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

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?

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

Error

• Everybody makes a mistake!!!!!!!!

DOH!!!!

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

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