Transcript Lecture 2 - Chemistry at Winthrop University

Introduction to
General Chemistry
Lecture 2
Suggested HW:
33, 37, 40, 43, 45,
46
Ch. 1.6 - 1.9
Accuracy and Precision
• Accuracy defines how close to the correct answer you are.
Precision defines how repeatable your result is. Ideally, data
should be both accurate and precise, but it may be one or the
other, or neither.
Accurate, but not
precise. Reached the
target, but could not
reproduce the result.
Precise, but not
accurate. Did not reach
the target, but result
was reproduced.
Accurate and precise.
Reached the target and
the data was
reproduced.
Measuring Accuracy
• Accuracy is calculated by percentage error (%E)
%E 
average value  true value
x100
true value
•We take the absolute value because you can’t have negative
error.
•GROUP PROBLEM
- A certain brand of thermometer is considered to be
accurate if the %E is < 0.8%. The thermometer is tested using
water (BP = 100oC). You bring a pot of distilled water to a boil
and measure the temperature 5 times. The thermometer
reads: 100.6o, 100.4o, 99.8o, 101.0o, and 100.4o. Is it
accurate?
Measuring Precision: Significant Figures
• Precision is indicated by the number of significant figures.
Significant figures are those digits required to convey a result.
– There are two types of numbers: exact and inexact
– Exact numbers have defined values and possess an infinite
number of significant figures because there is no limit of
confidence:
* There are exactly 12 eggs in a dozen
* There are exactly 24 hours in a day
* There are exactly 1000 grams in a kilogram
– Inexact number are obtained from measurement. Any number
that is measured has error because:
• Limitations in equipment
• Human error
Measuring Precision: Significant Figures
• Example: Some laboratory balances are
precise to the nearest cg (.01g). This is
the limit of confidence. The measured
mass shown in the figure is 335.49 g.
• The value 335.49 has 5 significant figures,
with the hundredths place (9) being the
uncertain digit. Thus, the (9) is estimated,
while the other numbers are known.
• It would properly reported as 335.49±.01g
- The actual mass could be anywhere between 335.485… g
and 335.494… g. The balance is limited to two decimal places,
so it rounds up or down. We use ± to include all possibilities.
Determining the Number of Significant Figures In a Result
• All non-zeros and zeros between non-zeros are significant
– 457 (3) ; 2.5 (2) ; 101 (3) ; 1005 (4)
• Zeros at the beginning of a number aren’t significant. They
only serve to position the decimal.
– .02 (1) ; .00003 (1) ; 0.00001004 (4)
• For any number with a decimal, zeros to the right of the
decimal are significant
– 2.200 (4) ; 3.0 (2)
Determining the Number of Significant Figures In a Result
• Zeros at the end of an integer may or may not be significant
– 130 (2 or 3), 1000 (1, 2, 3, or 4)
• This is based on scientific notation
– 130 can be written as:
1.3 x 102  2 sig figs
1.30 x 102  3 sig figs
– If we convert 1000 to scientific notation, it can be written as:
1 x 103  1 sig fig
1.0 x 103  2 sig figs
1.00 x 103  3 sig figs
1.000 x 103  4 sig figs
*Numbers that must be treated as significant CAN NOT
disappear in scientific notation
Calculations Involving Significant Figures
• You can not get exact results using inexact numbers
• Multiplication and division
– Result can only have as many significant figures as the
least precise number
6.2251 𝑐𝑚 𝑥 𝟓. 𝟖𝟐 𝑐𝑚 = 36.230082 𝑐𝑚2 = 36.2 𝑐𝑚2
(3 s.f.)
105.86643 𝑚
𝑚
𝑚
𝑚
= 108.0269694
= 110
𝑜𝑟 1.1 𝑥 102
0. 𝟗𝟖 𝑠
𝑠
𝑠
𝑠
(2 s.f.)
𝑚
𝑘𝑔 𝑚
𝑘𝑔 𝑚
𝑘𝑔 𝑚
5
43270.0 𝑘𝑔 𝑥 𝟒 2 = 173080
= 200000
𝑜𝑟 2 𝑥 10
𝑠
𝑠2
𝑠2
𝑠2
(1 s.f.)
Calculations Involving Significant Figures
• Addition and Subtraction
– Result must have as many digits to the right
of the decimal as the least precise number
20.4
1.322
83
+ 104.722
211.942
212
Group Work
• Using scientific notation, convert 0.000976392 to 3 sig. figs.
• Using scientific notation, convert 198207.6 to 1 sig. fig.
H=10.000 cm
W = .40 cm
L = 31.00 cm
•
•
Volume of rectangle ?
Surface area (SA = 2WH + 2LH + 2LW) ?
note: constants in an equation are exact numbers
= 2 4.0𝑐𝑚2 + 2 310.0𝑐𝑚2 + 2(1𝟐. 4𝑐𝑚2 )
=
8.0𝑐𝑚2
+ 620.0𝑐𝑚2
+
= 65𝟐. 8𝑐𝑚2 = 653𝑐𝑚2
2𝟒. 8𝑐𝑚2
Limit of
certainty is
the ones
place
Dimensional Analysis
• Dimensional analysis is an algebraic method used to
convert between different units
• Conversion factors are required
– Conversion factors are exact numbers which are
equalities between one unit set and another.
– For example, we can convert between inches and feet.
The conversion factor can be written as:
12 inches
1 foot
or
1 foot
12 inches
• In other words, there are 12 inches per 1 foot, or 1 foot
per 12 inches.
Dimensional Analysis
conversion factor (s)
desired units
given units x
given units
 desired units
• Example. How many feet are there in 56 inches?
• Our given unit of length is inches
• Our desired unit of length is feet
• We will use a conversion factor that equates inches
and feet to obtain units of feet. The conversion
factor must be arranged such that the desired units
are ‘on top’
1 𝑓𝑜𝑜𝑡
𝟓𝟔 𝑖𝑛𝑐ℎ𝑒𝑠 𝑥
= 4.6666 𝑓𝑡
12 𝑖𝑛𝑐ℎ𝑒𝑠
4.7 ft
Group Work
• Answer the following using dimensional analysis. Consider
significant figures.
– Convert 35 minutes to hours
– Convert 40 weeks to seconds
– Convert 4 gallons to cm3 (1 gallon = 4 quarts and
1 quart = 946.3 mL)
– *35
𝒎𝒊𝒍𝒆𝒔
𝒉𝒓
to
𝒊𝒏𝒄𝒉𝒆𝒔
𝒔𝒆𝒄
(1 mile = 5280 ft and 1 ft = 12 in)
High Order Exponent Unit Conversion (e.g. Cubic Units)
• As we previously learned, the units of volume can be
expressed as cubic lengths, or as capacities. When
converting between the two, it may be necessary to
cube the conversion factor
• Ex. How many mL of water can be contained in a
cubic container that is 1 m3
1 𝑚3
𝑥
𝑐𝑚 3
𝒎𝑳
𝑥
10−2 𝑚
𝒄𝒎𝟑
Must use this equivalence to convert
between cubic length to capacity
Cube this conversion factor
=1
𝑚3
𝒄𝒎𝟑
𝑚𝐿
𝑥
𝑥
𝟏𝟎−𝟔 𝒎𝟑 𝑐𝑚3
= 𝟏 𝒙 𝟏𝟎𝟔 𝒎𝑳
Group Work
• Convert 10 mL to m3 (c = 10-2)
• Convert 100 L to µm3 (µ = 10-6)
• Convert 48.3 ft2 to cm2 (1 in. = 2.54 cm)