English System | Metric System | Metric System Prefixes | Mass vs. Weight |
SI Units | Derived SI Units | Non-SI Units | Unit Conversions |
There are several systems of units, each containing units for properties such as length, volume, weight, and time. In the English system the units are defined in an arbitrary way.
Practice Problem 1 Convert 6.5 feet into inches. |
The Metric System is based on the fundamental units of measure for length, volume, and mass.
Length: | meter (m) | |
Volume: | liter (L) | |
Mass : | gram (g) |
Base units in the Metric System can be converted into units that are more appropriate for the quantity being measured by adding a prefix to the name of the base unit. The common metric prefixes are given below.
Prefix | Symbol | Meaning | |||
femto- | f | x 1/1,000,000,000,000,000 (10^{-15}) | |||
pico- | p | x 1/1,000,000,000,000 (10^{-12}) | |||
nano- | n | x 1/1,000,000,000 (10^{-9}) | |||
micro- | µ | x 1/1,000,000 (10^{-6}) | |||
milli- | m | x 1/1,000 (10^{-3}) | |||
centi- | c | x 1/100 (10^{-2}) | |||
deci- | d | x l/10(10^{-1}) | |||
kilo- | k | x 1,000 (10^{3}) | |||
mega- | M | x 1,000,000 (10^{6}) | |||
giga- | G | x 1,000,000,000 (10^{9}) | |||
tera- | T | x 1,000,000,000,000 (10^{12}) |
The base units of length and volume are linked in the metric system. By definition, a liter is equal to the volume of a cube exactly 10 cm tall, 10 cm long, and 10 cm wide. Because the volume of this cube is 1000 cubic centimeters and a liter contains 1000 milliliters, 1 milliliter is equivalent to 1 cubic centimeter.
1 mL = 1cm^{3}
The base units of volume and weight are also linked. The gram was originally defined as the mass of 1 mL of water at 4 degrees Celsius.
1g = 1mL H_{2}O at 4 °C
Practice Problem 2: Convert 0.135 kilometers into meters. |
Mass is a measure of the amount of matter in an object, so the mass of an object is constant.
Weight is a measure of the force of attraction of the earth acting on an object. The weight of an object is not constant.
Mass is a more fundamental quantity than weight. There is no English equivalent to the verb weigh that can be used to describe what happens when the mass of an object is measured. You are therefore likely to encounter the terms weigh and weight for operations and quantities that are more accurately associated with the term mass.
In 1960 the International System of Units was proposed as a replacement for the Metric System. The seven base units for the SI system are given below.
SI Base Units
Physical Quantity | Name of Unit | Symbol | ||
length | meter | m | ||
mass | kilogram | kg | ||
time | second | s | ||
temperature | kelvin | K | ||
electric current | ampere | D | ||
amount of substance | mole | mol | ||
luminous intensity | candela | cd |
The units of every measurement in the SI system must be derived from one or more of the seven base units. Some of the common derived SI units used in chemistry are given below.
Common Derived SI Units in Chemistry
Physical Quantity | Name of Unit | Symbol | ||
density | kg/m^{3} | |||
electric charge | coulomb | C (A · s) | ||
electric potential | volt | V (J/C) | ||
energy | joule | J (kg-m^{2}/s^{2}) | ||
force | newton | N (kg-m/s^{2}) | ||
frequency | hertz | Hz (s^{-1}) | ||
pressure | pascal | Pa (N/m^{2}) | ||
velocity (speed) | meters per second | m/s | ||
volume | cubic meter | m^{3} |
Strict adherence to SI units would require changing directions such as "add 250 mL of water to a 1-L beaker" to "add 0.00025 cubic meters of water to an 0.001-m^{3} container." Because of this, a number of units that are not strictly acceptable under the SI convention are still in use. Some of these non-SI units are given below.
Non-SI Units in Common Use
Physical Quantity | Name of Unit | Symbol | ||||||
volume | liter | L (10^{-3} m^{3}) | ||||||
length | angstrom | D (0.1 nm) | ||||||
pressure | atmosphere | atm (101.325 kPa) | ||||||
torr | mmHg (133.32 Pa) | |||||||
energy | electron volt | eV (1.601 x 10^{-19} J) | ||||||
temperature | degree Celsius | EC (K - 273.15) | ||||||
concentration | molarity | M (mol/L) |
Length | |
1 m = 1.094 yd | 1 yd = 0.9144 |
Volume | |
1 L = 1.057 qt | 1 qt = 0.9464 |
Mass | |
1 g = 0.002205 lb | 1 lb = 453.6 g |
Practice Problem 3 The record for the Kentucky Derby is held by Secretariat, who ran the 10 furlongs in 1 minute, 59.4 seconds. Calculate his average speed in miles per hour. |
Practice Problem 4 Calculate the volume in liters of a cubic container 0.500 meter tall. |
Practice Problem 5 What is the value of a gold ingot 20.0 cm long by 8.5 cm wide by 6.0 cm tall, if the mass of a cubic centimeter of gold is 19.3 grams and the price of gold is $356 per ounce? |
Units | Errors | Significant Figures | Scientific Notation
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