2.6 SI Units The International System of Units, SI, is a revised version of the metric system Correct units along with numerical values are critical when communicating measurements. The are seven base SI units (Table 2.1) of which other SI units are derived. Sometimes non-SI units are preferred for convenience or practical reasons

2.6 SI Units – Table 2.2 Quantity SI Base or Derived Unit Non-SI Unit Length meter (m) Volume cubic meter (m3) liter Mass kilogram (kg) Density grams per cubic centimeter (g/cm3); grams per mililiter (g/mL) Temperature kelvin (K) degree Celcius (°C) Time second (s) Pressure Pascal (Pa) atmosphere (atm); milimeter of mercury (mm Hg) Energy joule (J) calorie (cal)

Common SI Prefixes Units larger than the base unit Tera T e12 base units termeter (Tm) Giga G e9 base units gigameter (Gm) Mega M e6 base units megameter (Mm) Kilo k e3 base units kilometer (km) Hecto h e2 base units hectometer (hm) Deka da e1 base units decameter (dam) Base Unit e0 base units meter (m)

Common SI Prefixes Units smaller than the base unit Base Unit e0 base units meter (m) Deci d e-1 base units decimeter (dm) Centi c e-2 base units centimeter (cm) Milli m e-3 base units millimeter (mm) Micro μ e-6 base units micrometer (μm) Nano n e-9 base units Nanometer (nm) Pico p e-12 base units picometer (pm)

Common SI Prefixes A mnemonic device can be used to memorize these common prefixes in the correct order: The Great Monarch King Henry Died By Drinking Chocolate Mocha Milk Not Pilsner

2.7 Units of Length The basic unit of length is the meter Prefixes can be used with the base unit to more easily represent small or large measurements Example: A hyphen (12 point font) measures about 0.001 m or 1 mm. Example: A marathon race is approximately 42,000 m or 42 km.

2.7 Concept Practice 15. Use the tables in the text to order these lengths from smallest to largest. a. centimeter b. micrometer c. kilometer d. millimeter e. meter f. decimeter - 3 - 1 (smallest) - 6 (largest) - 2 - 5 - 4

2.8 Units of Volume The space occupied by any sample of matter is called its volume The volume of rectangular solids can be calculated by multiplying the length by width by height Units are cubed because you are measuring in 3 dimensions Volume of liquids can be measured with a graduated cylinder, a pipet, a buret, or a volumetric flask

2.8 Units of Volume A convenient unit of measurement for volume in everyday use is the liter (L) Milliliters (mL) are commonly used for smaller volume measurements and liters (L) for larger measurements 1 mL = 1 cm3 10 cm x 10 cm x 10 cm = 1000 cm3 = 1 L

2.8 Units of Volume

2.8 Concept Practice 17. From what unit is a measure of volume derived? A: Volume is a length measurement cubed.

2.8 Practice 18. What is the volume of a paperback book 21 cm tall, 12 cm wide, and 3.5 cm thick? A: 882 cm3 → 880 cm3; 8.8 x 102 cm3 19. What is the volume of a glass cylinder with an inside diameter of 6.0 cm and a height of 28 cm? V=πr2h A: 790 cm3; 7.9 x 102 cm3

2.9 Units of Mass A person on the moon would weigh 1/6 of his/her weight on Earth. This is because the force of gravity on the moon is approximately 1/6 of its force of Earth. Weight is a force – it is a measure of the pull on a given mass by gravity; it can change by location. Mass is the quantity of matter an object contains Mass remains constant regardless of location. Mass v. Weight

2.9 Units of Mass The kilogram is the basic SI unit of mass It is defined as the mass of 1 L of water at 4°C. A gram, which is a more commonly used unit of mass, is 1/1000 of a kilogram 1 gram = the mass of 1 cm3 of water at 4°C.

2.9 Concept Practice 20. As you climbed a mountain and the force of gravity decreased, would your weight increase, decrease, or remain constant? How would your mass change? Explain. A: Your weight would decrease; mass would remain constant. 21. How many grams are in each of these quantities? a. 1 cg b. 1 μg c. 1 kg d. 1mg A: 0.01g 0.000001g 1000g 0.001 g

2.10 Density Density is the ratio of the mass of an object to its volume. Equation → D = mass/volume Common units: g/cm3 or g/mL Example: 10.0 cm3 of lead has a mass 114 g Density (of lead) = 114 g / 10.0 cm3 = 11.4 g/cm3 See Table 2.7, page 46

2.10 Density Density determines if an object will float in a fluid substance. Examples: Ice in water; hot air rises Density can be used to identify substances See Table 2.8, page 46

2.10 Concept Practice 22. The density of silver is 10.5 g/cm3 at 20°C. What happens to the density of a 68-g bar of silver that is cut in half? A: Its density does not change.

2.10 Concept Practice 23. A student finds a shiny piece of metal that she thinks is aluminum. In the lab, she determines that the metal has a volume of 245 cm3 and a mass of 612 g. Is the metal aluminum? A: Density = 2.50 g/cm3; the metal is not aluminum. 24. A plastic ball with a volume of 19.7 cm3 has a mass of 15.8 g. Would this ball sink or float in a container of gasoline? A: Density = 0.802 g/cm3; the ball will sink.

2.10 Specific Gravity (Relative Density) Specific gravity is a comparison of the density of a substance to the density of a reference substance, usually at the same temperature. Water at 4°C, which has a density of 1 g/cm3, is commonly used as a reference substance. Specific gravity = density of substance (g/cm3) density of water (g/cm3) Because units cancel, a measurement of specific gravity has no units A hydrometer can be used to measure the specific gravity of a liquid.

2.11 Concept Practice 25. Why doesn’t a measurement of specific gravity have a unit? A: Because it is a ratio of two density measurements, the density units cancel out. 26. Use the values in Table 2.8 to calculate the specific gravity of the following substances. a. Aluminum b. Mercury c. ice A: 2.70 13.6 0.917

2.12 Measuring Temperature Temperature determines the direction of heat transfer between two objects in contact with each other. Heat moves from the object at the higher temperature to the object at a lower temperature. Temperature is a measure of the degree of hotness or coldness of an object. Almost all substances expand with an increase in temperature and contract with a decrease in temperature An important exception is water

2.12 Measuring Temperature There are various temperature scales On the Celsius temperature scale the freezing point of water is taken as 0°C and the boiling point of water at 100°C

2.12 Measuring Temperature The Kelvin scale (or absolute scale) is another temperature scale that is used On the Kelvin scale the freezing point of water is 273 K and the boiling point is 373 K (degrees are not used). 1°C = 1 Kelvin The zero point (0 K) on the Kelvin scale is called absolute zero and is equal to -273°C Absolute zero is where all molecular motion stops

2.12 Measuring Temperature Converting Temperatures: K = °C + 273 °C = K - 273

2.12 Concept Practice 27. Surgical Instruments may be sterilized by heating at 170°C for 1.5 hours. Convert 170°C to kelvins. A: K = 170°C + 273 = 443 K 28. The boiling point of the element argon is 87 K. What is the boiling point of argon in °C? A: °C = 87 K – 273 = -186°C

2.13 Evaluating Measurements Accuracy in measurement depends on the quality of the measuring instrument and the skill of the person using the instrument. Errors in measurement could have various causes In order to evaluate the accuracy of a measurement, you must be able to compare it to the true or accepted value.

2.13 Evaluating Measurements accepted value – the true or correct value based or reliable references experimental value – the measured value determined in the experiment The difference between the accepted value and the experimental value is the error. error = accepted value – experimental value

2.13 Evaluating Measurements The percent error is the error divided by the accepted value, expressed as a percentage of the accepted value. Percent Error = x 100 An error can be positive or negative, but an absolute value of error is used so that the percentage is positive |error| AV

2.13 Concept Practice 32. A student estimated the volume of a liquid in a beaker as 200 mL. When she poured the liquid into a graduated cylinder she measured the value as 200 mL. What is the percent error of the estimated volume from the beaker, taking the graduated cylinder measurement as the accepted value? A: Percent Error = x 100 = 4% |200 mL - 208 mL| 200 mL