GC-S003-Measurement

Henry R. Kang (1/2010)

General Chemistry

Lecture 3

Measurement


Contents

• SI Base Units Length, mass, time, temperature, etc. Prefixes

• SI Derived Units • English Units• Number

Scientific notation Significant figures Accuracy Precision

• Dimensional Analysis


SI Base Units


SI Base Units of Measurement• SI Units (International

System of Units) Length is meter (m)

In chemistry, centimeter (cm) is more often used than m.

Non-SI unit, angstrom (Å) = 10-10 m, is also used in spectroscopic measurements.

Mass is kilogram (kg) In chemistry, gram (g) is

more often used than kg.

Time (s or sec) Temperature is kelvin (K)

Fahrenheit: °F and Celsius: °C are also used

Base Quantity Name

of Unit

Symbol

Length meter m

Mass kilogram kg

Time second s (sec)

Temperature kelvin K

Electrical current ampere A

Amount mole mol

Luminous intensity candela cd

SI Base Units


Prefixes of SI UnitsPrefix Symbol Factor Example

Tera- T 1012 1 teragram (Tg) = 1×1012 g

Giga- G 109 1 gigagram (Gg) = 1×109 g

Mega- M 106 1 megagram (Mg) = 1×106 g

Kilo- k 103 1 kilogram (kg) = 1×103 g

hecto- h 102 1 hectogram (hg) = 100 g

deka- da 10 1 dekagram (da-g) = 10 g

Deci- d 10-1 1 decigram (dg) = 0.1 g

Centi- c 10-2 1 centigram (cg) = 0.01 g

Milli- m 10-3 1 milligram (mg) = 0.001 g

Micro- μ 10-6 1 microgram (μg) = 1×10-6 g

Nano- n 10-9 1 nanogram (ng) = 1×10-9 g

Pico- p 10-12 1 picogram (pg) = 1×10-12 g

Femto- f 10-15 1 femtogram (fg) = 1×10-15 g

Atto- a 10-18 1 attogram (ag) = 1×10-18 g


Mass and Weight• Mass is the quantity of matter that gives the

heaviness for an object of the matter. The mass of an object is the same wherever and whenever it

is measured. SI units

Kilogram (kg) and gram (g) 1 kg = 1000 g

• Weight is the force that gravity exerts on an object. Weight depends on the location when it is measured. W = m g

W is the weight, m is the mass, and g is the gravitational acceleration constant.

g = 9.81 m/s2


Measuring Devices for Mass

• Top loading balance Depending on the model and manufacturer,

they can measure mass to 1/10, 1/100, or 1/1000 of a gram.

• Analytical balance It can read to 1/10,000 of a gram.


Temperature Measure

• SI unit for temperature is kelvin (K)

• Celsius (°C) is defined from the boiling and freezing points of water. It has the same magnitude as kelvin, but

differ by an offset value of 273.15. 1 K = 1 °C

• Fahrenheit (°F) is used in United States. 1 K = 1.8 °F


Conversions between Temperature Scales

• Knowing one formula, one can derive the other

• K to °C °C = (1 °C/K) (K) 273.15°C

• °C to K K = (°C + 273.15 °C ) × (1 K / 1 °C)

• °C to °F

°F = (1.8 °F/°C) (°C) + 32°F

• °F to °C

°C = (°F 32°F) (1°C / 1.8°F)


Measuring Devices for Temperature

• Mercury Thermometer Depend on the division of the marks, usually

it can read to 1/10 of a degree.

• Alcohol Thermometer Depend on the division of the marks, usually

it can read to 1/10 of a degree.

• Digital Thermometer Depend on the digital readout.


Examples of Temperature Conversion• Solder is an alloy made of tin and lead that is used to connect electronic wires

and circuits. A solder has a melting point of 435°F. What is its melting point in degrees Celsius? Answer: Use the equation, °C = (°F 32°F) (1°C / 1.8°F) (435 °F – 32 °F) × (1 °C / 1.8 °F) = 224 °C

• Helium has the lowest boiling point of all the elements at -269 °C. Convert this temperature to degrees Fahrenheit. Answer: Use the equation, °F = (1.8 °F/°C) × (°C) + 32°F -269 °C × (1.8 °F/ °C) + 32°F = -452 °F

• Mercury, the only metal that exists as a liquid at room temperature, melts at 234.3 K. –38.9°C. Convert its melting point to degrees Fahrenheit. Answer: Use the equations, °C = (1 °C/K) (K) 273.15°C, then

°F = (1.8 °F/°C) × (°C) + 32°F (234.3 K) × (1 °C/K) – 273.15 K = -38.9 C (-38.9 C) (1.8 °F/°C) × (°C) + 32°F = -38.0 F


Derived Units


SI Derived Units

• Derived units are the compounded units from multiple base units. Area is the length squared. SI unit: m2

Volume is the length cubed. SI unit: m3

Density is the mass per unit volume SI unit: kg/m3

Speed is the distance per unit time SI unit: m/s

Acceleration is the speed per unit time SI unit: m/s2

Force is the mass multiplied by acceleration SI unit: kg.m/s2

Pressure is the force per unit area SI unit: kg/(m.s2)

Energy is the force multiplied by distance SI unit: kg.m2/s2


Volume Measure

• Cubic Meter (m3)• Cubic Centimeter (cm3)• Cubic Decimeter (dm3)• Liter (L)• Milliliter (mL)• Conversion Factors

1 m3 = 1,000 dm3 = 1,000,000 cm3

1 cm3 = (1 × 10-2 m)3 = 1 × 10-6 m3

1 dm3 = (1 × 10-1 m)3 = 1 × 10-3 m3

1 mL = 1 cm3

1 L = 1000 mL = 1000 cm3 = 1 dm3


Measuring Devices for Volume

• Burette The accuracy depend on the division of the marks.

50-mL and 25-mL burettes can be read to 1/100 of a mL.

• Pipette Deliver exact volume at the mark.

• Graduated cylinder Depend on the division of the marks:

10-mL cylinder can be read to 1/100 of a mL 100-mL cylinder can be read to 1/10 of a mL

• Volumetric flask Store exact volume at the mark.

• Others


Density Measure and Units

• Density = mass / volume d = m / V

• SI Unit kg/m3

• Solid Samples g/cm3

• Liquid Samples g/mL

• Gas Samples g/L


• A piece of gold with a mass of 243.2 g has a volume of 12.6 cm3. Calculate the density of gold. Answer: Use the equation, d = m / V d = m/V = 243.2 g / 12.6 cm3 = 19.3 g/cm3

• A piece of platinum metal with a density of 21.5 g/cm3 has a volume of 8.45 cm3. What is its mass? Answer: m = d × V = 21.5 g/cm3 × 8.45 cm3 = 182 g

Examples of Density


Example of Identification via Density• A colorless liquid is believed to be one of the following:

Substance Density (g/mL)

n-butyl alcohol 0.810

ethylene glycol 1.114

isopropyl alcohol 0.785

toluene 0.866

Identify the substance by measuring the density. A volume of 21.1 mL has a mass of 18.36 g. What is this substance?

• Answer: Use the equation, d = m / V d = 18.36 g / 21.1 mL = 0.870 g/mL Based on the measured density, the substance is “toluene”.


Example of Mass-Volume Conversion

• An experiment requires 33.0 g of isopropyl alcohol. The density of isopropyl alcohol is 0.785 g/mL. What volume of isopropyl alcohol will be needed to meet the mass required?

• Answer: Use the equation: d = m/V

Rearrange the equation

V= m/d

V = 33.0 g / (0.785 g/mL) = 42.0 mL


Conversion between English and Metric Units

Quantity English Metric

Mass 1 pound (lb) = 453.6 grams or 0.4546 kg

2.2 pounds = 1 kilograms

Length 1 inch = 2.54 centimeters

1 yard = 0.91 meters

Volume 1 quart = 0.946 liter

1 gallon = 3.78 litersNote that the pound (lb) is a rather troublesome unit. It is a unit of mass but also used as a unit for force. In the case of force, 1 lb is the force due to gravitational attraction on an object of that mass:

F = ma = 0.4536 kg × 9.81 m/s2 = 4.45 kg.m/s2 = 4.45 N; 1 lb = 4.45 N


Problem of “lb” Unit

• Problem: On 9/23/99, $125,000,000 Mars Climate Orbiter entered

Mar’s atmosphere 100 km lower than planned and was destroyed by heat.

• Reason NASA engineer mistook the conversion factor as

1 lb = 1 N “lb” is an English unit of force: 1 lb = 4.45 N Force = mass × acceleration

= 0.454 kg × 9.81 m/s2

= 4.45 kg.m/s2

= 4.45 N (1 N = 1 kg.m/s2)

GC-S003-Measurement

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