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Measurements and Calculations

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					Measuring Matter


    Holt Modern Chemistry (2006)
             Chapter 2
Using Measuring Instruments
(Lab Technique)
Measuring




             Volume
             Temperature
             Mass
Measuring Volume
Graduated Cylinders – used for
measuring volume


The glass cylinder has
etched marks to
indicate volumes, a
pouring lip, and quite
often, a plastic
bumper to prevent
breakage. Keep the
bumper pushed toward
the top.
Sit the graduated cylinder
 on a flat surface.
Get down to eye level ! ! !
And . . . .
Read the Meniscus



Always read volume from
the bottom of the
meniscus. The meniscus
is the curved surface of
a liquid in a narrow
cylindrical container.
  Try to avoid parallax errors.
Parallax errors arise when a meniscus or needle is
viewed from an angle rather than from straight-on
at eye level.




   Incorrect: viewing the          Correct: Viewing the
          meniscus                       meniscus
       from an angle                   at eye level
Measuring Volume


 Determine the volume contained in a graduated
cylinder by reading the bottom of the meniscus at
eye level.
 Read the volume using all certain digits and one
uncertain digit.
          Certain digits are determined from
         the calibration marks on the cylinder.
        The uncertain digit (the last digit of
        the reading) is estimated.
   Use the graduations to find all certain
   digits


There are two
unlabeled
graduations below
the meniscus, and
each graduation
represents 1 mL, so
the certain digits of
the reading are…

           52 mL.
  Estimate the uncertain digit and take a
  reading


The meniscus is about
eight tenths of the
way to the next
graduation, so the
final digit in the
reading is 0.8 mL .



   The volume in the graduated cylinder is 52.8 mL.
10 mL Graduate
What is the volume of liquid in the graduate?



                                  6 . _ _ mL
                                  _ 6 2
25mL graduated cylinder
 What is the volume of liquid in the graduate?




                                1 _ 5
                                _ 1 . _ mL
100mL graduated cylinder

What is the volume of liquid in the graduate?

_ _ 7
5 2 . _ mL
  Self Test
Examine the meniscus below and determine the
volume of liquid contained in the graduated
cylinder.
                                 The cylinder contains:

                                 7 _ _
                                 _ 6 . 0 mL
Measuring Temperature
                           The Thermometer
                              o Determine the
                              temperature by reading
                              the scale on the
                              thermometer at eye
                              level.
                              o Read the temperature
                              by using all certain
                              digits and one uncertain
                              digit.
o Certain digits are determined from the calibration
marks on the thermometer.
o The uncertain digit (the last digit of the reading) is
estimated.
o On most thermometers encountered in a general
chemistry lab, the tenths place is the uncertain digit.
   Do not allow the tip to touch the walls or
   the bottom of the flask.
If the thermometer bulb
touches the flask, the
temperature of the glass
will be measured instead of
the temperature of the
solution. Readings may be
incorrect, particularly if
the flask is on a hotplate
or in an ice bath.
Reading the Thermometer
Determine the readings as shown below on Celsius
thermometers:




  8 7 4
  _ _ . _ C                  _ _ 0
                              3 5 . _ C
Measuring Mass - The Beam Balance




 Our balances have 3 beams – the uncertain digit is
 the hundredths place ( _ _ _ . _ _ )
Balance Rules

In order to protect the balances and ensure accurate
results, a number of rules should be followed:

   Always check that the balance is level and
  zeroed before using it.
   Never weigh directly on the balance pan.
  Always use a piece of weighing paper to protect
  it.
   Do not weigh hot or cold objects.
   Clean up any spills around the balance
  immediately.
Mass and Significant Figures

o Determine the mass by reading the riders on
the beams at eye level.
o Read the mass by using all certain digits and
one uncertain digit.

                    oThe uncertain digit (the last
                    digit of the reading) is
                    estimated.
                    o On our balances, the
                    hundredths place is uncertain.
Determining Mass
                   1. Place object
                   on pan

                   2. Move riders
                   along beam,
                   starting with
                   the largest,
                   until the
                   pointer is at
                   the zero mark
Check to see that the balance scale
is at zero
        ? _ ? . _ ?
        _ ? _ ? _




Read Mass
        5 1 _ . 0 0
        _ _ 0 _ _




Read Mass More Closely
Self-Test   _ _ _ . _ _
            1 3 7   3 9
Units of Measurement
(Section 2-2)
Types of Observations

  There are two types of observations


       Qualitative: descriptive (color smell, etc…)

       Quantitative: numerical (mass, density, etc…)


  These notes will deal with quantitative.
Quantity

  something that has magnitude, size, or
   amount.
  NOT the same as a measurement!!


  Ex:     measurement         Quantity
           Teaspoon ----------- volume
               Feet ----------- length
SI Units
  Standard International Units
    adopted in 1960 by the General Conference on
     Weights & Measures.

  SI Base Units (see page 34)

  SI Prefixes (see page 35)

  SI Derived Units- combinations of base units
       (see page 36)
Mass: the amount of matter
 in an object (SI: kg)

Weight: the amount of
 gravitational pull on matter
 Volume: the amount of space occupied
  (SI: m3 or mL)
 Density: the ratio of mass to volume
  (SI: kg/m3)

  D   = m/v or -
 ÷
  M÷
D xV
Conversions
(using dimensional analysis)

  Going from one unit of measurement to
   another.
  Use a “line of equality” as a conversion
   factor
    For   example: 1 meter = 100 cm
  Each “line of equality” gives two
   conversion factors
      1 meter          100 cm
                  and
       100 cm           1 meter
 Since the factor on top “equals” the factor on
  the bottom, as a fraction (conversion factor)
  together they equal “1”
 Because the fraction equals “one”, it can be
  used as a multiplier without changing the
  quantity
 But since the unit of measurements are
  different, they can be used in combinations to
  cancel out unwanted units
Lets practice!! 
Example 1: Express a mass of 5.712
grams in milligrams.

 We will use a bracket for conversion
  problems.
 The given in this problem is 5.712 g.
 Write it as a fraction in the first part of
 the bracket.
           5.712 g
              1
Example 1: Express a mass of 5.712
grams in milligrams. (continued)
 You want to change the unit to milligrams.
 Use the “line of equality” 1 g = 1000 mg
 Since you want to get rid of grams, place
 1 g on the bottom to cancel-out the
 grams on the top.
 Then place 1000 mg on top.
          5.712 g   1000 mg
            1        1g
Example 1: Express a mass of 5.712
grams in milligrams. (continued)
 The grams on top will cancel-out the grams on
   bottom.
 Then multiple the top numbers together;
   multiple the bottom numbers together.
 Final step, divide the top total by the bottom
 total. DON’T FORGET TO WRITE THE NEW
 UNIT IN YOUR ANSWER!

 5.712 g   1000 mg       5712 mg
                     =             =   5712 mg
   1          1g           1
Example 2: Express a mass of 0.014 mg
in grams.


      0.014 mg    1 g
                           =   0.000014 g
                 1000 mg
Example 3: Express a length of 16.45 m
in km.


      16.45 m     1 km
                         =   0.01645 km
                1000 m
Using Scientific
Measurements (Section 2-3)
Accuracy vs. Precision

 Accuracy - how close a measurement is
 to the accepted value

 Precision - how close a series of
 measurements are to each other

  ACCURATE = CORRECT
  PRECISE = CONSISTENT
Accurate?   Accurate?   Accurate?             Accurate?
 Yes!         NO!        NO!                    Yes!*
Precise?    Precise?    Precise?              Precise?
 Yes!        Yes!        NO!                     NO!


                                    *The average is accurate
Let’s use a golf analogy
Accurate? No
Precise? Yes
Accurate? Yes
Precise? Yes
Precise?   No
Accurate? Maybe?
Accurate? Yes
Precise? We can’t say!
Percent Error

  Indicates accuracy of a measurement



             experiment al  accepted
   % error                           x 100
                    accepted

      your value            accepted
                            value
 B. Percent Error
 A student determines the density of a
  substance to be 1.40 g/mL. Find the % error if
  the accepted value of the density is 1.36 g/mL.

              1.40 g/mL  1.36 g/mL
  % error                                 100
                     1.36 g/mL

      % error = 2.94 %
C. Significant Figures (Sig Figs)

 Indicate precision of a measurement.
 Recording Sig Figs
   Sig figs in a measurement include the known
   digits plus a final estimated digit


                       2.33 cm
C. Significant Figures


 Counting Sig Figs
   Count   all numbers EXCEPT:
    • Leading zeros -- 0.0025
    • Trailing zeros without
      a decimal point -- 2,500
C. Significant Figures
   Counting Sig Fig Examples
     1. 23.50    4 sig figs

     2. 402      3 sig figs

     3. 5,280    3 sig figs

     4. 0.080    2 sig figs
C. Significant Figures

  Calculating with Sig Figs
                    - The # with the fewest sig
     Multiply/Divide
     figs determines the # of sig figs in the
     answer.
(13.91g/cm3)(23.3cm3) = 324.103g
      4 SF              3 SF
                                         3 SF

                                   324 g
C. Significant Figures

 Calculating with Sig Figs (con’t)
   Add/Subtract - The # with the lowest decimal
    value determines the place of the last sig fig in the
    answer.

  3.75 mL                        224 g
+ 4.1 mL                       + 130 g
  7.85 mL  7.9 mL               354 g  350 g
C. Significant Figures

 Calculating with Sig Figs (con’t)
   ExactNumbers do not limit the # of sig figs in the
    answer. For example:
     • Counting numbers: 12 students
     • Exact conversions: 1 m = 100 cm
     • “1” in any conversion: 1 in = 2.54 cm
Rounding Sig Fig Rules

Ex:        round to 3 sf       rule
42.68g      42.7g……………greater than 5,
                            round up
17.32g      17.3g…………...less than 5, stays
                            the same
2.7851m 2.79m… ………..a 5, round up (there
  are more specific rules here, but we will leave
  that to A.P. Chemistry!  )
C. Significant Figures
          Practice Problems

   5. (15.30 g) ÷ (6.4 mL)
       4 SF        2 SF
     = 2.390625 g/mL  2.4 g/mL
                             2 SF
 6. 18.9 g
    - 0.84 g
     18.06 g  18.1 g
D. Scientific Notation
        65,000 kg  6.5 × 104 kg

  Converting into Sci. Notation:
     Movedecimal until there’s 1 digit to its left.
     Places moved = exponent.
     Large# (>1)  positive exponent
     Small # (<1)  negative exponent
     Only   include sig figs.
D. Scientific Notation
         Practice Problems

  7.   2,400,000 g   2.4  106 g
  8.   0.00256 kg     2.56  10-3 kg
  9.   7  10-5 km    0.00007 km
  10. 6.2  104 mm    62,000 mm
 D. Scientific Notation

    Calculating with Sci. Notation
        (5.44 × 107 g) ÷ (8.1 × 104 mol) =

 Type on your calculator:
        EXP                     EXP          EXE
 5.44          7    ÷     8.1         4
         EE                     EE        ENTER


= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol
E. Graphical Analysis (Proportions)

   Direct Proportion
                        y
         x
           k
         y
                               x
 Inverse Proportion

                        y
        xy  k
                               x
Basic Temperature Conversions
Temperature Scales


  Fahrenheit


  Celsius


  Kelvin
Temperature Conversion Equations

  4 equations to use:
    oF = 9/5oC + 32

    oC = 5/9 (oF-32)

     K = oC + 273
    oC = K – 273
Helpful Hints
   Identify the equation needed.
   Plug in the numbers to solve
   Remember the math rules:
       • Solve what is in parenthesis first
       • Solve Multiplication & Division before
         addition and subtraction
   Show all work
   Put box around final answer
Practice Problem #1

  240oC = ____K


  K = oC + 273
  K = 240 + 273
  K = 513
Practice Problem #2

  50oF = ____ oC


  oC = 5/9 (oF-32)
  oC = 5/9 (50-32)
  oC = 0.55 (18)
  oC = 10
Practice Problem #3

  510K = ____ oC

  oC = K – 273
  oC = 510 – 273
  oC = 237
Practice Problem #4

  20 oC = ____ oF


  oF = 9/5oC + 32
  oF = 9/5o(20) + 32
  oF = 1.8(20) + 32
  oF = 36 + 32
  oF = 68
The End
Common Metric Prefixes

    Prefix   Symbol    Factor   Numerically          Name

  giga         G      109       1 000 000 000      billion**

  mega         M      106              1 000 000   million
  kilo         k      103                 1 000    thousand
  centi        c      10-2      0.01               hundredth
  milli        m      10-3      0.001              thousandth
  micro        μ      10-6      0.000 001          millionth

  nano         n      10-9      0.000 000 001      billionth**
SI Derived Units-
    combinations of base units
 Quantity       Symbol   Unit            Abbreviatio Derivation
                                         n
 Area           A        square meter    m2          LxW

 Volume         V        cubic meter     m3          LxWxH

 Density        D        kilograms per   kg            mass
                         cubic meter     m3           volume
 Molar mass     M        kilograms per   kg             mass
                         mole            mol          amt. of sub.
 Molar volume   Vm       cubic meters    m3            volume
                         per mole        mol          amt. of sub.
 Energy         E        joule           J           force x length
SI Base Units

 Base quantity               Name       Symbol
 length                      meter      m
 mass                        kilogram   kg
 time                        second     s
 electric current            ampere     A
 thermodynamic temperature   kelvin     K
 amount of substance         mole       mol
 luminous intensity          candela    cd

				
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