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Pure substances have unique and consistent physical and chemical properties. Physical Properties : Melting Temperature Boiling Temperature Color Density. Measurement and the Metric System.
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Pure substances have unique and consistent physical and chemicalproperties. • Physical Properties: • Melting Temperature • Boiling Temperature • Color • Density
Measurement and the Metric System • A measurement is always expressed as a number (containing a certain number of significant digits) accompanied by a unit (such as inches). • The set of units used in making scientific measurements is called the Système International d’Unités, or simply, SI units.
In the metric system of expressing numbers, all units can be prefixed by a multiple of 10. These multiples are written as prefixes immediately before the unit itself. • The following are the same number: 1.0 x 10-3 m = 1.0 mm.
Measurement, Uncertainty, and Significant Figures • Unless a measurement is made by counting a small number of objects, a measurement will always contain some uncertainty, or error. • This error is expressed by the number of significant digits reported for the measured number.
The number of significant digits in a number can be determined by the following rules: • A trailing zero, as in 4.130, is significant. • A zero within a number, as in 35.06 cm, is significant. • A zero before a digit, as in 0.082, is not significant. • A number ending in zero with no decimal point, as in 20, is ambiguous. • Ambiguities of this last type can be prevented by the use of scientific or exponential notation. • Numbers obtained by counting, or exact definitions such as 12 inches = 1 foot, or 2.54 cm = 1 inch, have an infinite number of significant digits.
Scientific Notation • To write a number in scientific notation we write it as a number between 1 and 10 multiplied by 10 raised to a whole-number power: 2.33 x 102. • The coefficient is the number between 1 and 10 (2.33) and the exponential factor is the whole number exponent of 10 (2). • Any number raised to the 0 power is 1. • 3 is written: 3 x 10o346 is written: 3.46 x 102 • 24 is written: 2.4 x 1012,537 is written: 2.537 x 103
Numbers less than 1 are written in a similar way: • 0.0003 is written: 3 x 10-4 0.0346 is written: 3.46 x 10-2 • 0.0024 is written: 2.4 x 10-3 0.2537 is written: 2.537 x 10-1 • In this case, the exponent represents the number of places to the left to move the decimal place to convert from scientific notation back into decimal notation.
Adding and subtracting numbers expressed in scientific notation: • (3.63 x 10-2) + (4.85 x 10-3) = (3.63 x 10-2) + (.485 x 10-2) • = (3.63 + .485) x 10-2 • = 4.115 x 10-2 • = 4.12 x 10-2
Multiplying numbers expressed in scientific notation: • (3.4 x 103) x (2.8 x 10-2) = (3.4 x 2.8) x (103 x 10-2) • = 9.52 x 103-2 • = 9.52 x 101 • Dividing numbers expressed in scientific notation: • (2.8 x 105) / (4.0 x 102) = (2.8 / 4.0) x (105 / 102) • = 0.70 x 105-2 • = 0.70 x 103 • = 7.0 x 102
When multiplying or dividing two numbers, the product or quotient generally contains more significant digits than either of the two numbers entering into the calculation. • 8.5 in. x 8.5 in. = 72.25 in. • In this case, the product or quotient should be rounded to contain the same number of significant digits as the lesser of the two numbers. • 8.5 in. x 8.5 in. = 72.25 in. = 72 in.
The process of rounding involves discarding digits to the right of the position we are rounding to. • If the next digit to the right of the rounding position is 5 or greater, we round to the next higher digit. If the next digit is less than 5, we round down: • 1.5546 = 1.555 To 4 significant digits • 1.5546 = 1.55 To 3 significant digits • 1.5546 = 1.6 To 2 significant digits • 1.5545 = 2 To 1 significant digit • (74 in. x 173 in.) = 12802 in2 Too many significant digits. • = 1.2802 x 104 in2 Convert to scientific notation. • = 1.3 x 104 in2 Round to 2 significant digits.
The process for determining the correct number of significant digits for the sum or difference of two numbers is somewhat different. • First express the two numbers to the same power of ten. • (9.3835 x 101) + (3.7 x 100) = (9.3835 x 101) + (0.37 x 101) • The sum or difference cannot have more digits to the right of the decimal point than either of the two numbers being added or subtracted. • (9.3835 x 101) + (0.37 x 101) = 9.7535 x 101 • = 9.75 x 101 • When adding two numbers, the number of significant digits may increase: • 9.9 + 9.9 = 19.8 • When subtracting two numbers, the number of significant digits may decrease: • 19.8 – 18.9 = 0.9
A method commonly used to solve problems involving numbers having units is the unit conversion method or factor analysis. • In this method, a number and its unit is converted to the corresponding new number and unit by means of a conversion factor. • N1 unit1 = (N2 unit2) x (factor) • = (2 feet) x (12 inches / 1 foot) • = (2 x 12 / 1) x (feet x inches / foot) • 24 inches = 24 inches (feet/foot) = 1 with no units
Conversion factors are generally expressed as definitions or equalities: • 1 mile = 5280 feet • From a definition two conversion factors may be derived: • (1 mile / 5280 feet) and (5280 feet / 1 mile) • The first factor can be used to convert feet into miles and the second to convert miles into feet. • 1760 feet x (1 mile / 5280 feet) = 1/3 mile • 1/3 mile x (5280 feet / 1 mile ) = 1760 feet • If a conversion factor is correctly applied, a unit will always cancel. • 1760 feet x (5280 feet / 1 mile) = (1760 x 5280) x (feet2/mile) Incorrect!!
Several conversion steps may be necessary to solve a problem: • How many mm are there in 2.5 km? • (2.5 km) x (103 m / 1 km) x (1 mm / 10-3 m) • = (2.5 x 103m) x (1 mm / 10-3m) • = 2.5 x 106 mm • How many seconds are there in 7 days? • (7 days) x (24 hr. / 1 day) x (60 min. / 1 hr.) x (60 sec. / 1 min.) • = 6.04800 x 105 sec. (if 7 days means exactly 7 days) • = 6 x 105 sec. (if 7 days means 7 days 1 day)
Mass is a measure of the quantity of matter and is independent of the temperature, pressure, or location of the measurement. • The mass of an object is usually measured as its weight, however, the weight of an object may change, depending upon location. • The weight of an object at the top of Mt. Everest is about 0.2% less than at sea level. • The weight of an object in a satellite, orbiting the Earth, is zero.
The mass of an object can be accurately measured by comparing its mass to that of a known standard mass by means of a balance. • The SI unit of mass is the kg. This is the only SI base unit that involves a metric prefix.
The volume of a sample is the amount of space that it occupies. • Devices commonly used to measure liquid volume: A graduated cylinder has an error of about 1% ( 0.1 mL in 10 mL). Volumetric flasks and pipettes (fixed volume) and burets (variable volume) have an error of about 0.1% ( 0.01 mL in 10 mL). Hypodermic syringes have an error of about 5–6% ( 0.5-0.6 mL in 10 mL).
All volumetric containers are calibrated in milliliters (mL). • One mL is exactly equal to 1 cm3. • 1000 mL = 1 Liter = 1000 cm3 • 1 Liter = 1000 cm3 x (10-2 m / 1 cm)3 • = 103 cm3 x (10-6 m3 / 1 cm3) • 1 Liter = 10-3 m3 • or • 103 Liter = 1 m3 0.1 m3 = 1 L
Density • The density of an object is the ratio of its mass to its volume: • The density of an object varies slightly with temperature because the volume of most substances increases with increasing temperature.
To measure the density of an object one must first measure its mass and its volume. • The mass of an object is generally measured using a laboratory balance. In the case of a gas or liquid, the sample and its container is weighed and the mass of the empty container is subtracted. • The volume of a liquid or gas can be obtained from the volume of its container. • The volume of a regular solid can be calculated from its dimensions. Alternatively, and for an irregular solid, the volume can be obtained from the volume of liquid displaced when the solid is placed in a partially filled graduated cylinder.
An alternative way to measure the density of a liquid is to compare its density to that of a series of objects of known density. • A solid whose density is greater than that of the liquid will sink in the liquid. • A solid whose density is less than that of the liquid will float on the liquid. • A solid whose density is equal to that of the liquid will remain wherever placed in the liquid and will neither sink nor float.
A hydrometer is a device based on the above principles that can be used to easily measure the density of a liquid. • Most hydrometers are calibrated to read the ratio of the unknown liquid to that of a reference liquid, usually water. This ratio is known as the specific gravity of the liquid. Specific gravity has no units, since it is the ratio of two densities.
Temperature • Heat will always flow from a hot object to a cold object if they are placed in contact. • The property that is measured to express the “hotness” of an object is called the temperature of the object and is measured using a thermometer. • Most common thermometers are based on the fact that liquids expand upon heating. If a tube is connected to a reservoir filled with a liquid, the liquid will be forced to rise up in the tube upon heating.
A thermometer can be calibrated by placing it in freezing water and marking the liquid level, and then placing it in boiling water and marking the new liquid level. • If 99 divisions are inscribed between the two marks (making 100 equally spaced intervals) and the freezing temperature is specified as 0, the thermometer will indicate temperature on the Celsius scale. • If 179 division are inscribed between the two marks (making 180 equally spaced divisions) and the freezing point is specified as 32, the thermometer will indicate temperature on the Fahrenheit scale.
Another temperature scale, the Kelvin scale, is almost always used when making scientific temperature measurements. On this scale, the freezing point of water is 273.15 K and the boiling point of water is 373.15 K. • There is a simple relationship between the Kelvin scale and the Celsius scale: • The relationship between the Fahrenheit and Celsius scales is slightly more complicated: