Scientific Measurement Chemistry Unit 2

Measurements Qualitative Measurement – give results in a descriptive nonnumerical form For example It is hot today It’s over yonder I’ll be ready in a bit That is too heavy to pick up The new store is huge

Measurements Qualitative measurements are relative to the person giving them, and can be confusing to other people For example If you live in Death Valley, it may not be hot What is a yonder? Should I start watching television? I can lift that with one hand Not compared to the mall

Measurements Quantitative measurements – give results in a definite form. They contain both numbers and units For example The temperature is 99◦F It’s 5 miles south I will be ready in 2 minutes That weighs 200 pounds The new store is ½ a block

Measurements For the purpose of science it is very important that we express measurements in a quantitative form It is more precise It is more accurate It is reproducible It removes any bias

Accuracy Accuracy – is a measure of how close a measurement is to the actual or true value of that measurement If we put a thermometer in a glass of ice water it should read 0◦C This is the accepted value Right away we can tell if our thermometer is accurate or not Calibrating thermometers, football passes, strikes in baseball, standard weights and scales, soccer goal is big

Precision Precision – a measure of how close a series of measurements are to each other Requires more than one measurement The closer the measurements are the greater the precision If we put three thermometers in the same cup of ice water, and all three measure 1◦C, we can say our measurement is precise. Is our measurement accurate? Leading somebody in a football pass, strike zone or ball, soccer goal

Accuracy vs. Precision Accuracy is about the true or accepted value Precision has nothing to do with the true value Accuracy can be achieved with one measurement Precision takes a series of measurements. Then are evaluated to see how close they are to each other

DOH!!!! Error Everybody makes a mistake!!!!!!!! Simpson’s get a good Homer impression

Error Error = Experimental value – accepted value Experimental value – the value obtained during a lab Accepted value – the correct value based on reliable sources

Error Error can be positive or negative If the experimental value is more than the accepted value the error is positive If the experimental value is less than the accepted value the error is negative

Error Error is expressed as a percent % error = (exp. Value – accep. Value) x 100% accep. Value % error = (980 – 1000) x 100% = -2% 1000 Error is a %, show equation, give ex. Of a light bulb w/1000 hrs only burning for 980.

Scientific Notation Numbers in Chemistry can be extremely large or small, and cumbersome to express For example Avagadro’s number: 602,200,000,000,000,000,000,000 Or the mass of one atom of carbon: 0.000000000000000000000019952g

Scientific Notation We need an easier way to deal with these quantities That is why we use scientific notation Scientific notation is the product of two numbers Avagadro’s number = 6.022 x 1023 1 atom of carbon = 1.9952 x 10-23g

Scientific Notation Scientific notation is the product of two numbers The first number is called the coefficient The coefficient must be a number greater than or equal to 1 and less than 10

Scientific Notation The second number is 10 to an exponent If the exponent is positive it indicates how many times you should multiply the coefficient by 10 If the exponent is negative it indicates how many times you should divide the coefficient by 10

Scientific Notation Since our number system is in base 10 we can just move the decimal the number of times the exponent indicates For a positive exponent we will move the decimal point to the right 3.12 x 103 = 3120 For a negative exponent we will move the decimal point to the left 1.56 x 10-4 = 0.000156

Scientific Notation Multiplication of numbers in scientific notation Multiply the coefficients Add the exponents (4.00 x 106) x (2.00 x 103) = 8.00 x 109 (3.20 x 104) x (2.30 x 104) = 7.36 x 108

Scientific Notation Division of numbers in scientific notation Divide the coefficients Subtract the exponents 9.00 x 108 / 3.00 x 104 = 3.00 x 104 8.17 x 107 / 4.13 x 103 = 1.98 x 104

Scientific Notation Addition and subtraction of numbers in scientific notation Remember the exponent means how many places to move the decimal point The decimal points must be aligned to add In order to line up the decimal points we need to make the exponents the same

Scientific Notation Take the following example 3.66 x 102 + 4.12 x 103 If they were not in scientific notation they would look like this 366 + 4120 Therefore we need to change one of the exponents to equal the other 0.366 x 103 + 4.12 x 103

Scientific Notation 0.366 x 103 + 4.12 x 103 Now we can add the coefficients and the exponent will be 103 0.366 x 103 + 4.12 x 103 = 4.486 x 103

Scientific Notation For subtraction the same rule applies, the exponents must be the same Subtract the coefficients from each other For example 3.66 x 102 - 4.12 x 103 0.366 x 103 - 4.12 x 103 0.366 x 103 - 4.12 x 103 = -3.754 x 103

Significant Figures Significant figures – include all digits that are known plus a last digit that is estimated We estimate all the time We can only estimate 1 digit beyond what is known In a measurement we must be able to determine the significant figures

Significant Figures There are six rules for determining how many significant figures there are Rule #1 – in a measurement every non zero digit is assumed to be significant For example 5489 23.69 1.657 359.7 All of these measurements have four significant figures

Significant Figures Rule #2 – All zeros between non zero digits are significant For example 10002 98.023 8.0604 580.06 All of these numbers have five significant figures

Significant Figures Rule # 3 – All zeros to the left of the first non zero digit are not significant For example 0.52 0.00084 0.021 0.000037 All of these numbers only have two significant figures

Significant Figures Rule # 3 cont. Writing in scientific notation helps prevent confusion with the zeros 5.2 x 10-1 8.4 x 10-4 2.1 x 10-2 3.7 x 10-5

Significant Figures Rule # 4 – Zeros at the end of a number, and to the right of a decimal point are significant For example 58,001.10 6.012700 98.50000 1.011000 All of these numbers have seven significant figures

Significant Figures Rule # 5 – Zeros at the end of a number, and to the left of the decimal point are not significant For example 1230. 107,000. 45,600 1,540,000 All these numbers have three significant figures

Significant Figures Rule # 5 – continued Again this is why scientific notation helps prevent confusion You know what is next 1.23 x 103 1.07 x 105 4.56 x 104 1.54 x 106

Significant Figures Rule # 6 – Unlimited significant figures occur in two situations The first situation is when something is counted For example There are ______ people in class today There are 50 stars on the U.S. flag There are six lab stations in the room There are three doors in the room

Significant Figures Rule # 6 continued The second situation with unlimited significant figures is when the number is an exactly defined quantity For example There are 100 yards between football end zones There are four quarters in a dollar There are 12 months in a year There are 1,000 milliliters in a liter

Significant Figures When we are using significant figures in calculations it is important to understand that the answer cannot be more precise than the measurements used in the calculation. This is why we need to be able to determine how many significant figures are in a number

Significant Figures For example: You measure a room to be 6.6m by 5.9m Both of these measurements have two significant figures When you multiply them to find the area 6.6m x 5.9m = 38.94m2 The area has four significant figures Is this a valid answer?

Significant Figures No, because the calculation cannot be more precise than the measurements To get the correct amount of significant figures, we must round 38.94m2 would be rounded to 39m2

Significant Figures Rules for rounding If the digit after the correct amount of significant figures is between 0 – 4 just drop the rest of the digits If the digit after the correct amount of significant figures is between 5 – 9 increase the last significant figure by 1 and drop the rest of the digits.

Significant Figures Multiplication and Division Round the answer to the same amount of significant figures as the measurement with the least amount of significant figures

Significant Figures Addition and Subtraction Round the answer to the number of decimal places (not digits) as the measurement with the least amount of decimal places

SI Units All measurements need a unit to be clearly understood The metric system, established in France in 1790 uses base 10 The advantage of the metric system is that conversions are very easy

SI Units In 1960 the International System of Units (abbreviated SI) was adopted by international agreement It is a revision of the metric system It consists of seven base units All other units of measurement can be derived from these seven

SI Units The seven base units in the SI system are: Length – meter (m) Mass – kilogram (k) Temperature – kelvin (K) Time – second (s) Amount of substance – mole (mol) Luminous intensity – candela (cd) Electric current – ampere (A)

SI Units From these base units we can derive other units with the use of a prefix mega (M) – 1,000,000 times larger (106) kilo (k) – 1,000 times larger (103) deci (d) – 10 times smaller (10-1) centi (c) – 100 times smaller (10-2)

SI Units Cont. milli (m) – 1,000 times smaller (10-3) micro (μ) – 1,000,000 times smaller (10-6) nano (n) – 1,000 million times smaller (10-9) pico (p) – 1 trillion times smaller (10-12)

Density Density = mass / volume Density can be affected by temperature Specific gravity = density of substance / density of water There are no units for specific gravity Specific gravity is measured by a hydrometer

Temperature Temperature determines the direction of heat transfer Celsius (◦C) – named for Anders Celsius sets the freezing point of water at 0◦C and the boiling point at 100◦C

Temperature Recall that the SI unit for temperature is Kelvin This temperature is named after Lord Kelvin The freezing point of water is 273K and the boiling point is 373K Notice the (◦) symbol is not used

Temperature 0K is known as absolute zero It is the temperature where all molecular vibration ceases Converting between Celsius and Kelvin K = ◦C + 273 ◦C = K - 273

Converting Units Conversion factors are a way to change a measurements units into different units They are expressed as a ratio and are equal to one For example 1000mL 1L