Unit 2: Measurement

Measurements are

Measurements include a number and a unit

Examples:

Measurement / Quantity
teaspoon / volume
meter / length
Celsius / temperature
mm Hg / pressure
g/mL / density
kilograms / mass

In science, we use the SI measurement system (Le Systeme International d’Unites). Why?

Seven SI base units: (all others considered “derived” units)

Quantity / Quantity Symbol / Unit name / Unit Abbreviation
length / ℓ / meter / m
mass / m / kilogram / kg
time / t / second / s
temperature / T / Kelvin / K
amount of substance / n / mole / mol
electric current / I / ampere / A
luminous intensity / Iv / candela / cd

Metric Prefixes:

prefix / abbreviation / amount of base unit
Tera- / T / 1012
Giga- / G / 109
Mega- / M / 106
kilo- / k / 103
base unit: meter, gram, second, liter, etc.
deci- / d / 10-1
centi- / c / 10-2
milli- / m / 10-3
micro- / μ / 10-6
nano- / n / 10-9
pico- / p / 10-12

MEMORIZE!

Metric Prefixes and Conversion Factors:

relationship to base unit / prefix / abbr / amount of base unit / conversion factor
larger than base unit / Tera- / T / 1012 = 1 000 000 000 000 (trillion) / 1 Tm = 1012 m
Giga- / G / 109 = 1 000 000 0000
(billion) / 1 Gm = 109 m
Mega- / M / 106 = 1 000 000
(million) / 1 Mm = 106 m
kilo- / k / 103 = 1000
(thousand) / 1 km = 1000 m
hecto- / h / 102 = 100
(hundred) / 1 hm = 100 m
deca- / da / 101 = 10
(ten) / 1 dam = 10 m
base unit: meter, gram, second, liter, etc.
smaller than base unit / deci- / d / 10-1 = 0.1
(tenth) / 1 m = 10 dm
centi- / c / 10-2 = 0.01
(hundredth) / 1 m = 100 cm
milli- / m / 10-3 = 0.001
(thousandth) / 1 m = 1000 mm
micro- / μ / 10-6 = 0.000 001
(millionth) / 1 m = 106 μm
nano- / n / 10-9 = 0.000 000 001
(billionth) / 1 m = 109 nm
pico- / p / 10-12 = 0.000 000 000 001 (trillionth) / 1 m = 1012 pm

Temperature Scales

There are three temperature scales in use today, Fahrenheit, Celsius and Kelvin.

Fahrenheit temperature scale is a scale based on 32 for the freezing point of water and 212 for the boiling point of water, the interval between the two being divided into 180 parts. The 18th-century German physicist Daniel Gabriel Fahrenheit originally took as the zero of his scale the temperature of an equal ice-salt mixture and selected the values of 30 and 90 for the freezing point of water and normal body temperature, respectively; these later were revised to 32 and 96, but the final scale required an adjustment to 98.6 for the latter value.

Until the 1970s the Fahrenheit temperature scale was in general common use in English-speaking countries; the Celsius, or centigrade, scale was employed in most other countries and for scientific purposes worldwide. Since that time, however, most English-speaking countries have officially adopted the Celsius scale. The conversion formula for a temperature that is expressed on the Celsius (C) scale to its Fahrenheit (F) representation is: F = 9/5C + 32.

Celsius temperature scale also called centigrade temperature scale, is the scale based on 0 for the freezing point of water and 100 for the boiling point of water. Invented in 1742 by the Swedish astronomer Anders Celsius, it is sometimes called the centigrade scale because of the 100-degree interval between the defined points. The following formula can be used to convert a temperature from its representation on the Fahrenheit (F) scale to the Celsius (C) value: C = 5/9(F - 32). The Celsius scale is in general use wherever metric units have become accepted, and it is used in scientific work everywhere.

Kelvin temperature scale is the base unit of thermodynamic temperature measurement in the International System (SI) of measurement. It is defined as 1/ 273.16 of the triple point (equilibrium among the solid, liquid, and gaseous phases) of pure water. The kelvin (symbol K without the degree sign ⁰) is also the fundamental unit of the Kelvin scale, an absolute temperature scale named for the British physicist William Thomson, Baron Kelvin. Such a scale has as its zero point absolute zero, the theoretical temperature at which the molecules of a substance have the lowest energy. Many physical laws and formulas can be expressed more simply when an absolute temperature scale is used; accordingly, the Kelvin scale has been adopted as the international standard for scientific temperature measurement. The Kelvin scale is related to the Celsius scale. The difference between the freezing and boiling points of water is 100 degrees in each, so that the Kelvin has the same magnitude as the degree Celsius.

Significant Figures

What are significant figures, why are they used?

To express uncertainty in measurement, cannot be more sure of the answer than your original measurements

Rules:Example:

digits 1 through 9: always significant123 has 3 sig figs

zero between 2 sig figs: always significant5004 has 4 sig figs

leading zeros (come before non-zero digits): never significant

0.000367 has 3 sig figs

trailing zeros (at the right end of the number)
are NOT significant when: no decimal point in the number

1160 has 3 sig figs

are significant only when: decimal point in the number

1160. has 4 sig figs

exact/counting numbers: sig figs do not make sense because these are not measurements: “infinite” number of significant figures

Rules for Rounding:

In a series of calculations, let your calculator hold all the digits, and round ONCE at the end.

The digit that determines rounding, once place PAST the last sig fig will be removed.
If it is less than 5, the preceding digit remains the same
If it is greater than or equal to 5, the preceding digit is rounded up by 1

Calculations With Sig Figs:Example:

Multiplication or Division:

Round answer to fewest number of sig figs in original 56.01 x 8.2 = 460

Measurements3 sig figs 2 sig figs 2 sig figs

Addition and Subtraction:

Round answer to fewest sig figs to the right of the 56.01 + 8.2 = 64.2

decimal point in original measurements 2 after dec 1 after dec 1 after dec

ChemistryName:______

Determining and Rounding Significant FiguresDate Due: ______

Determine the number of significant figures in the following numbers. Place your answer in the space provided.

1. _____ 5090 3

2. _____ 0.1010 4

3. _____ 260 001 6

4. _____ 89.000 5

5. _____ 87 000 2

6. _____ 0.9 1

7. _____ 10 000.01 7

8. _____ 1 001 000 7

9. _____ 0.000001 1

10. _____ 809.000 6

11. _____ 10 1

12. _____ 0.09650 4

13. _____ 0.808050 6

14. _____ 7000 1

15. _____ 43.000 5

16. _____ 2.160 4

17. _____ 23 000 000 000 000 000 001 20

18. _____ 5000 1

19. _____ 0.0000000000000400005006 9

20. _____ 9.090 4

21. _____ 63 000 2

22. _____ 1694.0 5

23. _____ 0.45980 5

24. _____ 12 000 000 2

25. _____ 911 3

Round the following numbers to 4 significant figures

26. ______333 999 3.340 x 105

27. ______3.09005 3.090

28. ______47.833 47.83

29. ______0.0038965 0.003897

30. ______88.889 88.89

31. ______13 475 13 480

32. ______1.0004 1.000

33. ______0.0357849 0.03578

34. ______99 999 1.000 x 10

Round the following numbers to 2 significant figures

35. ______3.93 3.9

36. ______708 710

37. ______0.00604 0.0060

38. ______34 999 35 000

39. ______76.09 76

40. ______5.95 6.0

41. ______100.0 1.0 x 102

42. ______4750 4800

43. ______0.000206 0.00021

44. ______119 120

45. ______6.948 6.9

46. ______900 9.0 x 102

47. ______690.9 690

48. ______8.100 8.1

49. ______1 890 000 1 900 000

50. ______8.0995 8.1

How should the number be written if when rounding, not enough significance is shown?

scientific notation

Which numbers on this page fall into this category?

26, 34, 41, 46

ChemistryName:______

Significant Figure PracticeDate Due: ______

Determine the number of significant figures in the following numbers. Place your answer in the space provided.

1. _____ 340 010 5

2. _____ 0.0009010 4

3. _____ 400.00 5

4. _____ 1.90001 6

5. _____ 900 1

6. _____ 0.7 1

7. _____ 19.00 4

8. _____ 2 010 000 3

9. _____ 560.000010

10. _____ 8.3070 5

11. _____ 1000 1

12. _____ 600.900 6

Round the following numbers to 3 significant figures

13. ______25.99 26.0

14. ______22 999 2.30 x 104

15. ______0.0038249 0.00382

16. ______1.099 1.10

17. ______84.94 84.9

18. ______7448 7450

19. ______0.09995 0.100

20. ______9996 1.00 x 104

21. ______4.0005 4.00

22. ______6008 6010

23. ______81 850 81 900

24. ______30.04489 30.0

Calculate the answers for the following problems. All answers must be expressed with the proper number of significant figures!

Rule for multiplication and division: ______

Rule for addition and subtraction: ______

23.73 + 76.27 = 100.00

345.0 x 1.80 = 621

.004890 ÷ .035 = 0.14

3000.90 - 2.975 = 2997.93

27 - 9.5 = 18

23.000 x 13.8900 = 319.47

186.654 + 8.65291 = 195.307

7.9025 ÷ 83.0 = 0.0952

Scientific Notation

Why is scientific notation used?

1) Express extremely large and really tiny numbers

2) Express the correct number of sig figs

Form:Examples:

one digit to* keep same # sig figs

the left of the

decimal point

large numbers: 460 000 000 = 4.6 x 108

positive exponent tells how

many places the decimal point is moved

tiny numbers: 0.000 000 000 046 = 4.6 x 10-11

negative exponent tells how

many places the decimal point is moved

How do you use scientific notation on your calculator?

EE or EXP

More Uncertainty in Measurement:

Accuracy vs. Precision:

Accuracy: closeness to accepted or actual value (literature value)

Precision: closeness of trials to one another “reproducibility”

Percent error: x 100%

Practice:

Students were asked to find the density of an unknown white powder. Each student measured the volume and mass of three separate samples. They reported calculated densities for each trial and an average of the three calculations. The powder was sucrose, also called table sugar, which has a density of 1.59 g/cm3.

Density Data Collected by Three Different Students
Student A / Student B / Student C
Trial 1 / 1.54 g/cm3 / 1.40 g/cm3 / 1.70 g/cm3
Trial 2 / 1.60 g/cm3 / 1.68 g/cm3 / 1.69 g/cm3
Trial 3 / 1.57 g/cm3 / 1.45 g/cm3 / 1.71 g/cm3
Average / 1.57 g/cm3 / 1.51 g/cm3 / 1.70 g/cm3

Who collected the most accurate data? Why? A

Which students collected the most precise data? Why? C

Use the table to explain why averages could be misleading. B has data that is neither accurate nor precise, but the average makes it seem like it is good data

Percent Error:

Below, calculate the percent error from each student’s average calculated densities in the table above. SHOW ALL WORK!

Student A:

x 100% = 1.26 % error

Student B:

x 100% = 5.03 % error

Student C:

x 100% = 6.92 % error

ChemistryName:______

2.2 Numerical Problem SolvingDate: ______

SI units/Metric

Complete the table:

Quantity / Unit / Unit Symbol
electric current / ampere / A
length / meter / m
time / second / s
mass / kilogram / kg
Temperature / Kelvin / K
amount of substance / mole / mol
luminous intensity / candela / cd

List the units from largest to smallest: meter, millimeter, kilometer, centimeter, picometer.

kilo, meter, centi, milli, pico

Match each quantity to be measured with the most appropriate SI unit.

centimeter
gram
Kelvin
kilogram
meter
Newton
second

e 4. length of swimming pool

a 5. length of a pencil

b 6. mass of a pencil

d 7. mass of a bag of apples

g 8. time between two heartbeats

c 9. temperature of boiling water

f 10. weight of a textbook

SIGNIFICANT FIGURES

11. For each group of digits indicated in the three numbers below, state whether the digits are significant. State the rule that applies.

4500.60 0.000799 220

a. yes, digits 1-9 significant

b. yes, captive zeroes significant

c. yes, digits 1-9 significant, trailing zero with decimal in number significant

d. no, leading zeros never significant

e. yes, digits 1-9 significant

f. no, trailing zero without decimal in number not significant

12. A stack of books contains 10 books, each of which is determined, by a ruler graduated in centimeters, to be 25.0 cm long. How do these two quantities differ in terms of significant digits?

10 is a count. They can only be whole numbers. 25.0 is a measurement so we can describe it as having 3 significant figures. The certainty is set by the measuring tool.

Percent Error

13. What is the percent error in a determination that yields a value of 8.38 g/cm3 as the density of copper? The literature value for this quantity is 8.92 g/cm3.

x 100% = 6.05 % error

14. Yusuf measures the melting point of ammonium acetate, NH4C2H3O2, as 117 ˚C, but the literature value is 114 ˚C. What is the percent error in the measurement?

x 100% = 2.63 % error

GRAPHING:

Graph the data in the following data table and answer the questions. Use the graph paper provided.

Graph Requirements:

** Use a Straight Edge!

1) Descriptive Title

2) Indent axes so you have room to label them

3) Label x-axis with measurement and units (independent variable)

4) Label y-axis with measurement and units (dependent variable)

5) Choose a convenient scale - your graph should take up at least ¾ of the graph area

6) Plot points as an X or a dot with a circle around it

7) Use a line of “best fit” or connect with a smooth curve when applicable

Volume and Mass of Aluminum at 20.0 C

Volume (cm3) (independent = x) / Mass (g) (dependent = y)
11.7 / 27.0
19.7 / 54.7
30.9 / 79.4
42.0 / 108.3
49.3 / 134.6
59.8 / 150.0

Is it valid to begin the graph at the origin (0, 0) ? Explain.

What is the mass, in grams, of the aluminum at:
17.0 cm3

35.0 cm3

0.0 cm3

What is the volume, in cubic centimeters, of aluminum at:
189.0 g

50.0 g

1.0 g

Which of the determinations in questions #3 and #4 are
interpolations

extrapolations

Find the slope of the line and units.

What value does the slope of this data represent?

Density

What is density?

How closed packed the particles are

How is it different from weight?

Weight is a force, gravity’s pull on mass

possible SI mass units?

g, kg, mg

possible SI volume units?

cm3, mL, L

**Remember: 1 mL = 1 cm3

1 L = 1 dm3

SI Density units?

Solids: g/cm3 (water displacement: g/mL)

Liquids: g/mL

Gases: g/L

Equation for calculating Density:

Reminder: 4 steps for full credit:

1. write the equation

2. list variables

3. plug in the numbers

4. answer

(needs rounded to proper sig figs and correct units)

Density practice:

The largest meteorite discovered on earth is the Hoba West stone in Namibia, Africa. The volume of the stone is about 7 500 000 cm3. If the meteorite has a density of 8.0 g/cm3, what is its mass? answer: 6.0 x 107 g

One of the largest emeralds ever discovered had a mass of 17 230 g. Assuming its density to be 4.02 g/cm3, what was the emerald's volume? answer: 4290 cm3

3. Lithium is the lightest of metals and the least dense of all nongaseous elements. A pure lithium sample with a volume of 13.0 cm3 has a mass of 6.94 g. What is the density of lithium? 0.534 g/cm3

D = m/V

ChemistryName:______

Density WorksheetDate:______

SHOW ALL WORK!

What is the density of a sample of ore that has a mass of 74.0 g and occupies 20.3 cm3?

What is the density of an 84.7 g sample of an unknown substance if the sample occupies 49.6 cm3?

What is the density of an object that has a mass of 3.05 g and a volume of 8.47 mL?

What is the density of an object that has a mass of 6.00 g and is 6.10 cm long, 0.25 cm wide and 4.90 cm high?

Find the volume of a sample of wood that has a mass of 95.10 g and a density of 0.857 g/cm3.

What is the mass of a sample of material that has a volume of 55.1 cm3 and a density of 6.72 g/cm3?

A student calculates the density of iron as 6.80 g/cm3 using lab data for mass and volume. A handbook reveals that the correct value is 7.86 g/cm3. What is the percent error.

Answer Bank: (I did not include units below, be sure that your answers have units!)

0.803.64 11113.50.360370.1.71

ChemistryName:______

Specific HeatDate:______

Using your knowledge of specific heat, why might the fish love it?

The specific heat is the amount of heat required to raise one gram of a substance one degree.

swater = 1.00 cal/g deg C

swater = 4.184 J/g deg C’

ChemistryName:______

CalorimetryDate:______

Where: q = total heat flow

m = mass

T = change in temp.

s = specific heat

Example 1:

Calculate the number of joules (and kilojoules) required to warm 1.00 x 102grams of water from 25.0 oC to 80.0 oC. answer: 2.30 x 104 J = 23.0 kJ

Heat energy = mass x change in temperature x specific heat

Specific Heat:

Many times Calorimetry problems involve solving for one of the other quantities such as specific heat or temperature change. This is done by simply using algebra to rearrange the formula q = mTs.

Example 2:

Calculate the specific heat of gold if it required 48.0 joules of heat to warm 25.0 grams of gold from 40.0 oC to 55.0 oC. answer: 0.128 J/g °C

Problems:

Show all work for full credit!

How many joules are needed to warm 25.5 grams of water from 14 oC to 22.5 oC?

Calculate the number of joules released when 75.0 grams of water are cooled from 100.0oC to 27.5 oC.

How much heat is absorbed by 60.0 g of copper when it is heated from 20.0 oC to 80.0 oC? The specific heat of copper is 0.385 J/gCo.

A 38 kg block of lead is heated from 26.0oC to 180oC. How much heat does it absorb during the heating? The specific heat of lead is .138 J/g Co.

How many joules are needed to warm 45.0 grams of water from 30.0oC to 75.0oC?

What would be the final temperature if 3.31 x 103 joules were added to 18.5 grams of water at 22.0oC

A sample of lead, specific heat 0.138J/goC, released 1.20 x 103J when it cooled from 93.0oC to 29.5oC. What was the mass of this sample of lead?

Energy Transfer

One of the major uses of Calorimetry is to measure the specific heats of metals and various metallic alloys. Chemists use specific heats in their study of the structure and attractive forces in the materials. Specific heats are useful for engineers in planning structures or processes.

This use of Calorimetry is based upon the law of conservation of energy energy is neither created nor destroyed but can be transformed from one form to another.

In this application, hot metal is added to cold water in an insulated container called a calorimeter. The cold water gains the heat lost by the hot metal as they come to the same final temperature. If you measure the temperature changes you can calculate the heat gained by the water and thus the heat lost by the metal, and finally can calculate the specific heat of the metal.

Example 3:

A 175 gram sample of a metal at 93.5oC was added to 105 grams of water at 23.5oC in a perfectly insulated calorimeter. The final temperature of the water and metal was 33.8oC. Calculate the specific heat of the metal in joules/gram oC.

heat lost by the metal = - heat gained by the water

mmTmsm = - mwTwsw

Problems: Show all work for full credit.

A 185 gram sample of copper at 98.0 oC was added to 102 grams of water at 20.0 oC in a perfectly insulated calorimeter. The final temperature of the copper water mixture was 31.2 oC. Calculate the specific heat of copper using this data.

A chemistry student added 225 grams of aluminum at 85.0 oC to 115 grams of water at 23.0 oC in a perfect calorimeter. The final temperature of the aluminum water mixture was 41.4 oC. Use this student's data to calculate the specific heat of aluminum in joules/gram Co.

A student was given a sample of a silvery gray metal and told that it was bismuth, specific heat 0.122 J/goC, or cadmium, specific heat 0.232 J/g oC. The student measured out a 250 gram sample of the metal, heated it to 96.0oC and then added it to 98.5 grams of water at 21.0oC in a perfect calorimeter. The final temperature in the calorimeter was 30.3oC. Use the student's data to calculate the specific heat of the metal sample and then identify the metal.

Unit 2 Studyguide:

Vocabulary/To know:

quantitative/qualitative
accuracy/precision
SI base units (see table in notes)
Metric prefixes and conversions (see “memorize” table)
Determining, rounding with significant figures and scientific notation
% error calculations
Why do sig figs not apply to counting and exact numbers?
Solving density problems for mass, volume, or density

SHOW ALL STEPS FOR FULL CREDIT!

Solving calorimetry problems for heat, mass, temperature difference, or specific heat

SHOW ALL STEPS FOR FULL CREDIT!

Measurements are taken to ONE PLACE after the “minor scale”

Beverage Density Lab