CHEM 101 / 105 LECT 1 Rules of the road: Your Loyola computer account (activate it). Class Web site (visit and send me an e-mail B4 Tues.) spavko1@luc.edu Chapter 1. Chemistry is... Matter is... Classifications of matter... animal, plant, mineral; organic, inorganic; SLG; elements, compounds, mixtures;... Just what is an element? a compound? a mixture? Homogeneous and heterogeneous mixtures. Chemical reaction; new products/substances formed having different properties compared to reactants. Symbolism. Measurement: number values obtained from a measurement and units of the measuring device are inseparable. When units of a measurement are changed, then number values must also change. Consider the metric and English systems of measurement (conversion factors and prefixes) length: meter ONE meter is equal to 9.7 in. Express this relationship as an equation, 1 m = 9.7 inches () both sides by 9.7 in, which leads to) 1 m / (9.7 in) = (9.7 in)/(9.7 in) = 1 Accordingly, be forever convinced that conversion factors always equal UNITY, and multiplying and/or dividing BY conversion factors is the same as multiplying and/or dividing by ONE. 1 m = 100 cm = 1000 mm; 1 km = 1000 m; 1 m = 10 9 nm; 1 nm = 10-9 m height/girth in cm? mass: kilogram 1 kg = 1000 g; 1 g = 1000 mg; 454 g = 1 pound (lb) Mass vs. Weight Mass in grams? temperature: Celsius scale Fahrenheit scale (Temperature boiling point of water 100N 212N vs. Heat) freezing point of water 0N 2N T = 100N T = 180N relate these two temperature scales in graphical form. Use graph to find a linear mathematical relation, i.e., (conversion formula) between NC and NF. Write the relation in the form NF =...; and also as NC =... The highest temperature experienced in Chicago one Saturday was 9NF. Express this temperature in Celsius. The Kelvin (absolute) temperature scale. K = 27 + NC What temperature (in K) is -50NC? is -75EF? volume: liter one liter = a cube measuring 10 cm on an edge; 1 L = 1000 cm 1 cm = 1 ml 1.06 qts = 1 L? Liters = 1 meter Significant Figures - numbers coming from MEASUREMENTS must convey information about the uncertainty (i.e., the useful scale limit) of the measuring device. Consider some examples on the reverse side: Fig. A *.+.*..*.+.*..*. 17 18 Use this ruler to measure the length of the object. 16 and 5/8 (covert to decimal) 16.625 (calculator display) The scale used for this measurement has smallest divisions of 1/8 = 0.125 units. This scale can distinguish between 1/10ths of units, so the measured numerical value should be reported to the 1/10ths place as 16.6 (i.e., the measurement shows the value lies between 16.5 and 16.7). The number has three significant figures. Fig. B.....+...*...+...!...+...*...+..... 14 15 Use this ruler to measure the length of the object. 14 and 19/2 (convert to decimal) 14.5975 (calculator display) The scale used for this measurement has smallest divisions of 1/2 = 0.0 units. This scale can distinguish between /100ths of units, so the measured numerical value should be reported to the 1/100ths place as 14.59 (i.e., the measurement shows the value lies between 14.56 and 14.62). The number has four significant figures. Some examples showing usage of significant figures in mathematical operations: 1. Lunch for the four of us was $17.4. It is decided to include an 18% tip. How much is the tip? What is the total bill? What is each persons share (in significant figures)?
2. A sample of liquid has a mass of 5 lbs and 7 oz, and a volume of 2.17 qts. What is the density of this liquid in g/cm?. How would you report the total mass of the following items, each of which was "weighed" on a different balance? A. 1.05 g NaCl B. 45.7 g CaSO 4 C. 7 g (NH 4 ) PO 4 item mass sig.fig place value of least sig.fig. A. 1.05 4 1/1000 ths (x. x 5) (calculator says: 119.75, B. 45.7 1/10 ths (x. 7 ) C. 7 2 ones place ( ) Should be reported as 120 grams) Conversions: represent the most common mathematical operation used throughout the entire course. The factor-label method is suggested for making conversions. It uses both number values and units, and operates under rules of algebra. When expressing numbers in scientific notation a two-part system is used; the first part is a decimal value between 1.000 and 9.999, and the second part is an exponential value. The entire number is obtained by multiplying the two parts together. Thus the number 0.00051 would be written as 5.1 x 10-4 and read as "five point three one times ten to the minus fourth power". This measurement contains three significant figures. Magnitudes of measured numbers are often expressed in scientific notation because they conveniently display very large and/or very small numbers (magnitude information is controlled by the exponential part), while retaining the proper number of significant figures (uncertainty information is controlled by the decimal part). 1. Suppose your family's home is 9.84 miles from Flanner Hall. How many inches is this distance? 2. A 25 cent coin has a surface area of about 460 mm 2. What is its area in square feet?...in meters 2?. The diameter of a cesium atom is given as 0.524 nm. What is its volume in meters? (V(sphere) = 4 (radius) /) 4. Which is the smaller volume, 1.50 cm, or 1.50E+ nm? (Note exponentiation of both magnitudes and units.) 5. Which is a more dense material, one having a density of 25 g/cm, or one with density of 2.50E- kg/m? Density is a distinguishing and unique property for each example of matter. We are likely to use some form of density information in every chapter in the text. Density and other properties of matter such as solubility, are used to differentiate and distinguish between different examples of matter. 1. A solid has a mass of 11.4 oz, and a volume of 0.57 L. What is the density of this material (in g/cm )? 2. Given: mass MT graduated cylinder = 4.751 g, mass grad.cyl. + 8.16 ml liquid = 52.08 g. Density of liquid?. A 50 ml graduated cylinder contains 25.6 ml of water. A solid is introduced into this cylinder and the water level rises to read 2.9 ml. In a separate experiment the solid is weighed and found to have a mass of 9.526 g. What is the density of the solid? Note: it is usually the case that mass determinations (weighings) contain more sig.fig. than volume measurements, b/c balances are more precise instruments than burets, beakers, cylinders or pipets. Can density be determined using only mass determinations? Follow work in the next problem to see how this can be accomplished... 4. An empty flask has a mass of 27.5941 g, and when filled with water the combined mass is 5.4174 g. A solid sample is introduced into the dry flask and the combined mass is 75.985 g. When enough water is added so as to completely cover the solid, and fill the flask, the combined mass is 86.152 g. What is the density of the solid? class web site: http://www.luc.edu/faculty/spavko1/c105/ Read Chapter 1. Find and work text problems similar to those on today's lecture handout. Tomorrow, Tuesday, August 26, we meet again in FH-1 auditorium, at 8:0 A.M.
Measurement ANSWERS length: meter - convert a height of 5 feet 10 inches to centimeters i.? inches = 5 feet 12 inches 1 foot = 60 inches ii.? cm = (60+10 = 70)inches 254. cm 1inch = 177.8 cm (?sig.fig.?) mass: gram - convert 175 pounds to grams? grams = 175 lbs 454 grams 1 pound = 79450 grams (?sig.fig.?) temperature convert 9 deg.f to deg.c, and deg.kelvin 9 deg.f = 9/5(deg.C) + 2 (9-2) = 9/5(deg.C) (5/9)(61) = deg.c =.9 K = 27+deg.C = 27+.9 = 06.9 Significant Figures 1. i. tip = (0.18)(17.4) =.1212 (least sig.fig. is the cent, so...) ii. bill = 17.45+.12 = 20.46 iii. share = (20.46/4) = 5.115 (but rounding up to 5.12 produces more than required. Usually the calculating person gets the bonus.) 2. i. Mass? grams = 5 lbs and 7 oz. (express units in one base only)? oz = 5 lbs 16 oz. 1 lb = 80 oz.? g = 87 oz 1 lb 454 grams 16 oz 1 lb Total mass = 80 + 7 = 87 ounces = 2468.625 grams (so calc says) ii. Volume? cm = 2.17 qt 1 L 1000 cm 106. qt 1 L = 2185.849057 cm (so calc says) iii. Density=mass/volume Density = 2468.625/2185.849057 = 1.1296668 (so calc says)
However... when MULTIPLYING or DIVIDING measured numbers, the result should display no more digits then there are significant figures in the measurement having the fewest number of significant figures. 87 oz has TWO significant figures 2.17 qt has FOUR significant figures So the result should only contain two significant figures, Accordingly, report density = 1.1 g/cm. total mass = 1.05 + 45.7 + 7 = 119.75 (so calc says) However... when ADDING or SUBTRACTING measured numbers, the reported result should not extend beyond the place value of that measurement having the highest place value for its least significant figure (i.e., the most uncertain digit). Place values for least significant figures are as shown... 1.05 is in the thousandths place, 0.00X 45.7 is in the tenths place, 0.X 7 is in the ones place, X. Note, the highest place value of these least significant figures is in the ones place (as in the measurement 7). So the result should only contain significant figures up to (and including) the ONES place. So report the total mass = 120 (rounding off the trailing 7) Conversions 1.? inches = 9.84 miles 5280 feet 12 inches 1 mile 1 foot = 62462.4 (calculator says) But should only report significant figures based on 9.84. How is this accomplished? Reporting the length as 62000 is not considered good form. Better to express it using scientific notation, i.e., as a two-part number, firstly a value between 1.000... and 9.999... showing the correct number of significant figures; and secondly ten raised to a power to properly locate the decimal point. Accordingly, the length is reported as = 6.2 x 10 5 inches 2.? sq.ft. = 460 mm 2 1meter 1000 mm 97. inches 1 meter 1 foot 12 inches 2 2 2 = 4.95E- ft 2
. i.? m = 0.524 nm 1 meter 10 9 = 5.24E-10 meters (note, this a diameter) nm radius = diameter/2 = 2.62E-10 meters ii. use volume formula for sphere V = (4*pi/)(2.62E-10 m) = (4.188790205)(1.7984728E-29) = 7.5425248E-29 m (so calc says) However, diameter only has sig.fig., so report volume so as to display three significant figures... Vol. = 7.5E-29 m 4. Need to convert either volume to units of the other: 9 10 100? cm = 1.50 E + nm meter cm 1 = 1.50 E - 18 cm nm 1 meter Accordingly, 1.50 E + nm is much smaller than 1.50 cm 5. Need to convert either density to units of the other? g / cm = 2.50 E - kg / m 1000 g 1meter 1kg = 2.50 E -6 g/cm 100 cm Accordingly, a density of 2.50 E - kg / m is much smaller than 25 g / cm. Density = mass / volume 1. A. Convert mass from ounces to grams? grams = 11.4 oz 1 lb 454 g 16 oz 1 lb = 728.475 (4 sig.figs.) B. Convert volume to cm? cm = 0.57 L 1000 cm = 57 cm 1 Liter C. Density (solid) = 6.94 g / cm ( sig.figs.) 2. A. mass MT grad.cyl. = 4.751 g B. mass grad.cyl. + 8.16 ml liquid = 52.08 g C. Density = (52.08-4.751) / 8.16 = 1.02 g / ml
. Volume liquid in cyl. = 25.6 ml ( sig.figs.) Vol. (liquid + solid) = 2.9 ml Vol. solid = 2.9-25.6 = 7. ml* mass solid = 9.526 g (4 sig.figs.) Density solid = 9.526 / 7. = 1. g / cm (2 sig.figs.)* 4. mass flask = 27.5941 g mass water to fill flask mass flask (5.174-27.941)=25.82 g + water = 5.4174 g to fill Vol.flask = volume of water needed to fill = 25.82 g H 2 O 1 cm = 25.82 cm 1 g mass flask + solid = 75.985 g Mass Solid = (75.985-27.5941) = 48.444 g mass flask + solid = 86.152 g + water to cover solid and fill flask*** Mass of water covering the solid and filling remaining space in the flask = (86.152-75.985 ) = 10.767 g Vol. of this water = 10.767 g H 2 O 1 cm = 10.767 cm 1 g Vol. of solid is difference in total volume of flask, less volume of water covering the solid. In other words, volume of solid is volume NOT occupied by water in ***. Vol. solid = (25.82-10.767) = 15.4466 cm Density (solid ) = 48444. =.1298 g/cm 15. 4466 (lots of sig.fig.)