Presentation on theme: "Introduction to General Chemistry Ch"— Presentation transcript:
1 Introduction to General Chemistry Ch. 1.6 - 1.9 Lecture 2Suggested HW:33, 37, 40, 43, 45, 46
2 Accuracy and Precision Accuracy defines how close to the correct answer you are. Precision defines how repeatable your result is. Ideally, data should be both accurate and precise, but it may be one or the other, or neither.Accurate, but not precise. Reached the target, but could not reproduce the result.Precise, but not accurate. Did not reach the target, but result was reproduced.Accurate and precise.Reached the target and the data was reproduced.
3 Measuring Accuracy Accuracy is calculated by percentage error (%E) We take the absolute value because you can’t have negative error.GROUP PROBLEM- A certain brand of thermometer is considered to be accurate if the %E is < 0.8%. The thermometer is tested using water (BP = 100oC). You bring a pot of distilled water to a boil and measure the temperature 5 times. The thermometer reads: o, 100.4o, 99.8o, 101.0o, and 100.4o. Is it accurate?
4 Measuring Precision: Significant Figures Precision is indicated by the number of significant figures. Significant figures are those digits required to convey a result.There are two types of numbers: exact and inexactExact numbers have defined values and possess an infinite number of significant figures because there is no limit of confidence:* There are exactly 12 eggs in a dozen* There are exactly 24 hours in a day* There are exactly 1000 grams in a kilogramInexact number are obtained from measurement. Any number that is measured has error because:Limitations in equipmentHuman error
5 Measuring Precision: Significant Figures Example: Some laboratory balances are precise to the nearest cg (.01g). This is the limit of confidence. The measured mass shown in the figure is g.The value has 5 significant figures, with the hundredths place (9) being the uncertain digit. Thus, the (9) is estimated, while the other numbers are known.It would properly reported as ±.01g- The actual mass could be anywhere between … g and … g. The balance is limited to two decimal places, so it rounds up or down. We use ± to include all possibilities.
6 Determining the Number of Significant Figures In a Result All non-zeros and zeros between non-zeros are significant457 (3) ; 2.5 (2) ; 101 (3) ; 1005 (4)Zeros at the beginning of a number aren’t significant. They only serve to position the decimal..02 (1) ; (1) ; (4)For any number with a decimal, zeros to the right of the decimal are significant2.200 (4) ; 3.0 (2)
7 Determining the Number of Significant Figures In a Result Zeros at the end of an integer may or may not be significant130 (2 or 3), (1, 2, 3, or 4)This is based on scientific notation130 can be written as:1.3 x 2 sig figs1.30 x 102 3 sig figsIf we convert 1000 to scientific notation, it can be written as:1 x 103 1 sig fig1.0 x 2 sig figs1.00 x 3 sig figs1.000 x 4 sig figs*Numbers that must be treated as significant CAN NOT disappear in scientific notation
8 Calculations Involving Significant Figures You can not get exact results using inexact numbersMultiplication and divisionResult can only have as many significant figures as the least precise number𝑐𝑚 𝑥 𝟓.𝟖𝟐 𝑐𝑚= 𝑐 𝑚 2 =36.2 𝑐 𝑚 2(3 s.f.)𝑚 0.𝟗𝟖 𝑠 = 𝑚 𝑠 =110 𝑚 𝑠 𝑜𝑟 1.1 𝑥 𝑚 𝑠(2 s.f.)𝑘𝑔 𝑥 𝟒 𝑚 𝑠 2 = 𝑘𝑔 𝑚 𝑠 2 = 𝑘𝑔 𝑚 𝑠 2 𝑜𝑟 2 𝑥 𝑘𝑔 𝑚 𝑠 2(1 s.f.)
9 Calculations Involving Significant Figures Addition and SubtractionResult must have as many digits to the right of the decimal as the least precise number20.41.32283
10 Limit of certainty is the ones place Group WorkUsing scientific notation, convert to 3 sig. figs.Using scientific notation, convert to 1 sig. fig.H= cmW = .40 cmL = cmVolume of rectangle ?Surface area (SA = 2WH + 2LH + 2LW) ?note: constants in an equation are exact numbers=2 4.0𝑐 𝑚 𝑐 𝑚 2 +2(1𝟐.4𝑐 𝑚 2 )Limit of certainty is the ones place=8.0𝑐 𝑚 𝑐 𝑚 2 +2𝟒.8𝑐 𝑚 2=65𝟐.8𝑐 𝑚 2 =653𝑐 𝑚 2
11 Dimensional AnalysisDimensional analysis is an algebraic method used to convert between different unitsConversion factors are requiredConversion factors are exact numbers which are equalities between one unit set and another.For example, we can convert between inches and feet. The conversion factor can be written as:In other words, there are 12 inches per 1 foot, or 1 foot per 12 inches.
12 Dimensional Analysis conversion factor (s) Example. How many feet are there in 56 inches?Our given unit of length is inchesOur desired unit of length is feetWe will use a conversion factor that equates inches and feet to obtain units of feet. The conversion factor must be arranged such that the desired units are ‘on top’𝟓𝟔 𝑖𝑛𝑐ℎ𝑒𝑠 𝑥 1 𝑓𝑜𝑜𝑡 12 𝑖𝑛𝑐ℎ𝑒𝑠 = 𝑓𝑡4.7 ft
13 Group WorkAnswer the following using dimensional analysis. Consider significant figures.Convert 35 minutes to hoursConvert 40 weeks to secondsConvert 4 gallons to cm3 (1 gallon = 4 quarts and quart = mL)*35 𝒎𝒊𝒍𝒆𝒔 𝒉𝒓 to 𝒊𝒏𝒄𝒉𝒆𝒔 𝒔𝒆𝒄 (1 mile = 5280 ft and 1 ft = 12 in)
14 High Order Exponent Unit Conversion (e.g. Cubic Units) As we previously learned, the units of volume can be expressed as cubic lengths, or as capacities. When converting between the two, it may be necessary to cube the conversion factorEx. How many mL of water can be contained in a cubic container that is 1 m33Must use this equivalence to convert between cubic length to capacity1 𝑚 3 𝑥 𝑐𝑚 1 0 −2 𝑚 𝑥 𝒎𝑳 𝒄 𝒎 𝟑Cube this conversion factor=1 𝑚 3 𝑥 𝒄𝒎 𝟑 𝟏 𝟎 −𝟔 𝒎 𝟑 𝑥 𝑚𝐿 𝑐 𝑚 3=𝟏 𝒙 𝟏 𝟎 𝟔 𝒎𝑳
15 Group Work Convert 10 mL to m3 (c = 10-2) Convert 100 L to µm3 (µ = 10-6)Convert 48.3 ft2 to cm2 (1 in. = 2.54 cm)