = 2.78 g/mL Example: What is the mass of a 2.34 mL sample with a density of 2.78 g/mL? 2.34 mL × × 2.34 mL

Example 3—Solving for Volume
A sample is 45.4 g and has a density of 0.87 g/mL. What is the volume?

Example 3—Solving for Volume
m = 45.4 g D = 0.87 g/mL V = ? Example: A sample is 45.4 g and has a density of 0.87 g/mL. What is the volume? V × × V 0.87 g/mL 0.87 g/mL

Is it aluminum? The metal has a mass of 612 g and a volume of 345 cm3.
SELF CHECK Example: Is it aluminum? The metal has a mass of 612 g and a volume of 345 cm3. The accepted density of aluminum is 2.70 g/cm3

Graphing Density Slope of line = DENSITY
If we make the y-axis mass and the x-axis volume then… 1. Pick 2 points on the best fit line 2. Calculate Y ( = 8.25g) 3. Calculate X ( 11-3 = 8 ml) 4. Plug into above equation and divide to solve for density . (8.25g/8 ml = 1.03 g/ml)

Section 5—Metric System & Dimensional Analysis

The Metric System Universal system of measurements
Based on the powers of ten Only the US and Myanmar do not use this system

Metric Prefixes Used in the metric system to describe smaller or larger amounts of base units The Great Magistrate King Henry Died by drinking chocolate milk monday near paris T • • G • • M • • K H D b d c m • • μ • • n • • p 1 x x x x x x 10-12 TERA GIGA MEGA KILO HECTA DECA BASE DECI CENTI MILLI MICRO NANO PICO Base Units have a value of 1 Examples are: Liters (L) meters (m) grams (g) seconds (s) Place a prefix in front of a base unit to make a larger or smaller number Example: ks = kilosecond mm = millimeter cg = centigram m = meter

Converting with the Metric System Using the Ladder Method
Determine the starting point. Count the jumps to your endpoint. Move the decimal the same number of jumps in the same direction If using the other prefixes, remember that there is a difference of 1000 or 3 places between each. T • • G • • M • • K H D b d c m • • μ • • n • • p EXAMPLE: 4 km = ______ m 4000

Examples T • • G • • M • • K H D b d c m • • μ • • n • • p
Convert 15 cl into ml Convert 6000 mm into Km Convert 1.6 Dag into dg Convert 3.4 nm into m 150 ml .006 Km 160 dg m

A Different Way to Convert between Units
Dimensional Analysis is another method It uses equivalents called conversion factors to make the exchange

Conversion Factors Change the Equivalents to Conversion Factors
1 foot = 12 inches or 4 quarters = 1 dollar What happens if you put one on top of the other? You create a ratio equal to 1 1 foot 12 inches 4 quarters 1 dollar

Common Equivalents = = = = = = = 1 ft 12 in 1 in 2.54 cm 1 min 60 s
1 hr = 3600 s 1 quart (qt) = 0.946 L 4 pints = 1 quart = 1 pound (lb) 454 g

Steps for using Dimensional Analysis
1 Write down your given information 2 Determine what you want. Use or create a conversion factor to compare what you have to what you want 3 4 Set up the math so that the given unit is on the bottom of the conversion factor… 5 Calculate the answer. Multiply across the top. Multiply across the bottom of the expression. Divide the bottom by the top

How many yards are in 52 feet?
Example #1 1 Write down your given information Example: How many yards are in 52 feet? 52 ft

Example #1 Determine what you want. 2 Example: How many yards are in 52 feet? 52 ft = ________ yds

Example #1 Use or create a conversion factor to compare what you have to what you want 3 &4 Example: How many yards are in 52 feet? 1 yd 52 ft  = ________ yds 3 ft Put the unit on bottom that you want to cancel out! The equivalent with these 2 units is: 3 ft = 1 yd A tip is to arrange the units first and then fill in numbers later!

Example #1 Calculate the answer. Multiply across the top. Multiply across the bottom of the expression. Divide the bottom by the top 5 Example: How many yards are in 52 feet? 1 yd  17.33 52 ft = ________ yd 3 ft Enter into the calculator: 52  1  3

How many grams are equal to 127.0 mg?
Example #2 1 Write down your given information Example: How many grams are equal to mg? 127.0 mg

Example #1 Write down an answer blank and the desired unit on the right side of the problem space 2 Example: How many grams are equal to mg? 127.0 mg = ________ g

Example #1 Use or create a conversion factor to compare what you have to what you want 3 & 4 Example: How many grams are equal to mg? 1 g 127.0mg  = ________ g 1000 mg Put the unit on bottom that you want to cancel out! The equivalent with these 2 units is: 1 g = 1000 mg A tip is to arrange the units first and then fill in numbers later!

Example #1 Calculate the answer. Multiply across the top. Multiply across the bottom of the expression. Divide the bottom by the top 5 Example: How many grams are equal to mg? 1 g  .127 127.0 mg = ________ g 1000 mg Enter into the calculator: 127  1  1000

Metric Conversion Factors
Many students get confused where to put the number shown in the previous chart… Select which unit is greater. Make that unit 1 and then determine how many smaller units are in the bigger unit. Example: Write a correct equivalent between “kg” and “g” 1 kg = 1000 g my way OR .001Kg = 1 g the other way

Try More Metric Equivalents
Example: Write a correct equivalent between “mL” and “L” There are two options: 1 L = 1000 ml my way 0.001 L = 1 mL the other way Example: Write a correct equivalent between “cm” and “mm” There are two options: 1 cm = 10 mm my way .1cm = 1mm the other way

Multi-step problems There isn’t always an equivalent that goes directly from where you are to where you want to go! With multi-step problems, it’s often best to plug in units first, then go back and do numbers.

How many kilograms are equal to 345 cg?
Example #3 Example: How many kilograms are equal to 345 cg? 345 cg = _______ kg There is no direct equivalent between cg & kg With metric units, you can always get to the base unit from any prefix! And you can always get to any prefix from the base unit! You can go from “cg” to “g” Then you can go from “g” to “kg”

Example #3 Example: How many kilograms are equal to 345 cg? g kg 345 cg   = _______ kg cg g Go to the base unit Go from the base unit

Example #3 Example: How many kilograms are equal to 345 cg? 1 g 1 kg 345 cg   = _______ kg 100 cg 1000 g 100 cg = 1 g 1000 g = 1 kg Remember—the # goes with the base unit & the “1” with the prefix!

Example #3 Example: How many kilograms are equal to 345 cg? 1 g 1 kg 345 cg   = _______ kg 100 cg 1000 g Enter into the calculator: (345  1 x 1)  (100 x 1000)

0.250 kg is equal to how many grams?
You Try! #1 Example: 0.250 kg is equal to how many grams?

0.250 kg is equal to how many grams?
You Try! #1 Example: 0.250 kg is equal to how many grams? 1000 g 0.250 kg  = ______ g 250. 1 kg 1 kg = 1000 g Enter into the calculator:  1000  1

Metric Volume Units To find the volume of a cube, measure each side and calculate: length  width  height height width length But most chemicals aren’t nice, neat cubes! Therefore, they defined 1 milliliter as equal to 1 cm3 (the volume of a cube with 1 cm as each side measurement) 1 cm3 = 1 mL

147 cm3 is equal to how many liters?
You Try! #3 Example: 147 cm3 is equal to how many liters?

147 cm3 is equal to how many liters?
You Try! #3 Example: 147 cm3 is equal to how many liters? Remember—cm3 is a volume unit, not a length like meters! 1 mL 1 L 147 cm3   = _______ L 0.147 1 cm3 1000 mL There isn’t one direct equivalent 1 cm3 = 1 mL 1 L = 1000 mL or .001L = 1mL Enter into the calculator: 147  1   1  1

MULTI-UNIT PROBLEM On the ICE Train in Germany: Picking up Speed!
What is the speed of the train in miles per hour?

MULTI-UNIT PROBLEM On the ICE Train in Germany: Picking up Speed!
What is the speed of the train in miles per second?

Section 6—Scientific Notation

Scientific Notation Scientific Notation is a form of writing very large or very small numbers that you’ve probably used in science or math class before Scientific notation uses powers of 10 to shorten the writing of a number.

Writing in Scientific Notation
The decimal point is put behind the first non-zero number The power of 10 is the number of times it moved to get there A number that began large (>1) has a positive exponent & a number that began small (<1) has a negative exponent

Write the following numbers in scientific notation.
Example #1 m g g m Example: Write the following numbers in scientific notation.

Example #1 4 m g g m  10 m Example: Write the following numbers in scientific notation. -5  10 g 2  10 m -7 7.532  10 m The decimal is moved to follow the first non-zero number The power of 10 is the number of times it’s moved

Example #1 4 m g g m  10 m Example: Write the following numbers in scientific notation. -5  10 g 2  10 m -7 7.532  10 m Large original numbers have positive exponents Tiny original numbers have negative exponents

Reading Scientific Notation
A positive power of ten means you need to make the number bigger and a negative power of ten means you need to make the number smaller Move the decimal place to make the number bigger or smaller the number of times of the power of ten

Write out the following numbers.
Example #2 1.37  104 m 2.875  102 g 8.755  10-5 g 7.005 10-3 m Example: Write out the following numbers.

Write out the following numbers.
Example #2 1.37  104 m 2.875  102 g 8.755  10-5 g 7.005 10-3 m 13700 m Example: Write out the following numbers. 287.5 g m m Move the decimal “the power of ten” times Positive powers = big numbers. Negative powers = tiny numbers

Scientific Notation & Significant Digits
Scientific Notation is more than just a short hand. Sometimes there isn’t a way to write a number with the needed number of significant digits …unless you use scientific notation!

Take a look at this… Write 120004.25 m with 3 significant digits
Remember…120 isn’t the same as ! Just because those zero’s aren’t significant doesn’t mean they don’t have to be there! This answer isn’t correct!

Let’s Practice 0.0007650 g with 2 sig figs 120009.2 m with 3 sig figs
mL with 4 sig figs Example: Write the following numbers in scientific notation. 1.34 × 10-3 g 2.009  10-4 mL 3.987  105 g Example: Write out the following numbers

Let’s Practice 0.0007650 g with 2 sig figs 7.7 × 10-4 g
m with 3 sig figs mL with 4 sig figs 7.7 × 10-4 g Example: Write the following numbers in scientific notation. 1.20 × 105 g 2.391 × 105 g 1.34 × 10-3 g 2.009  10-4 mL 3.987  105 g g Example: Write out the following numbers mL g

How to input scientific notation numbers into the calculator
1. Punch the number (the digit number) into your calculator. 2. Push the EE or EXP button. Do NOT use the x (times) button! 3. Enter the exponent number. Use the +/- button to change its sign. Practice: Multiply 6.0 x 105 times 4.0 x 103 on your calculator. Your answer is _____________

Unit 0: Scientists’ Tools

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