Chapter 02 - Standards for Measurement

Standards for Measurement

Writing numbers

• _{In chemistry we will use scientific notation for}

writing large and small numbers.

• _{We will always write numbers to the correct}

number of significant figures.

– _{Rules for writing numbers correctly will be}

Mass: amount of matter in an object Mass is measured on a balance.

Weight: effect of gravity on an object.

Mass is independent of location, but weight is not. Weight is measured on a scale,

which measures force against a spring.

Mass is the standard measurement of the metric system.

The SI unit of mass is the kilogram.

(The gram is too small a unit of mass to be the standard unit.)

Volume: the amount of space occupied by matter. The SI unit of volume is the cubic meter (m3) The metric volume more typically used is the

liter (L) or milliliter (mL).

A liter is a cubic decimeter of water (1 kg) at 4 °C.

Volume can be

measured with several laboratory devices.

Thermal energy: A form of energy involving the motion of small particles of matter.

Temperature: measure of the intensity of thermal energy of a system (i.e. how hot or cold).

Heat: flow of energy due to a temperature difference.

Heat flows from regions of higher to lower temperature.

The SI unit of temperature is the Kelvin (K).

Temperature is measured using a thermometer.

kilo k 103 or 1000 base units

deci d 10-1 or 0.1 base units

centi c 10-2 or 0.01 base units

milli m 10-3 or 0.001 base units

micro _ 10-6 or 0.000 001 base units

nano n 10-9 or 0.000 000 001 base units

kilo k 1 kunit = 1000unit

deci d 10 dunit = 1unit

centi c 100 cunit = 1unit

milli m 1000 munit = 1unit

micro _{ 1,000,000 unit = 1unit}

nano n 1,000,000,000 nunit = 1unit

Conversion Factors

• _{Anytime we have an equality, we can turn it}

into a conversion factor.

– _Examples:

– _{3 ft = 1 yd -->}

1

3

1

1

3





ft

yd

yd

ft

Remember to keep the units!

Any unit can be converted to another unit by multiplying the quantity by a conversion factor.

Unit₁ x conversion factor = Unit₂

Example

A conversion factor must cancel the original unit and leave behind only the new (desired) unit.

The original unit must be in the denominator (bottom) and new unit must be in the numerator (top) to

1 km

1000 m

2 m x = 0.002 km

Units are treated like numbers and can cancel.

© 2014 John Wiley & Sons, Inc. All rights

Dimensional Analysis:

Many chemical principles or problems are illustrated mathematically.

A systematic method to solve these types of numerical problems is key.

Our approach: the dimensional analysis method

Create solution maps to solve problems.

Overall outline for a calculation/conversion progressing from known to desired quantities.

Dimensional Analysis:

Convert 215 centimeters to meters.

Solution Map:

known quantity desired quantity

1 m

100 cm = 2.15 m 215 cm x

Convert 125 meters to kilometers.

Solution Map:

1 km

1000 m = 0.125 km 125 m x

cm m

known quantity m km desired quantity

Dimensional Analysis:

a. 30,000 b. 300,000 c. 300

d. 3000

Solution Map:

1,000,000 μm

1 m = 30,000 μm 0.03 m x

How many micrometers are in 0.03 meters?

known quantity m m desired quantity

Some problems require a series of conversions to get to the desired unit.

Each arrow in the solution map corresponds to the use of a conversion factor.

Example

Convert from days to seconds.

Solution Map:

24 hours 1 day

60 minutes

1 hour = 8.64 x 104 sec

1 day 60 seconds

1 minute

days hours minutes seconds

x x

x

Dimensional Analysis:

How many feet are in 250 centimeters?

Solution Map:

1 inch 2.54 cm

1 foot

12 inches = 8.20 ft 250 cm

Metric to English Conversions

x x

cm inches ft

Dimensional Analysis:

2.54 cm

How many meters are in 5 yards?

Solution Map:

3 feet 1 yard

12 inches

1 foot = 4.57 m

5 yards

Metric to English Conversions

x x

a. 9.14 b. 457 c. 45.7 d. 4.57

1 inch x

100 cm x 1 m

yards feet inches cm m

Dimensional Analysis

Volume conversions

• _{How many fluid ounces (fl. oz.) are in a 355 mL}

Dimensional Analysis

Volume conversions

• _{A sheet of aluminum has dimensions of 2.50}

cm by 1.00 cm by 0.00150 cm.

Useful Conversion Factors

• _{1 in = 2.54 cm}

• _{1lb = 454 g or 1 kg = 2.20 lb}

Examples

• _{How many inches are in 6.27 yds?}

• _{You have just won 2410 nickels in Las Vegas.}

• _{Convert 750 ml to L.}

• _{A glass of orange juice contains 0.85 dL of}

• _{The recommended daily allowance of}

phosphorus for an adult male is 800 mg. How many grams of phosphorus are

recommended?

• _{A student's height is 175 cm. How tall is the}

student in meters?

• _{A hummingbird has a mass of 0.0055 kg.}

• _{A person is 60.0 in tall. What is this height in}

cm?

• _{If someone weighs 80.7 kg, how much is this}

• _{The daily dose of ampicillin for the treatment}

of an ear infection is 115 mg/kg body weight. What is the daily dose for a 34-lb toddler?

• _{A person on a diet has been losing weight at}

the rate of 3.5 lb. per week. If the person has been on the diet for 6.0 weeks, how many

• _{A plastics manufacturing plant uses 3.3 tons of}

oil per week. If oil costs $4.65/kg, how much will exactly 1 years worth of oil cost the

plastics manufacturer?

• _{Mercury has a density of 13.6 g per mL. What}

Bad Unit Conversions

• Story 1: On September 23, 1999 NASA lost the $125 million Mars Climate Orbiter spacecraft after a 286-day journey to Mars. Miscalculations due to the use of English units instead of metric units apparently sent the craft slowly off course -- 60 miles in all.

• Story 2: On January 26, 2004 at Tokyo Disneyland's Space Mountain, an axle broke on a roller coaster train mid-ride, causing it to derail. The cause was a part being the wrong size due to a conversion of the master plans in 1995 from English units to Metric units.

• Story 3: On 23 July 1983, Air Canada Flight 143 ran completely out of fuel about halfway through its flight from Montreal to Edmonton. Fuel loading was miscalculated through misunderstanding of the recently adopted

Density (d): the ratio of the mass of a substance to the volume occupied by that mass.

Density is a physical property of a substance.

The units of density are generally expressed as g/mL or g/cm3 for solids and liquids and g/L for gases.

The volume of a liquid changes as a function of temp, so density must be specified for a given temperature.

Ex. The density of H₂O at 4 ºC is 1.0 g/mL while the density is 0.97 g/mL at 80 ºC.

d =

volume mass

Specific gravity (sp gr): ratio of the density of a substance to the density of another substance (usually H₂O at 4 ºC).

Specific gravity is unit-less (in the ratio all units cancel).

volume

mass

• _{Ebony is a dark hard wood. A rectangular}

piece of ebony has a mass of 522g and a

volume of 435 cm3_{. Find the density of ebony.}

• _{Gasoline has a density of 0.68 g/mL. What is}

• _{A bottle containing 325 g of cleaning solution has}

fallen and broken on the floor. If the solution in the bottle has a density of 0.850 g/mL, what volume of solution needs to be cleaned up?

• _{A fish tank holds 30.0 gal of water. Using a density of}

Percentage

• _{A sample of sugar weighing 2.47 g contains}

0.988g of carbon. What is the mass % carbon in sugar?

%

100

%

x

Percentage (cont.)

• _{Mrs. Vasquez’s Chem115 class began with 127}

students. Of the original enrollment, 11.2% received a final grade A. How many students earned an A?

• _{Water is composed of 11.2% H and 88.8% O.}

Squared units

• _{A poster has an area of 2 yd}2_{. What is the area}

Temperature can be expressed in 3 commonly used scales. Celsius (°C), Fahrenheit (°F), and Kelvin (K).

Celsius and Fahrenheit are both measured in degrees, but the scales are different.

The Fahrenheit scale has a range of 180° between freezing and boiling.

H₂O °C °F K

Freezing Point 0 °C 32 °F 273.15 K

Boiling Point 100 °C 212 °F 373.15 K

The lowest temperature possible on the Kelvin scale is absolute zero (-273.15 °C).

Mathematical Relationships Between Temperature Scales

Convert 723 °C to temperature in both K and °F.

°F = 1.8(723) + 32 = 1333 °F

K = 723 + 273.15 = 996 K

Temperature Problem

Solution Map:

K = °C + 273.15 °F = 1.8(°C) + 32

°C K

°C °F

Temperature Conversions

• _T(o_{F) = 1.8 T(}o_{C) + 32}

• _T(o_{C) = [T(}o_{F) – 32] / 1.8}

• _{If I set my thermostat at 72}o_{F, what will the}

• _{A young woman recovered from extreme}

hypothermia, during which her temperature had dropped to 20.6o_C.

• _{What was her temperature on}

• _{A 4-year-old child has a temperature of 38.7}o_C.

Since high fevers cause convulsions in children, it is recommended that

Phenobarbital be given if the temperature

exceeds 101.0o_{F. Should Phenobarbital be}