Unit 1 Notes Guide Name # Part 2 – Quantitative Chemistry Block Chemistry

I. Measurement Qualitative deals with the ________ ____________, but quantitative deals with ________________. Quantitative data can be reported using various units of measurements.

i. SI System An international system of measurement based on the metric system Standards of measurement are preserved and used to base all other measurements.

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ii. Derived units are defined by a combination of base units.a. Volume = l x w x h = cm3 or dm3 or mL or Lb. Density = g/mL or g/cm3 = mass/volume

Special notes on units:i. The SI unit for temperature is _____________________ not ___________________________

ii. Different units can be used to describe equivalent volumes

Weight vs. Mass

i. Mass is a measurement of the ____________ of ____________ something contains

Mass is measured using a __________________

ii. Weight is a measurement the ________ of _____________ on an object

Weight is measured using a ____________

iii. Mass is always the same, but weight will change depending on __________________

iv. An object can be weightless, but it can NEVER be massless

II. Liquid Volume Measuring liquid volumes

1. Pour liquid into correct measuring device

2. At eye level check volume

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K ¿℃ + 273.151dm

3 = 1 L

1 cm3

= 1 mL

Always look at the ____________ of the ______________

3. If certain volume is needed, adjust volume by adding more or taking out liquid

Any removed liquid should be correctly discarded

Why should you never pick up a graduated cylinder to read the volume?

Graduated Cylinder vs. Buret

Graduated Cylinder Buret

___________ ___________III. Significant Figures (or Significant Digits)

When we make measurements, we are limited by the instrument.

We can only state values in a measurement that we are sure are correct.

with each measurement there is a degree of uncertainty beyond the markings

the last digit in a measurement is called the uncertain digit

Significant Figures – includes all measured digits ________ the __________________ digits

(also called sig figs)

Recording measurements with proper sig figs:

1. Include all certain digits (those with markings)

2. Estimate and include one digit beyond the physical markings on the instrument

3. Include units!

**A halfway marking does NOT increase the number of sig figs, but it does make it easier to

estimate the uncertain digit

Examples:

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PRACTICEDirections: Based on the diagrams below, make the best estimate for each of the measurements indicated by the arrows.

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Measurement & Precision Precision refers to the number of significant digits

The __________ markings on the instrument, the ________ significant figures, the ________ precise the instrument

Counting Significant Figures

The Atlantic-Pacific Rule When determining the number of significant digits in a measurement, follow the Atlantic-Pacific

rule.

PRACTICE:

Number # of Sig. Figs.

0.00965 3

940500

409000000

0.0003400

78000.

5.600

Number # of Sig. Figs.

0.000450

9203000000

0.0300

600

0.01

Rounding If the number to the right is between 0 and 4, then you keep the number the same. If the number to the right is between 5 and 9, then you round the number up.

EXAMPLES: Round the following

4300 (1 sig fig) 0.0909889 (4 sig figs)

4300 (4 sig figs) 0.0909889 (3 sig figs)

Whole numbers

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o Round the last number and ____________ remaining numbers to _________o 9567 (2 sig figs) 9600

Decimalso Round the last number and ____________the remaining numberso 0.9567 (2 sig figs) 0.96

PRACTICE

Round the following measurements to the requested number of significant figures:

1) 0.03256 (2 sig figs)

2) 564025000 (3 sig figs)

3) 0.236578 (4 sig figs)

4) 0.008965 (2 sig figs)

5) 4.2254 (3 sig figs)

6) 84999 (1 sig fig)

Calculating with Sig Figs Your answer cannot be more precise then the least precise measurement When calculating with significant figures, round off your answer __________ the calculation. Addition (+) and Subtraction (-)

i. The answer cannot have more digits to the right of the decimal point than any of the original numbers.

ii. Round to the least number of decimal places

PRACTICE1) 293.11

+ 34.72) 640.

- 23.1153) 35.89

-10.4) 235.7889

+ 310.2

Multiplication (x) and Division ()i. The number of significant figures in the result is set by the original number that has the smallest

number of significant figures.ii. Round to the least number of significant figures

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PRACTICE1) 0.8102

x 3.442) 94.20

3.16722

3) 2.41

x 11

4) 635.7889

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Scientific Notationi. Science deals with numbers that are very large and very small.

ii. A short-hand way to write these numbers is done using scientific notation.iii. There are two parts to a number written in scientific notation:

NOTE: If the decimal is moved to the right, the sign on the exponent is negative. If the decimal is moved to the left, the sign on the exponent is positive.

PRACTICE: Convert the following into scientific notation with 3 significant figures

1) 2400 4) 50.0

2) 0.0320 5) 634,000

3) 5610

Unit ConversionInquiry Activity

Purpose: To be able to take measurements with a specified unit and converting it to another unit of measurement.

Part 1 – Equivalence Statements:

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Equivalence statement is when two values are set to equal each other Equivalence statements can be written out in a form of a sentence.

Example: The gas station is currently selling gas at $2.00 per gallon

The sentence can then be written out using an equal sign in between the two valuesExample: The gas station is currently selling gas at $2.00 per gallon

1 gallon = $2.00Sentence Equivalence Statement

She walked 1 mile in 18 minutes 1 mile = 18 minutesA hamburger at McBurgers costs $1.50 1 hamburger = $1.50

There are 500 sheets of paper in 1 ream of paper 1 ream = 500 sheets

MODEL 1: During a car trip, the car travelled 90 miles away. The trip took 75 minutes to complete. According to the gauge, the car trip used up 3 gallons of gasoline. The driver took 1 stop for a bathroom/stretch break during the trip. He noticed that he played 28 songs by the end of the trip.

Write at least 5 equivalent statements from the description above.

1 trip = 1 trip =

1 trip = 1 trip =

1 trip =

Here are 3 other ratio relationships that we can obtain from the model:

90 miles = 3 gallons of gas 90 miles = 1 bathroom break 75 minutes = 28 songs

Write 4 other such relationships that you can obtain from the Model 1.

Part 2 – Conversion Factors:

A conversion factor changes a number of a specified unit to a number with a different unity

Conversion factors are typically written in a fraction. Equivalent statements can be written as a conversion factor. There are two ways to write the conversion factor for an equivalent statement

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Sentence Equivalence Statement

Conversion Factor 1

Conversion Factor 2

She walked 1 mile in 18 minutes

1 mile = 18 minutes

1mile18minutes

18 minutes1mile

A hamburger at McBurgers costs $1.50

1 hamburger = $1.50

1hamburger$1.50

$1.501hamburger

There are 500 sheets of paper in 1 ream of paper

1 ream = 500 sheets

1 ream500 sheets

500 sheets1 ream

Using the scenario from Model 1, choose four equivalence statement you came up with in part 1 and the 2 conversion factors for the statement in the table below.

Equivalence Statement Conversion Factor 1

Conversion Factor 2

1 trip = 90 miles

75minutes3gallons

90 miles28 songs

75 minutes = 28 songs

Critical Questions: 1. How long does it take to drive 90 miles?

2. How long does it take to drive 180 miles?

3. How many miles can you drive on 3 gallons of gas?

4. How many miles can you drive on 1 gallon of gas?

Part 3 – Unit Conversion & Conversion factors:

Unit conversions = Begin with one unit and want to express that value in a different unit.

Conversion factors are used when converting one unit to another. It is possible that one or more conversion factors are required to convert to the wanted unit. Using conversion factors to solve a problem is called Dimensional Analysis. 9

MODEL 2:

#s 16 x 178

x 317

=? 16 x 178

x 317

=? 16 x 38=6

Units days x hoursdays

x minhours

days x hoursdays

x minhours min

#s & units

2.5 days x 24 hrs1day

x 60 min1 hr

2.5 days x 24 hrs1 day

x 60 min1 hr

2.5 x 241

x 60 min1

=3600 min

Use the examples in the table above to complete the activities for the one-step, two-step and multi-step conversions.

One-Step Conversion: Convert 5.64 cm to inches

1 inch = 2.54 cm

1inch2.54 cm

2.54 cm1inch

Using the conversion factors above, fill in the box below that correctly converts 5.64 cm to inches. Like Model 2, show the cancellation and calculate the final answer with the correct unit.

5.64cm X =

Two-Step Conversion: Convert 5.64 m to inches

1 inch = 2.54 cm 1 m = 100 cm

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Equivalence Statement

The 2 Conversion Factors

1inch2.54 cm

2.54 cm1inch

Write the conversion factors for the second equivalence statement. Using the conversion factors above, fill in the boxes below that correctly converts 5.64 m to inches. Like Model 2, show the cancellation and calculate the final answer with the correct unit.

5.64 m X X =

Multi-Step Conversion: Convert 2.1 weeks to seconds

1 week = 7 days 1 day = 24 hrs 1 hr = 60 min 1 min = 60 s

1 week7 days

24 hours1 day

60 min1hour

1 min60 secs

Write the conversion factors for the equivalence statements. Using the conversion factors above, fill in the boxes below that correctly converts 2.1 weeks to seconds. Like Model 2, show the cancellation and calculate the final answer with the correct unit.

2.1wks X X X X =¿

Critical Questions:

1. What is the difference between, one step, two step, and multistep conversions? (Hint: look at how many conversion factors present in the problem)

2. Why do scientists use dimensional analysis?

Practice Unit Conversion:

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Fill in the proper conversion factor to complete the problem. Then, show the cancellation and calculate the final answer with the correct unit.

1. Convert 25.9 mL to ounces (oz)1 oz = 29.57 mL

25.9 mL X =

2. How many grams are in 1.78 tons?1 ton = 2000 lbs 1 kg = 2.2 lbs 1 kg = 1000 g

1.78 tons X X X =¿

3. Convert 5.33 miles to inches.1 mile = 5280 ft 1 ft = 12 inches

5.33mi X X =

4. How many miles are in 2500 inches?

2500∈X X =

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IV. Prefix Conversions Metric prefixes are used with base units to indicate the scale. Dimensional Analysis (AKA Factor method) can be used to convert prefixes

FROM TO Equivalent Statement(s)Prefix Unit Prefix Unit

km m

L mL

kJ MJ

ms µs

cm mm

µL L

*Each of the prefixes can be paired with any of the base units, but the scale remains the same.

Practice Prefix Conversions using Dimensional Analysis1. 3.98 km m

Equivalent statement(s) needed:

Dimensional analysis work:

2. 1.98 mm cm

Equivalent statement(s) needed:

Dimensional analysis work:

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V. Accuracy vs. Precision Accuracy refers to how __________ a measurement is to the ________ ___________

Precision refers to how close a _______ of measurements are to ________ ____________

Accuracy and precision are __________________ of each other.o Any set of data may be both, neither, or one but not the other

Identify the following as precise/accurate or not:

*For a set of data to be precise, the range of data should be no more than __________ in the last decimal place

Average

The average or mean is the ________ of all measurements ______________ by the ____________ of

measurements

Average is a measure of ___________________

Example: 2.56, 2.80, 2.57, 2.33, 2.61

Percent Error Percent Error is the ratio of absolute value of the ____________________ between theoretical and

_______________________ values divided by the theoretical value, multiplied by _________.

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% error=|Theoretical−Experimental|Theoretical

x100 % 

Synonyms for Theoretical: Synonyms for Experimental:

VI. Density Density refers to the degree of _______________________ of a substance by comparing the amount of

________ in a given unit of ____________.

o Units: __________ or ____________

Density= massvolume

PRACTICE: Calculate the following problems using your knowledge with density

1. If a sample of copper has a mass of 4.23 g and has a measured volume of 1.31 mL, what is its density?

2. What is the volume of a sample that has a mass of 20 g and a density of 4 g/mL?

3. The mass of the element is 10.23 g. The volume of the water it was placed in was 20.0 mL. The volume of the water after the element was placed in it was 21.5 mL

a. Calculate the volume of the element.

b. Calculate the density of the element.

c. If the accepted value is 6.93 grams per milliliter, calculate the percent error in significant figures.

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