Measurements in Chemistry

Measurements in Chemistry Scientific Notation, Significant Figures, Percent Error

Units of Measurement • Put the following units in order from smallest to largest. • Meter, centimeter, millimeter, kilometer • Kilogram, centigram, milligram, gram • Liter, microliter, picoliter, kiloliter

SI Units

Units of Measurement • Put the following units in order from smallest to largest. • millimeter, centimeter, meter, kilometer • milligram, centigram, gram, kilogram • picoliter, microliter, liter, kiloliter • What information do the prefixes centi, milli, kilo, etc. provide?

Prefixes

Scientific Notation • When studying chemistry it is common to encounter very large or very small numbers. • Need a system in which to shorten long number chains. • Ex: The number of air molecules in a liter of air at 20oC and normal barometric pressure is 25,000,000,000,000,000,000,000. • Ex: The distance between two hydrogen atoms in a diatomic hydrogen molecule is 0.000,000,000,074 meters. • In Scientific Notation, these long chains of numbers are written in the form of; M x 10n

Scientific Notation M x 10n • Scientific notation is simply a number time 10 raised to an exponent. • M is a number greater than or equal to 1 and less than 10. • n is the exponent (the nth power or 10). It can be either positive or negative and represent the number of decimal places moved. • Positive (+) n means a large number so the decimal moves to the right by n places. • Negative (-) n means a small number so the decimal moves to the left by n places.

Practice • Convert the following from scientific notation to their usual form. • 6.39 x 10-4 • 3.275 x 10-2 • 8.019 x 10-6

Practice • Convert the following from scientific notation to their usual form. • 6.39 x 10-4= 0.000639 • 3.275 x 102= 327.5 • 8.019 x 10-6= 0.000008019

Practice • Express the following numbers in scientific notation. • 843.4 • 0.00421 • 1.54

Practice • Express the following numbers in scientific notation. • 843.4 = 8.434 x 102 • 0.00421 = 4.21 x 10-3 • 1.54 = 1.54 or 1.54 x 100

Scientific Notation Cheat Sheet • When converting from standard notation to scientific notation… • If the number is one or greater you will have a positive exponent and move the decimal to the left. • If the number is less than one you will have a negative exponent and move the decimal to the right. • # of spaces moved by decimal = exponent 801236.98 8.0123698 x 105 0.0000508 5.08 x 10-5

Scientific Notation Cheat Sheet • When converting from scientific notation to standard notation… • If the exponent is positive you will have a large number (>1) and move the decimal to the right. • If the exponent is negative you will have a small number (<1) and move the decimal to the left. • Exponent = # of spaces to be moved by decimal 8.0123698 x 105 801236.98 5.08 x 10-5 0.0000508

Significant Figures • If you were measuring this granite block in inches, what would you determine its width to be?

Significant figures • In measurements there is always some amount of uncertainty.

Significant Figures • Repeating a particular measurement will usually not obtain precisely the same result. • The measured values vary slightly from one another. • Precision – refers to the closeness of a set of values obtained from identical measurements of something. • Accuracy – refers to the closeness of a single measurement to its true value.

Rules for Sig Figs • The number of digits reported for the value of a measured quantity. • All nonzero numbers and zeros between are significant. • 909 cm, 1002 cm, 100,003 cm • Zeros at the beginning of a number are never significant. • 0.000912 cm, 0.01 cm, 0.000001001 cm • Zeros at the end of a number are significant only if a decimal is present, and to the right of the decimal. • 900 cm, 900.0 cm

Significant Figures in Calculations • Multiplication and Division • The answer is given with as many significant figures in the measurement with the least amount of significant figures. • Addition and Subtraction • The answer is given with as many significant figures as the measurement with the least number of decimal places.

Percent Error • Sometimes it is important to calculate how far off a measured value has deviated from the true or accepted value. • For this we use Percent (%) Error.

A problem to consider • A student measures the volume of a piece of zinc, by water displacement, to be 75.0 cm3 and the mass to be 562.5 g. • Now look up the accepted value for the density of zinc in Table S on your reference tables.

A Problem to consider • Does your calculated value agree with the scientifically accepted value?

A Problem to consider • How “ far off ” is your calculated value from the accepted value?

Measurements in Chemistry