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Units of Measurement

CH. 2 - MEASUREMENT

A. Number vs. Quantity

Quantity - number + unit

UNITS MATTER!!

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II. Using Measurements

CH. 2 - MEASUREMENT

A. Accuracy vs. Precision

Accuracy - how close a measurement is to the accepted value

Precision - how close a series of measurements are to each other

ACCURATE = CORRECT

PRECISE = CONSISTENT

A. Accuracy vs. Precision

B. Percent Error

Indicates accuracy of a measurement

100accepted

acceptedalexperimenterror %

your value

given value

B. Percent Error

A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.

100g/mL 1.36

g/mL 1.36g/mL 1.40error %

% error = 2.9 %

C. Significant Figures

Indicate precision of a measurement.

Recording Sig Figs

Sig figs in a measurement include the known digits plus a final estimated digit

2.31 cm

C. Significant Figures Counting Sig Figs

Digits from 1-9 are always significant.

Zeros between two other sig figs are always significant

One or more additional zeros to the right of both the decimal place and another sig digit are significant

Count all numbers EXCEPT: Leading zeros -- 0.0025 Trailing zeros without

a decimal point -- 2,500

5085

2.60

739

4. 0.080

3. 5,280

2. 402

1. 23.50

C. Significant Figures

Counting Sig Fig Examples

1. 23.50

2. 402

3. 5,280

4. 0.080

4 sig figs

3 sig figs

3 sig figs

2 sig figs

C. Significant Figures

Calculating with Sig Figs

Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.

(13.91g/cm3)(23.3cm3) = 324.103g

324 g

4 SF 3 SF3 SF

C. Significant Figures

Calculating with Sig Figs (con’t)

Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.

3.75 mL

+ 4.1 mL

7.85 mL

224 g

+ 130 g

354 g 7.9 mL 350 g

3.75 mL

+ 4.1 mL

7.85 mL

224 g

+ 130 g

354 g

C. Significant Figures

Calculating with Sig Figs (con’t)

Exact Numbers do not limit the # of sig figs in the answer.Counting numbers: 12 studentsExact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm

C. Significant Figures

5. (15.30 g) ÷ (6.4 mL)

Practice Problems

= 2.390625 g/mL

18.1 g

6. 18.9 g

- 0.84 g18.06 g

4 SF 2 SF

2.4 g/mL2 SF

D. Scientific Notation

A way to express any number as a number between 1 and 10 (coefficient) multiplied by 10 raised to a power (exponent)

Number of carbon atoms in the Hope diamond

460,000,000,000,000,000,000,000

4.6 x 1023

Mass of one carbon atom

0.00000000000000000000002 g

2 x 10-23 g coefficient exponent

D. Scientific Notation

Converting into Sci. Notation:

Move decimal until there’s 1 digit to its left. Places moved = exponent.

Large # (>1) positive exponentSmall # (<1) negative exponent

Only include sig figs.

65,000 kg 6.5 × 104 kg

D. Scientific Notation

7. 2,400,000 g

8. 0.00256 kg

9. 7 10-5 km

10. 6.2 104 mm

Practice Problems

2.4 106 g

2.56 10-3 kg

0.00007 km

62,000 mm

D. Scientific Notation

Calculating with Sci. Notation

(5.44 × 107 g) ÷ (8.1 × 104 mol) =

5.44EXPEXP

EEEE÷÷

EXPEXP

EEEE ENTERENTER

EXEEXE7 8.1 4

= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

Type on your calculator:

D. Scientific Notation

11. (4 x 102 cm) x (1 x 108cm)

12. (2.1 x 10-4kg) x (3.3 x 102 kg)

13. (6.25 x 102) ÷ (5.5 x 108)

14. (8.15 x 104) ÷ (4.39 x 101)

15. (6.02 x 1023) ÷ (1.201 x 101)

Practice Problems

4 1010 cm2

6.9 10-2 kg2

1.1 x 10-6

1.86 x 103

5.01 x 1022

Chemistry Binder Organization

Chemistry Binder: (8 tabs)

Reference:

Administrative papers (policies & procedures, etc)

Chemistry reference handouts (Periodic Table, Chemical Reference Sheet, etc)

Notes

Filler Paper for lecture notes

Handouts or worksheets to supplement textbook

Divided by chapter or unit – there are 7 separate sections for the first semester

E. Derived Units

Combination of base units.

Volume (m3 or cm3) length length length

D = MV

1 cm3 = 1 mL1 dm3 = 1 L

Density (kg/m3 or g/cm3)mass per volume

F. DensityM

ass

(g)

Volume (cm3)

Δx

Δyslope D

V

M

F. Density

An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass.

GIVEN:

V = 825 cm3

D = 13.6 g/cm3

M = ?

WORK:

M = DV

M = (13.6 g/cm3)(825cm3)

M = 11,200 g

V

MD

F. Density

A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid?

GIVEN:

D = 0.87 g/mL

V = ?

M = 25 g

WORK:

V = M D

V = 25 g

0.87 g/mL

V = 29 mLV

MD

Homework

Complete Worksheet “Using Measurements – Chapter 2”: due Monday (skip section on Dimensional Analysis – we will learn this next week )

Study for test tomorrow

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Dimensional Analysis

Conversion Factors

Problems

A. Problem-Solving Steps

1. Analyze

2. Plan

3. Compute

4. Evaluate

B. Dimensional Analysis

Dimensional Analysis A tool often used in science for

converting units within a measurement system

Conversion Factor A numerical factor by which a quantity

expressed in one system of units may be converted to another system

3

3

cm

gcm

B. Dimensional Analysis

The “Factor-Label” Method Units, or “labels” are canceled, or

“factored” out

g

B. Dimensional Analysis

Steps:

1. Identify starting & ending units.

2. Line up conversion factors so units cancel.

3. Multiply all top numbers & divide by each bottom number.

4. Check units & answer.

Fractions in which the numerator and Fractions in which the numerator and denominator are EQUAL quantities denominator are EQUAL quantities expressed in different unitsexpressed in different units

Example: 1 in. = 2.54 cm

Factors: 1 in. and 2.54 cm

2.54 cm 1 in.

C. Conversion FactorsC. Conversion Factors

Conversion factor

cancel

By using dimensional analysis / factor-label method, By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the side up, and the UNITS are calculated as well as the

numbers!numbers!

How many minutes are in 2.5 hours?

2.5 hr 2.5 hr x x 60 min60 min

1 hr

= 150 min

Write conversion factors that Write conversion factors that relate each of the following relate each of the following pairs of units:pairs of units:

1. Liters and mL1. Liters and mL

2. Hours and minutes2. Hours and minutes

3. Meters and kilometers3. Meters and kilometers

C. Conversion FactorsLearning Check:

1 L1000 mL

1 hr60 min

1000 m1 km

You have $7.25 in your You have $7.25 in your pocket in quarters. How pocket in quarters. How many quarters do you many quarters do you have?have?

7.25 dollars 4 quarters7.25 dollars 4 quarters

1 dollar1 dollar

X = 29 quarters= 29 quarters

D. Dimensional Analysis Practice

How many seconds are in 1.4 days?

Plan: days hr min seconds1.4 days x 24 hr x 60 min x 60 sec =

1 day1 hr 1 min

D. Dimensional Analysis Practice

120960 sec 120000 sec

D. Dimensional Analysis Practice

How many milliliters are in 1.00 quart of milk?

1.00 qt 1 L

1.057 qt= 946 mL

qt mL

1000 mL

1 L

You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3.

lb cm3

1.5 lb 1 kg

2.2 lb= 35 cm3

1000 g

1 kg

1 cm3

19.3 g

D. Dimensional Analysis Practice

5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off?

8.0 cm 1 in

2.54 cm= 3.1 in

cm in

D. Dimensional Analysis Practice

6) Roswell football needs 550 cm for a 1st down. How many yards is this?

550 cm 1 in

2.54 cm= 6.0 yd

cm yd

1 ft

12 in

1 yd

3 ft

D. Dimensional Analysis Practice

7) A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?

1.3 m 100 cm

1 m= 86 pieces

m pieces

1 piece

1.5 cm

D. Dimensional Analysis Practice

How many liters of water would fill a container that measures 75.0 in3?

75.0 in3 (2.54 cm)3

(1 in)3= 1.23 L

in3 L

1 L

1000 cm3

D. Dimensional Analysis Practice