1. Chapter 2 Measurement and Problem Solving

2. Homework Exercises (optional) Exercises (optional) 1 through 27 (odd) 1 through 27 (odd) Problems Problems 29-65 (odd) 29-65 (odd) 67-91 (odd) 67-91 (odd) 93-99 (odd) 93-99 (odd) Cumulative Problems Cumulative Problems 101-117 (odd) 101-117 (odd) Highlight Problems (optional) Highlight Problems (optional) 119, 121 119, 121

3. 2.2 Scientific Notation: Writing Large and Small Numbers In scientific (chemistry) work, it is not unusual to come across very large and very small numbers In scientific (chemistry) work, it is not unusual to come across very large and very small numbers Using large and small numbers in measurements and calculations is time consuming and difficult Using large and small numbers in measurements and calculations is time consuming and difficult Recording these numbers is also very prone to errors due to the addition or omission of zeros Recording these numbers is also very prone to errors due to the addition or omission of zeros A method exists for the expression of awkward, multi-digit numbers in a compact form: scientific notation A method exists for the expression of awkward, multi-digit numbers in a compact form: scientific notation

4. 2.2 Scientific Notation: Writing Large and Small Numbers Scientific Notation Scientific Notation A system in which an ordinary decimal number (m) is expressed as a product of a number between 1 and 10, multiplied by 10 raised to a power (n) A system in which an ordinary decimal number (m) is expressed as a product of a number between 1 and 10, multiplied by 10 raised to a power (n) Used to write very large or very small numbers Used to write very large or very small numbers Based on powers of 10 Based on powers of 10

5. 2.2 Scientific Notation: Writing Large and Small Numbers Numbers written in sci. notn. consist of a number (coefficient) followed by a power of 10 (x 10 n ) Numbers written in sci. notn. consist of a number (coefficient) followed by a power of 10 (x 10 n ) Negative exponent: number is less than 1 Negative exponent: number is less than 1 Positive exponent: number is greater than 1 Positive exponent: number is greater than 1 coefficient or decimal part exponential term or part exponent

6. 2.2 Scientific Notation: Writing Large and Small Numbers In an ordinary cup of water there are: In an ordinary cup of water there are: Each molecule has a mass of: Each molecule has a mass of: 0.0000000000000000000000299 gram In scientific notation: 7.91 х 10 24 molecules 2.99 х 10 -23 gram 7,910,000,000,000,000,000,000,000 molecules

7. To Express a Number in Scientific Notation: For small numbers (<1): 1)Locate the decimal point 2)Move the decimal point to the right to give a number (coefficient) between 1 and 10 3)Write the new number multiplied by 10 raised to the “n th power” where “n” is the number of places you moved the decimal point so there is one non-zero digit to the left of the decimal. where “n” is the number of places you moved the decimal point so there is one non-zero digit to the left of the decimal. If the decimal point is moved to the right, from its initial position, then the exponent is a negative number (× 10 -n ) If the decimal point is moved to the right, from its initial position, then the exponent is a negative number (× 10 -n )

8. To Express a Number in Scientific Notation: For large numbers (>1): 1) Locate the decimal point 2) Move the decimal point to the left to give a number (coefficient) between 1 and 10 3) Write the new number multiplied by 10 raised to the “n th power” where “n” is the number of places you moved the decimal point so there is one non-zero digit to the left of the decimal. where “n” is the number of places you moved the decimal point so there is one non-zero digit to the left of the decimal. If the decimal point is moved to the left, from its initial position, then the exponent is a positive number (× 10 n ) If the decimal point is moved to the left, from its initial position, then the exponent is a positive number (× 10 n )

9. Examples Write each of the following in scientific notation Write each of the following in scientific notation 12,500 12,500 0.0202 0.0202 37,400,000 37,400,000 0.0000104 0.0000104

10. Examples 12,500 12,500 Decimal place is at the far right Decimal place is at the far right Move the decimal place to a position between the 1 and 2 (one non-zero digit to the left of the decimal) Move the decimal place to a position between the 1 and 2 (one non-zero digit to the left of the decimal) Coefficient (1.25) Coefficient (1.25) The decimal place was moved 4 places to the left (large number) so exponent is positive The decimal place was moved 4 places to the left (large number) so exponent is positive 1.25x10 4 1.25x10 4

11. Examples 0.0202 0.0202 Move the decimal place to a position between the 2 and 0 (one non-zero digit to the left of the decimal) Move the decimal place to a position between the 2 and 0 (one non-zero digit to the left of the decimal) Coefficient (2.02) Coefficient (2.02) The decimal place was moved 2 places to the right (small number) so exponent is negative The decimal place was moved 2 places to the right (small number) so exponent is negative 2.02x10 -2 2.02x10 -2

12. Examples 37,400,000 37,400,000 Decimal place is at the far right Decimal place is at the far right Move the decimal place to a position between the 3 and 7 Move the decimal place to a position between the 3 and 7 Coefficient (3.74) Coefficient (3.74) The decimal place was moved 7 places to the left (large number) so exponent is positive The decimal place was moved 7 places to the left (large number) so exponent is positive 3.74x10 7 3.74x10 7

13. Examples 0.0000104 0.0000104 Move the decimal place to a position between the 1 and 0 Move the decimal place to a position between the 1 and 0 Coefficient (1.04) Coefficient (1.04) The decimal place was moved 5 places to the right (small number) so exponent is negative The decimal place was moved 5 places to the right (small number) so exponent is negative 1.04x10 -5 1.04x10 -5

14. Using Scientific Notation on a Calculator  Enter the coefficient (number)  Push the key: Then enter only the power of 10  If the exponent is negative, use the key:  DO NOT use the multiplication key: to express a number in sci. notation (+/-) X EXPEE or

15. Converting Back to Standard Notation 1)Determine the sign of the exponent, n If n is + the decimal point will move to the right (this gives a number greater than one) If n is + the decimal point will move to the right (this gives a number greater than one) If n is – the decimal point will move to the left (this gives a number less than one) If n is – the decimal point will move to the left (this gives a number less than one) 2)Determine the value of the exponent of 10 The “power of ten” determines the number of places to move the decimal point The “power of ten” determines the number of places to move the decimal point Zeros may have to be added to the number as the decimal point is moved Zeros may have to be added to the number as the decimal point is moved

16. Using Scientific Notation To compare numbers written in scientific notation, with the same coefficient, compare the exponents of each number To compare numbers written in scientific notation, with the same coefficient, compare the exponents of each number The number with the larger power of ten (the exponent) is the larger number The number with the larger power of ten (the exponent) is the larger number If the powers of ten (exponents) are the same, then compare coefficients directly If the powers of ten (exponents) are the same, then compare coefficients directly Which number is larger? Which number is larger? 21.8 х 10 3 or 2.05 х 10 4 2.18 х 10 4 > 2.05 х 10 4 3.4 х 10 4 < 3.4 х 10 7

17. 2.3 Significant Figures: Writing Numbers to Reflect Precision Two kinds of numbers exist: Two kinds of numbers exist: Numbers that are counted (exact) Numbers that are counted (exact) Numbers that are measured Numbers that are measured It is possible to know the exact value of a counted number It is possible to know the exact value of a counted number The exact value of a measured number is never known The exact value of a measured number is never known Counting objects does not entail reading the scale of a measuring device Counting objects does not entail reading the scale of a measuring device

18. 2.3 Exact Numbers Exact numbers occur in definitions or in counting Exact numbers occur in definitions or in counting These numbers have no uncertainty These numbers have no uncertainty Unlimited number of significant figures (never limit the no. of sig. figures in a calculation) Unlimited number of significant figures (never limit the no. of sig. figures in a calculation) They are either They are either Counting numbers Counting numbers 7 pennies, 6 apples, 4 chairs 7 pennies, 6 apples, 4 chairs Defined numbers (one exact value) Defined numbers (one exact value) 12 in = 1 ft 12 in = 1 ft 1 gal = 4 quarts 1 gal = 4 quarts 1 minute = 60 seconds 1 minute = 60 seconds

19. Measured Numbers Unlike counted (or defined) numbers, measured numbers always contain a degree of uncertainty (or error) Unlike counted (or defined) numbers, measured numbers always contain a degree of uncertainty (or error) A measurement: A measurement: involves reading a measuring device involves reading a measuring device always has some amount of uncertainty always has some amount of uncertainty uncertainty comes from the tool used for comparison uncertainty comes from the tool used for comparison A measuring device with a smaller unit will give a more precise measurement, e.g., some rulers show smaller divisions than others A measuring device with a smaller unit will give a more precise measurement, e.g., some rulers show smaller divisions than others

20. Measured Numbers Whenever a measurement is made, an estimate is required, i.e., the value between the two smallest divisions on a measuring device Whenever a measurement is made, an estimate is required, i.e., the value between the two smallest divisions on a measuring device Every person will estimate it slightly differently, so there is some uncertainty present as to the true value Every person will estimate it slightly differently, so there is some uncertainty present as to the true value 2.8 to 2.9 cm 2.8 cm2.9 cm

21. 2.3 Significant Figures: Writing Numbers to Reflect Precision Scientific numbers are reported so that all digits are certain except the last digit which is estimated Scientific numbers are reported so that all digits are certain except the last digit which is estimated To indicate the uncertainty of a single measurement, scientists use a system called significant figures To indicate the uncertainty of a single measurement, scientists use a system called significant figures Significant Figures: All digits known with certainty plus one digit that is uncertain Significant Figures: All digits known with certainty plus one digit that is uncertain

22. 2.3 Counting Significant Figures The last digit written in a measurement is the number that is considered to be uncertain (estimated) The last digit written in a measurement is the number that is considered to be uncertain (estimated) Unless stated otherwise, the uncertainty in the last significant digit is ±1 (plus or minus one unit) Unless stated otherwise, the uncertainty in the last significant digit is ±1 (plus or minus one unit) The precision of a measured quantity is determined by number of sig. figures The precision of a measured quantity is determined by number of sig. figures A set of guidelines is used to interpret the significance of: A set of guidelines is used to interpret the significance of: a reported measurement a reported measurement values calculated from measurements values calculated from measurements

23. 2.3 Counting Significant Figures Four rules (the guidelines): Four rules (the guidelines): 1. Nonzero integers are always significant Zeros (may or may not be significant) Zeros (may or may not be significant) significant zeros significant zeros place-holding zeros (not significant) place-holding zeros (not significant) It is determined by its position in a sequence of digits in a measurement It is determined by its position in a sequence of digits in a measurement 2. Leading zeros never count as significant figures 3. Captive (interior) zeros are always significant 4. Trailing zeros are significant if the number has a decimal point

24. 2.4 Significant Figures in Calculations Calculations cannot improve the precision of experimental measurements Calculations cannot improve the precision of experimental measurements The number of significant figures in any mathematical calculation is limited by the least precise measurement used in the calculation The number of significant figures in any mathematical calculation is limited by the least precise measurement used in the calculation Two operational rules to ensure no increase in measurement precision: Two operational rules to ensure no increase in measurement precision: addition and subtraction addition and subtraction multiplication and division multiplication and division

25. 2.4 Significant Figures in Calculations: Multiplication and Division Product or quotient has the same number of significant figures as the factor with the fewest significant figures Product or quotient has the same number of significant figures as the factor with the fewest significant figures Count the number of significant figures in each number. The least precise factor (number) has the fewest significant figures Count the number of significant figures in each number. The least precise factor (number) has the fewest significant figures Rounding Rounding Round the result so it has the same number of significant figures as the number with the fewest significant figures Round the result so it has the same number of significant figures as the number with the fewest significant figures

26. 2.4 Significant Figures in Calculations: Rounding To round the result to the correct number of significant figures To round the result to the correct number of significant figures If the last (leftmost) digit to be removed: If the last (leftmost) digit to be removed:  is less than 5, the preceding digit stays the same (rounding down)  is equal to or greater than 5, the preceding digit is rounded up  In multiple step calculations, carry the extra digits to the final result and then round off

27. 2.4 Multiplication/Division Example: The number with the fewest significant figures is 1.1 so the answer has 2 significant figures The number with the fewest significant figures is 1.1 so the answer has 2 significant figures 2 SF 5 SF3 SF 2.1 4 SF 2 SF

28. 2.4 Multiplication/Division Example: The number with the fewest significant figures is 273 (the limiting term) so the answer has 3 significant figures The number with the fewest significant figures is 273 (the limiting term) so the answer has 3 significant figures 0.1021 × 0.082103 × 273 = 2.288481 2.29 3 SF 5 SF4 SF

29. 2.4 Significant Figures in Calculations: Addition and Subtraction Sum or difference is limited by the quantity with the smallest number of decimal places Sum or difference is limited by the quantity with the smallest number of decimal places Find quantity with the fewest decimal places Find quantity with the fewest decimal places Round answer to the same decimal place Round answer to the same decimal place

30. 2.4 Addition/Subtraction Example: The number with the fewest decimal places is 171.5 so the answer should have 1 decimal place The number with the fewest decimal places is 171.5 so the answer should have 1 decimal place 1 d.p. 3 d.p. 2 d.p. 236.2 1 d.p.

31. 2.5 The Basic Units of Measurement The most used tool of the chemist The most used tool of the chemist Most of the basic concepts of chemistry were obtained through data compiled by taking measurements Most of the basic concepts of chemistry were obtained through data compiled by taking measurements How much…? How much…? How long…? How long…? How many...? How many...? These questions cannot be answered without taking measurements These questions cannot be answered without taking measurements The concepts of chemistry were discovered as data was collected and subjected to the scientific method The concepts of chemistry were discovered as data was collected and subjected to the scientific method

32. 2.5 The Basic Units of Measurement The estimation of the magnitude of an object relative to a unit of measurement The estimation of the magnitude of an object relative to a unit of measurement Involves a measuring device: Involves a measuring device: meter stick, scale, thermometer meter stick, scale, thermometer The device is calibrated to compare the object to some standard (inch/centimeter, pound/kilogram) The device is calibrated to compare the object to some standard (inch/centimeter, pound/kilogram) Quantitative observation with two parts: A number and a unit Quantitative observation with two parts: A number and a unit Number tells the total of the quantity measured Number tells the total of the quantity measured Unit tells the scale (dimensions) Unit tells the scale (dimensions)

33. 2.5 The Basic Units of Measurement A unit is a standard (accepted) quantity A unit is a standard (accepted) quantity Describes what is being added up Describes what is being added up Units are essential to a measurement Units are essential to a measurement For example, you need “six of sugar” For example, you need “six of sugar” teaspoons? teaspoons? ounces? ounces? cups? cups? pounds? pounds?

34. 2.5 The Standard Units (of Measurement) The unit tells the magnitude of the standard The unit tells the magnitude of the standard Two most commonly used systems of units of measurement Two most commonly used systems of units of measurement U.S. (English) system: Used in everyday commerce (USA and Britain*) U.S. (English) system: Used in everyday commerce (USA and Britain*) Metric system: Used in everyday commerce and science (The rest of the world) Metric system: Used in everyday commerce and science (The rest of the world) SI Units (1960): A modern, revised form of the metric system set up to create uniformity of units used worldwide (world’s most widely used) SI Units (1960): A modern, revised form of the metric system set up to create uniformity of units used worldwide (world’s most widely used)

35. 2.5 The Standard Units (of Measurement): The Metric/SI System The metric system is a decimal system of measurement based on the meter and the gram The metric system is a decimal system of measurement based on the meter and the gram It has a single base unit per physical quantity It has a single base unit per physical quantity All other units are multiples of 10 of the base unit All other units are multiples of 10 of the base unit The power (multiple) of 10 is indicated by a prefix The power (multiple) of 10 is indicated by a prefix

36. 2.5 The Standard Units: The Metric System In the metric system there is one base unit for each type of measurement In the metric system there is one base unit for each type of measurement length length volume volume mass mass The base units multiplied by the appropriate power of 10 form smaller or larger units The base units multiplied by the appropriate power of 10 form smaller or larger units The prefixes are always the same, regardless of the base unit The prefixes are always the same, regardless of the base unit milligrams and milliliters both mean 1/1000 of the base unit milligrams and milliliters both mean 1/1000 of the base unit

37. 2.5 The Standard Units: Length Meter Meter Base unit of length in metric and SI system Base unit of length in metric and SI system About 3 ½ inches longer than a yard About 3 ½ inches longer than a yard 1 m = 1.094 yd 1 m = 1.094 yd

38. 2.5 The Standard Units: Length Other units of length are derived from the meter Other units of length are derived from the meter Commonly use centimeters (cm) Commonly use centimeters (cm) 1 m = 100 cm 1 m = 100 cm 1 inch = 2.54 cm (exactly) 1 inch = 2.54 cm (exactly)

39. 2.5 The Standard Units: Volume Measure of the amount of three-dimensional space occupied by a object Measure of the amount of three-dimensional space occupied by a object Derived from length Derived from length SI unit = cubic meter (m 3 ) SI unit = cubic meter (m 3 ) Metric unit = liter (L) or 10 cm 3 Metric unit = liter (L) or 10 cm 3 Commonly measure smaller volumes in cubic centimeters (cm 3 ) Commonly measure smaller volumes in cubic centimeters (cm 3 ) Volume = side × side × side volume = side × side × side

40. 2.5 The Standard Units: Volume Since it is a three- dimensional measure, its units have been cubed Since it is a three- dimensional measure, its units have been cubed SI base unit = cubic meter (m 3 ) SI base unit = cubic meter (m 3 ) This unit is too large for practical use in chemistry This unit is too large for practical use in chemistry Take a volume 1000 times smaller than the cubic meter, 1dm 3 Take a volume 1000 times smaller than the cubic meter, 1dm 3

41. 2.5 The Standard Units: Volume Metric base unit = 1dm 3 = liter (L) Metric base unit = 1dm 3 = liter (L) 1L = 1.057 qt 1L = 1.057 qt Commonly measure smaller volumes in cubic centimeters (cm 3 ) Commonly measure smaller volumes in cubic centimeters (cm 3 ) Take a volume 1000 times smaller than the cubic decimeter, 1cm 3 Take a volume 1000 times smaller than the cubic decimeter, 1cm 3

42. 2.5 The Standard Units: Volume Metric base unit = 1dm 3 = liter (L) Metric base unit = 1dm 3 = liter (L) 1L = 1.057 qt 1L = 1.057 qt Commonly measure smaller volumes in cubic centimeters (cm 3 ) Commonly measure smaller volumes in cubic centimeters (cm 3 ) Take a volume 1000 times smaller than the cubic decimeter, 1cm 3 Take a volume 1000 times smaller than the cubic decimeter, 1cm 3

43. 2.5 The Standard Units: Volume The most commonly used unit of volume in the laboratory: milliliter (mL) The most commonly used unit of volume in the laboratory: milliliter (mL) 1 mL = 1 cm 3 1 mL = 1 cm 3 1 L= 1 dm 3 = 1000 mL 1 L= 1 dm 3 = 1000 mL 1 m 3 = 1000 dm 3 = 1,000,000 cm 3 1 m 3 = 1000 dm 3 = 1,000,000 cm 3 Use a graduated cylinder or a pipette to measure liquids in the lab Use a graduated cylinder or a pipette to measure liquids in the lab

44. 2.5 The Standard Units: Mass Measure of the total quantity of matter present in an object Measure of the total quantity of matter present in an object SI unit (base) = kilogram (kg) SI unit (base) = kilogram (kg) Metric unit (base) = gram (g) Metric unit (base) = gram (g) Commonly measure mass in grams (g) or milligrams (mg) Commonly measure mass in grams (g) or milligrams (mg) 1 kg = 1000 g 1 kg = 1000 g 1 g = 1000 mg 1 g = 1000 mg 1 kg = 2.205 pounds 1 kg = 2.205 pounds 1 lb = 453.6 g 1 lb = 453.6 g

45. 2.5 Prefixes Multipliers One base unit for each type of measurement One base unit for each type of measurement Length (meter), volume (liter), and mass (gram*) Length (meter), volume (liter), and mass (gram*) The base units are then multiplied by the appropriate power of 10 to form larger or smaller units The base units are then multiplied by the appropriate power of 10 to form larger or smaller units base unit = meter, liter, or gram

46. 2.5 Prefixes Multipliers (memorize) Mega (M) 1,000,000 10 6 Mega (M) 1,000,000 10 6 Kilo (k) 1,000 10 3 Kilo (k) 1,000 10 3 Base 1 10 0 Base 1 10 0 Deci(d) 0.1 10 -1 Deci(d) 0.1 10 -1 Centi(c) 0.01 10 -2 Centi(c) 0.01 10 -2 Milli(m) 0.001 10 -3 Milli(m) 0.001 10 -3 Micro(µ) 0.000001 10 -6 Micro(µ) 0.000001 10 -6 Nano (n) 0.000000001 10 -9 Nano (n) 0.000000001 10 -9 × base unit meter liter gram

47. 2.5 Prefix Multipliers For a particular measurement: For a particular measurement: Choose the prefix which is similar in size to the quantity being measured Choose the prefix which is similar in size to the quantity being measured Keep in mind which unit is larger Keep in mind which unit is larger A kilogram is larger than a gram, so there must be a certain number of grams in one kilogram A kilogram is larger than a gram, so there must be a certain number of grams in one kilogram Choose the prefix most convenient for a particular measurement Choose the prefix most convenient for a particular measurement n < µ < m < c < base < k < M

48. 2.6 Converting from One Unit to Another: Dimensional Analysis Many problems in chemistry involve converting the units of a quantity or measurement to different units Many problems in chemistry involve converting the units of a quantity or measurement to different units The new units may be in the same measurement system or a different system, i.e., U.S. System to Metric and the converse The new units may be in the same measurement system or a different system, i.e., U.S. System to Metric and the converse Dimensional Analysis is the method of problem solving used to achieve this unit conversion Dimensional Analysis is the method of problem solving used to achieve this unit conversion Unit conversion is accomplished by multiplication of a given quantity (or measurement) by one or more conversion factors to obtain the desired quantity or measurement Unit conversion is accomplished by multiplication of a given quantity (or measurement) by one or more conversion factors to obtain the desired quantity or measurement

49. 2.6 Converting from One Unit to Another: Equalities An equality is a fixed relationship between two quantities An equality is a fixed relationship between two quantities It shows the relationship between two units that measure the same quantity It shows the relationship between two units that measure the same quantity The relationships are exact, not measured The relationships are exact, not measured 1 min = 60 s 1 min = 60 s 12 inches = 1 ft 12 inches = 1 ft 1 dozen = 12 items (units) 1 dozen = 12 items (units) 1L = 1000 mL 1L = 1000 mL 16 oz = 1 lb 16 oz = 1 lb 4 quarts = 1 gallon 4 quarts = 1 gallon

50. 2.6 Converting from One Unit to Another: Dimensional Analysis Conversion factor: An equality expressed as a fraction Conversion factor: An equality expressed as a fraction It is used as a multiplier to convert a quantity in one unit to its equivalent in another unit It is used as a multiplier to convert a quantity in one unit to its equivalent in another unit May be exact or measured May be exact or measured Both parts of the conversion factor should have the same number of significant figures Both parts of the conversion factor should have the same number of significant figures

51. 2.7 Solving Multistep Conversion Problems: Dimensional Analysis Example (Conversion Factors Stated within a Problem) The average person in the U.S. consumes one-half pound of sugar per day. How many pounds of sugar would be consumed in one year? The average person in the U.S. consumes one-half pound of sugar per day. How many pounds of sugar would be consumed in one year?  State the initial quantity given (and the unit): One year State the final quantity to find (and the unit): Pounds  Write a sequence of units (map) which begins with the initial unit and ends with the desired unit: year day pounds

52. 2.7 Solving Multistep Conversion Problems: Dimensional Analysis Example  For each unit change, State the equalities: Every equality will have two conversion factors Every equality will have two conversion factors year day pounds 0.5 lb sugar =1day 365 days = 1 year

53. 2.7 Solving Multistep Conversion Problems: Dimensional Analysis Example State the conversion factors: State the conversion factors:  Set Up the problem:

54. Guide to Problem Solving when Working Dimensional Analysis Problems Identify the known or given quantity and the units of the new quantity to be determined Identify the known or given quantity and the units of the new quantity to be determined Write out a sequence of units which starts with your initial units and ends with the desired units (“solution map”) Write out a sequence of units which starts with your initial units and ends with the desired units (“solution map”) Write out the necessary equalities and conversion factors Write out the necessary equalities and conversion factors Perform the mathematical operations that connect the units Perform the mathematical operations that connect the units Check that the units cancel properly to obtain the desired unit Check that the units cancel properly to obtain the desired unit Does the answer make sense? Does the answer make sense?

55. 2.9 Density The ratio of the mass of an object to the volume occupied by that object The ratio of the mass of an object to the volume occupied by that object Density tells how tightly the matter within an object is packed together Density tells how tightly the matter within an object is packed together Units for solids and liquids = Units for solids and liquids = 1 cm 3 = 1 mL so can also use 1 cm 3 = 1 mL so can also use Unit for gases = g/L Unit for gases = g/L Density of three states of matter: solids > liquids >>> gases Density of three states of matter: solids > liquids >>> gases g/mL g/cm 3

56. 2.9 Density Can use density as a conversion factor between mass and volume Can use density as a conversion factor between mass and volume Density of some common substances given in Table 2.4, page 33 Density of some common substances given in Table 2.4, page 33 You will be given any densities on tests EXCEPT water You will be given any densities on tests EXCEPT water Density of water is 1.0 g/cm 3 at room temperature Density of water is 1.0 g/cm 3 at room temperature 1.0 mL of water weighs how much? 1.0 mL of water weighs how much? How many mL of water weigh 15 g? How many mL of water weigh 15 g?

57. 2.9 Density To determine the density of an object To determine the density of an object Use a scale to determine the mass Use a scale to determine the mass Determine the volume of the object Determine the volume of the object Calculate it if possible (cube shaped) Calculate it if possible (cube shaped) Can also calculate volume by determining what volume of water is displaced by an object Can also calculate volume by determining what volume of water is displaced by an object Volume of Water Displaced = Volume of Object

58. Density Problem Iron has a density of 7.87 g/cm 3. If 52.4 g of iron is added to 75.0 mL of water in a graduated cylinder, to what volume reading will the water level in the cylinder rise? Iron has a density of 7.87 g/cm 3. If 52.4 g of iron is added to 75.0 mL of water in a graduated cylinder, to what volume reading will the water level in the cylinder rise?

59. Density Problem Solve for volume of iron

60. End