Ch # 3 Unit system and dimensional analysis.
The standard unit of mass in the SI system is the kilogram. 1 kilogram is equal to the mass of a platinum-iridium cylinder kept in a vault at Sevres, France. 1 kg = 2.205 pounds
Metric Units of mass Exponential Unit Abbreviation Gram Equivalent Equivalent kilogram kg 1,000 g 103 g gram g 1 g 100 g decigram dg 0.1 g 10-1 g centigram cg 0.01 g 10-2 g milligram mg 0.001 g 10-3 g microgram g 0.000001 g 10-6 g
Matter: Anything that has mass and occupies space. • Mass : The quantity or amount of matter that an object possesses. • Fixed • Independent of the object’s location • Weight: A measure of the earth’s gravitational attraction for an object. • Not fixed • Depends on the object’s location.
Mass : The quantity or amount of matter that an object possesses. • Fixed • Independent of the object’s location. • Weight: A measure of the earth’s gravitational attraction for an object. • Not fixed • Depends on the object’s location.
Volume is the amount of space occupied by matter. • In the SI system the standard unit of volume is the cubic meter (m3). • The liter (L) and milliliter (mL) are the standard units of volume used in most chemical laboratories.
Density is the ratio of the mass of a substance to the volume occupied by that substance.
The density of gases is expressed in grams per liter. Mass is usually expressed in grams and volume in mL or cm3.
A 13.5 mL sample of an unknown liquid has a mass of 12.4 g. What is the density of the liquid?
46.0 mL 35.0 mL 98.1 g A graduated cylinder is filled to the 35.0 mL mark with water. A copper nugget weighing 98.1 grams is immersed into the cylinder and the water level rises to the 46.0 mL. What is the volume of the copper nugget? What is the density of copper?
The density of ether is 0.714 g/mL. What is the mass of 25.0 milliliters of ether? Method 1 (a) Solve the density equation for mass. (b) Substitute the data and calculate.
The density of ether is 0.714 g/mL. What is the mass of 25.0 milliliters of ether? Method 2 Dimensional Analysis. Use density as a conversion factor. Convert: mL → g The conversion of units is
The density of oxygen at 0oC is 1.429 g/L. What is the volume of 32.00 grams of oxygen at this temperature? Method 1 (a) Solve the density equation for volume. (b) Substitute the data and calculate.
% error • Measured value-accepted value ____________________________x 100 Accepted value
Heat • A form of energy that is associated with the motion of small particles of matter. • Heat refers to the quantity of this energy associated with the system. • The system is the entity that is being heated or cooled.
Temperature • A measure of the intensity of heat. • It does not depend on the size of the system. • Heat always flows from a region of higher temperature to a region of lower temperature.
Temperature Measurement • The SI unit of temperature is the Kelvin. • There are three temperature scales: Kelvin, Celsius and Fahrenheit. • In the laboratory temperature is commonly measured with a thermometer.
Degree Symbols degrees Celsius = oC Kelvin (absolute) = K degrees Fahrenheit = oF
To convert between the scales use the following relationships.
It is not uncommon for temperatures in the Canadian plains to reach –60oF and below during the winter. What is this temperature in oC and K?
It is not uncommon for temperatures in the Canadian planes to reach –60oF and below during the winter. What is this temperature in oC and K?
The metric or International System (SI, Systeme International) is a decimal system of units. • It is built around standard units. • It uses prefixes representing powers of 10 to express quantities that are larger or smaller than the standard units.
International System’s Standard Units of Measurement Quantity Name of Unit Abbreviation Length meter m Mass kilogram kg Temperature Kelvin K Time second s Amount of substance m mole Electric Current ampere A Luminous Intensity candela cd
Prefixes and Numerical Values for SI Units Power of 10 Prefix Symbol Numerical Value Equivalent exa E 1,000,000,000,000,000,000 1018 peta P 1,000,000,000,000,000 1015 tera T 1,000,000,000,000 1012 giga G 1,000,000,000 109 mega M 1,000,000 106 kilo k 1,000 103 hecto h 100 102 deca da 10 101 — —1 100
Prefixes and Numerical Values for SI Units Power of 10 Prefix Symbol Numerical Value Equivalent deci d 0.1 10-1 centi c 0.01 10-2 milli m 0.001 10-3 micro 0.000001 10-6 nano n 0.000000001 10-9 pico p 0.000000000001 10-12 femto f 0.00000000000001 10-15 atto a 0.000000000000000001 10-18
Dimensional Analysis Dimensional analysis converts one unit to another by using conversion factors. unit1 x conversion factor = unit2
Basic Steps • Read the problem carefully. Determine what is to be solved for and write it down. • Tabulate the data given in the problem. • Label all factors and measurements with the proper units.
Basic Steps • Determine which principles are involved and which unit relationships are needed to solve the problem. • You may need to refer to tables for needed data. • Set up the problem in a neat, organized and logical fashion. • Make sure unwanted units cancel. • Use sample problems in the text as guides for setting up the problem.
Basic Steps • Proceed with the necessary mathematical operations. • Make certain that your answer contains the proper number of significant figures. • Check the answer to make sure it is reasonable.
Metric Units of Length Exponential Unit Abbreviation Metric Equivalent Equivalent kilometer km 1,000 m 103 m meter m 1 m 100 m decimeter dm 0.1 m 10-1 m centimeter cm 0.01 m 10-2 m millimeter mm 0.001 m 10-3 m micrometer m 0.000001 m 10-6 m nanometer nm 0.000000001 m 10-9 m angstrom Å 0.0000000001 m 10-10 m
It must cancel meters. It must introduce millimeters How many millimeters are there in 2.5 meters? The conversion factor must accomplish two things: unit1 x conversion factor = unit2 m x conversion factor = mm
The conversion factor is derived from the equality. 1 m = 1000 mm conversion factor conversion factor Divide both sides by 1000 mm Divide both sides by 1 m
How many millimeters are there in 2.5 meters? Use the conversion factor with millimeters in the numerator and meters in the denominator.
Convert 16.0 inches to centimeters. Use this conversion factor