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
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.
on a flat surface.
Get down to eye level ! ! !
And . . . .

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
Use the graduations to find all certain
digits

There are two
unlabeled
the meniscus, and
represents 1 mL, so
the certain digits of

52 mL.
Estimate the uncertain digit and take a

eight tenths of the
way to the next
final digit in the

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

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

1 _ 5
_ 1 . _ mL

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
the scale on the
thermometer at eye
level.
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
If the thermometer bulb
temperature of the glass
the temperature of the
incorrect, particularly if
the flask is on a hotplate
or in an ice bath.
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
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
? _ ? . _ ?
_ ? _ ? _

5 1 _ . 0 0
_ _ 0 _ _

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

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

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:
• 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
(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

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
• 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) =

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
 Identify the equation needed.
 Plug in the numbers to solve
 Remember the math rules:
• Solve what is in parenthesis first
• Solve Multiplication & Division before
 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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