Chem180; Chapter 2: Measurements

setting up the problem

given plan equalities -conversion factors cancel units

length is measured in

-units of meters (m) in both metric and SI systems -units of centimeters (cm) by chemists

exact numbers are

-not measured -do not have a limited number of SFs -do not affect the number of SFs in a calculation

the metric length of 1 m is the same length as

10 dm, 100 cm, and 1000 mm

Write the following number in the correct scientific notation, 0.000 058 g

5,8 x 10^-5

Osmium is a very dense metal. What is its density, in g/cm3, if 50.0 g of osmium has a volume of 2.22 cm3?

50.0 g osminum/2.22 cm^3 = 22.5g/cm^3

conversion factor that is squared or cubed

Distance = length Area = length × length = length2 Volume = length × length × length = length3

density

the relationship of the mass of an object to its volume expressed as grams per cubic centimeter (g/cm³), grams per milliliter (g/mL), or grams per liter (g/L).

temperature

an indicator of the hotness or coldness of an object, or helps determine a fever

International System of Units (SI)

an international system of units that modifies the metric system.

equalities; food labels

are listed in both metric and U.S. units -indicate the same amount of a substance in two different units

scientists measure mass rather than weight

b/c mass does not depend on gravity

equalities can be

between units of the metric system, or US units, or between metric and US units 1 m = 1000 mm 1 lb = 16 oz 2.205 lb = 1kg

problem-solving process

by analyzing the problem in order to identify the given unit and needed unit write a plan that converts the given unit to the needed unit identify one or more conversion factors that cancel units and provide the needed unit set up a calculation

the relationship of a prefix to a unit can be expressed

by replacing the prefix with its numerical value ex. 1 km = 1000 m

international prototype kilogram (IPK)

the standard of mass; a cylinger that is made of platinum-iridium alloy

density is the mass of a substance

divided by its volume density = mass of substance/volume of substance

volume is measured using

-units of m3 in the SI system -commonly measured in liters (L) and milliliters (mL) by chemists

power of 10

-when a number greater than ONE is converted to scientific notation, the power of 10 is a POSITIVE number -when a number less than ONE is written in scientific notation, the power of 1o is a NEGATIVE number

units of length

1 m = 1.094 yd 1 m = 39.37 in 1 m = 100 cm 2.54 cm = 1 in.

equality is written

1 m = 100 cm = 1 x 10^2 1 m = 1000 mm = 1 x 10^3 1 cm = 10 mm = 1 x 10^1

units of volume

1 m3 = 1000 L 1 L = 1000 mL 1 mL = 1 cm3 1 L = 1.057 qt 9.43 = mL = 1 qt

Write the equality and conversion factors for the relationships between the following units: A. grams - milligrams B. square inches - square centimeters

a. 1g/1000mg and 1000mg/1g b. (1 in.)^2/(2.54cm)^2 and (2.54 cm)^2/(1 in.)^2

when measuring the mass of laboratory samples, mass is reported in

grams, milligrams, or micrograms 1 kg = 1000 g = 1 × 103 g 1 g = 1000 mg = 1 × 103 mg 1 mg = 1000 μg = 1 × 103 μg

a percent (%) is written as a conversion factor by

choosing a unit and expressing the numerical relationship of the parts of this unit to 100 parts of the whole ex: a person has 18% body fat by mass. equality: 18 mass units of fat per 100 mass units of body mass

prefixes that decrease the size of the unit

deci (d) 0.1, 10^-1 centi (c) 0.01, 10^-2 millil (m) 0.001, 10^-3 micro (u) 10^-6 nano (n) 10^-9 pico (p) 10^-12 femto (f) 10^-15

liter divided into 10 equal parts, each is called a

deciliter (dL) 1 L = 10 dL = 1 x 10^1 dL 1 L = 1000 mL = 1 10^3 mL 1 dL = 100 mL = 1 x 10^2 mL

equalities between two metric quantities or two U.S. system quantities are obtained by

definition, and are not used to determine significant figures 1 m = 1000 mm 1 lb = 16 oz 1 min = 60 sec

significant figures (SFs)

in a measured number, the SFs are all the digits, including the estimated digit -all nonzero numbers are counted as SFs -zeros may or may not be signifiant, depending on the position of the number

weight

is a measure of the gravitational pull on an object

time

is based on an atomic clock; used to determine a second -measured in units of seconds (s); metric/SI -also measured in time units such as: years (y), days, hours (h), minutes (min)

coefficient

is obtained by moving the decimal point

in chemistry, the metric and SI measure

length, volume, mass, temperature, and time

chemists use the metric system and the international system of units (SI) for measurment when they

measure quantities do experiments solve problems

mass; measurement

metric: (g) gram SI: (kg) kilogram

volume; measurement

metric: (l) liter SI: (m3) cubic meter

length; measurement

metric: (m) meter SI: (m) meter

time; measurement

metric: (s) second SI: (s) second

temperature; measurment

metric: (°C) degree celsius SI: (K) kelvin

prefixes that increase the size of the unit

peta (P) 1000000000000000, 10^15 tera (T) 1000000000000, 10^12 giga (G) 1000000000, 10 ^9 mega (M) 1000000, 10 ^6 kilo (k) 1000, 10^3

scientific notation

used to write very large or small numbers; a number written in scientific notation consists of: coefficient, a power of 10, and a unit of measurement ex. 2400 m = 2.4 x 10³

substances; density

substances that have: -higher densities contain particles that are closely packed together -lower densities contain particles that are farther apart *metals such as gold and lead have higher densities because their atoms are packed closely together

if the first digit to be dropped is 5 or greater

than the last retained digit is increased by 1

volume

the amount of space occupied by a substance SI: cubic meter (m3) is the volume of a cube that has sides that measure 1 m in length -chemists work with metric units of volume (smaller, convenient) such as liter, milliliter

rounding rules are used to obtain

the correct number of significant figures -in calculations, calculated answers are usually rounded off

in the metric system, densities of solids, liquids, and gases are expressed with different units

the density of a solid or liquid is usually given in grams per cubic centimeter (g/cm3) grams per milliliter (g/mL) the density of a gas is usually given in grams per liter (g/L).

conversion factors with powers

to square the equality 1 m = 100 cm, we square both the number and the unit on each side. Equality: 1 m = 100 cm Area: (1 m)2 = (100 cm)2 or 1 m2 = (100)2 cm2 ** both the number and the unit must be squared

equalities can be written for mass in the metric (SI) system.

when metric equalities are used, 1 gram is the same mass as 1000 mg and 0.001 kg. 1 kg = 1000 g 1 g = 1000 mg 1 mg = 0.001 g 1 mg = 1000 µg

parts per billion (ppb)

units: micrograms per kilogram (ug/kg)

parts per million (ppm)

units: milligrams per kilogram (mg/kg)

metric system

a system of measurement used by scientists and in most countries of the world.

Kelvin (K) temperature scale

a temperature scale on which the lowest possible temperature is 0 K

Celsius (°C) temperature scale

a temperature scale on which water freezes at 0°C and boils at 100°C

Fahrenheit (°F)

a temperature scale on which water freezes at 32°F and boils at 212 °F

second (s)

a unit of time used in both the SI and metric systems.

to report the length of an object

-observe the numerical values of the marked lines at the end of an object -estimate the last digit by visually dividing the space between the smallest marked line; the estimated number is the final digit that is reported for the measured number

mass is measured

-on an electronic balance -has the SI unit of kilogram (kg) -is often measured by chemists in grams (g)

temperature is measured

-on the Celsius scale -on the Kelvin scale in SI

a cubic centimeter has the same volume as a milliliter.

1 cm³ is equal to 1 mL

units of time

1 day = 24 hr 1 h = 60 min 1 min = 60 s

units of mass

1 kg = 1000 g 1 kg = 2.205 lb 453.6 = 1 lb

a cube measuring 10 cm on each side has a volume of

1000 cm3, or 1 L;

a cubic meter (m3) is the same volume as

1000 mL, 1 L

two conversion factors for the equality 60 min = 1 h

60 min #numerator and 1 hr 1 hr #denominator 60 min *these conversion factors are read as 60 minutes per hour and 1 hour per 60 minutes. The per means "divide."

mass

a measure of the quantity of material in an object -kg: used for larger masses; ie. body mass -g: used for smaller masses 1000 g = 1 kg 1 kg = 2.205 lb 453.6 g = 1 lb

kilogram (kg)

a metric mass of 1000 g, equal to 2.2 lb. The kilogram is the SI standard unit of mass.

milliliter (mL)

a metric unit of volume equal to one-thousandth of a liter (0.001 L).

significant numbers rules

a number IS a SF if it is: -not a zero -one or more zeros at the end of a decimal -in the coefficient of a number written in scientific notation a zero IS NOT a SF if it is: -at the beginning of a decimal number -used as a placeholder in a large number without a decimal point

exact numbers

a number obtained by counting items or by definitions that compare two units in the same measuring system

measured numbers

a number obtained when a quantity is determined by using a measuring device.

measuring tool is used to determine

a quantity such as the length or the mass of an object -provides numbers for a measurement; measured numbers

conversion factors

a ratio in which the numerator and denominator are quantities from an inequality or given relationship. For example, the conversion factors for the relationship 1 kg = 2.20 lb are written as: 2.20 lb / 1 kg and 1 kg / 2.20 lb

centimeter (cm)

a smaller unit of length in the metric system. 2.54 cm = 1 in. (equal to the width of 5th digit)

Write conversion factors for each pair of units: A. liters and milliliters B. meters and kilometers

a. 1 L/1000 mL and 1000 mL/1 L b. 1 km/1000 m and 1000m/1km

Write the equality and conversion factors for each of the following: A. jewelry that contains 18% gold B. a water sample with 55 ppb of chromium (Cr)

a. 18g/100g and 100g/18g b. 1kg/55mg CR and 55mg CR/1 kg

For each calculation, round the answer to give the correct number of digits. A. 235.05 + 19.6 + 2 = (1) 257 (2) 256.7 (3) 256.65 B. 58.925 - 18.2 = (1) 40.725 (2) 40.73 (3) 40.7

a. (1) 257 b. (3) 40.7

A. Which answer contains three significant figures? (1) 0.4760 (2) 0.00476 (3) 4.076 × 103 B. All the zeros are significant in (1) 0.00307 (2) 25.300 (3) 2.050 × 103 C. The number of significant figures in 5.80 × 102 is (1) one (2) two (3) three

a. (2) 0.00476 b. (2) 25.300 and (3) 2.50 x 10^3 c. (3) three

Indicate the unit that completes each of the following equalities: 1000 m = _____ (1) 1 mm (2) 1 km (3) 1 dm 0.01 m = _____ (1) 1 mm (2) 1 cm (3) 1 dm

a. (2) 1 km b. (2) 1 cm

select the correct scientific notation for each. a. 0.000 008 (1) 8 × 106 (2) 8 × 10−6 (3) 0.8 × 10−5 b. 72 000 (1) 7.2 × 104 (2) 72 × 103 (3) 7.2 × 10−4

a. (2) 8 x 10^-06 b. (1) 7.2 x 10 ^4

Give an answer for each with the correct number of significant figures. 2.19 × 4.2 = (1) 9 (2) 9.2 (3) 9.198 B. 2.54 × 0.0028 = 0.0105 × 0.060 (1) 11.3 (2) 11 (3) 0.041

a. (2) 9.2 b. (2) 11

for each of the following, indicate whether the unit describes (1) length (2) mass (3) volume a. a bag of onions has a mass of 2.6 kg b. a person is 2.0 m tall c. a medication contains 0.50 g of aspirin d. a bottle contains 1.5 L of water

a. (2) mass b. (1) length c. (2) mass d. (3) volume

write each as a standard number. a. 2.0 × 10−2 (1) 200 (2) 0.0020 (3) 0.020 b. 1.8 × 105 (1) 180 000 (2) 0.000 018 (3) 18 000

a. (3) 0.020 b. (1) 180,000

Complete each of the following equalities: 1 kg = _____ (1) 10 g (2) 100 g (3) 1000 g B. 1 mm = _____ (1) 0.001 m (2) 0.01 m (3) 0.1 m

a. (3) 1000 g b. (1) 0.001 m

Identify the measurement that has an SI unit. a. John's height is _____. (1) 1.5 yd (2) 6 ft (3) 2.1 m b. The mass of a lemon is _____. (1) 12 oz (2) 0.145 kg (3) 0.6 lb c. The temperature is _____. (1) 85 ºC (2) 255 K (3) 45 ºF

a. (3) 2.1 m b. (2) 0.145 kg c. (2) 255 K

State the number of significant figures in each of the following measurements: A. 0.030 m B. 4.050 L C. 0.0008 g D. 2.80 m

a. 0.030 m = 2 SF b. 4.040 L = 4 SF c. 0.0008 g = 1 SF d. 2.80 m = 3 SF

Adjust the following calculated answers to give answers with three significant figures: a. 824.75 cm b. 0.112486 g c. 8.2 L

a. 825 cm b. 0.112 g c. 8.20 L

prefixes used with the unit meter

centi: one-hundredth of a meter (0.01m) milli: one-thousandths of a meter (0.001m)

the density of a solid is calculated

from its mass and volume -when a solid is submerged, it displaces a volume of water equal to the volume of the solid

cubic centimeter (cm³ or cc)

is the volume of a cube with 1cm sides 1 cm x 1 cm x 1 cm

when measuring the mass of your body, the mass is measured in

kilograms (kg)

scientific notation; casio fx-300ms

mode (1) fixed: enter coeffecient x EXP 10^= (2) sci: decimals placed

a cube measuring 1 cm on each side has a volume

of 1 cm3 1cc2 or 1 mL.

equalities written between metric and U.S. system quantities contain

one number obtained by measurement and therefore count toward significant figures 1 lb = 453.6 g 1 in = 2.54 cm

equalities

shows the relationship between two units that measure the same quantity ex. 1 m is the same length as 100 cm

addition/subtracton with measured numbers

the final answer is written so that it has the same number of decimal places as the measurement having the fewest decimal places

multiplication/divison with measured numbers

the final answer is wrtieen to have the same number of SFs at the measurment with the fewest SFs

meter (m)

the metric unit for length that is slightly longer than a yard. The meter is the SI standard unit of length. meter (m) = 39.37 in. (slightly longer than a yd (1.094 yd)

liter (L)

the metric unit for volume that is slightly larger than a quart.

gram (g)

the metric unit used in measurements of mass.

prefix

the part of the name of a metric unit that precedes the base unit and specifies the size of the measurement; prefixes are related on a decimal scale -a prefix attached to any unit increases or decreases its size by some factor of 10

if the first digit to be dropped is 4 of less

then it and all following digits are dropped from the number