Transcript Chemistry: The Study of Change

Unit 2: Measurements
Temperature is a measurement of the
movement of particles.
Absolute Scale
Relative Scales
°F
9
=
 °C + 32
5
K = 0C + 273.15
0 K = -273.15 0C
0 K = -460 ° F
“Water based” ✔
“Weather/human based”
Absolute Zero: Theoretical temp where all atomic movements stops
SciShow: Absolute Zero_ Absolute Awesome; https://www.youtube.com/watch?v=TNUDBdv3jWI
Example 1.3 Temperature Conversions
a) A certain solder has a melting point of 224°C. What is its melting point
in Fahrenheit?
(b) Helium has the lowest boiling point of all the elements at -452°F.
Convert this temperature to degrees Celsius.
(c) Mercury melts at only -38.9°C. Convert the melting point to Kelvin.
Matter - anything that occupies space and has mass
mass – measure of the quantity of matter
SI unit of mass is the kilogram (kg)
1 kg = 1000 g = 1 x 103 g
La Grande K
1 Kg Pt/Ir alloy
weight – force that gravity exerts on an object
weight = mass  g (F = ma)
on earth, g = 1.0
on moon, g ~ 0.1
Veritasium: World’s Roundest Object
https://www.youtube.com/watch?v=ZMByI4s-D-Y
A 1 kg bar will weigh
1 kg on earth
0.1 kg on moon
International System of Units (SI) Base Units
Used in this class and should have memorized
Derived Units: All other units are derived from
base units
Velocity: m/s
Volt = kg⋅m2/s3⋅A
Volume: m3
Newton = 1 kg⋅m/s2
Prefixes can be used to simplify for extremely large
or small quantities of base units
“mu”
Used most often in this class, be sure to memorize.
Prefix examples
Driving 321,000 meters to LR = 321 kilometers
Radio station 90.9 MHz = 90,900,000 Hz
A mosquito weighs 2.5 milligrams (mg) = 0.0025 grams (g)
A dust mites length 0.0002 meters = 200 micrometers (mm)
Conversion factors to know (e.g. using Liters)
6
1 ML = 10 L
3
10
1kL =
L
Liter (base)
-2
1 cL = 10 L
-3
1 mL = 10 L
-6
1 mL = 10 L
-9
1 nL = 10 L
Volume – SI derived unit for volume is cubic meter (m3)
(cm3 is commonly used)
1 cm3 = 1 mL
Density – SI derived unit for density is kg/m3
1 g/cm3 = 1 g/mL = 1000 kg/m3
*more commonly used
density =
mass
volume
m
d= V
2 L of Os
= 100 lbs
Example
Density Calculations
Gold is a precious metal that is chemically unreactive.
It is used mainly in jewelry, dentistry, and electronic devices.
A piece of gold ingot with a mass of 301 g has a volume of 15.6
Calculate the density of gold.
m
301 g
d=
=
3
V
15.6 cm
= 19.3
3
cm .
3
g/cm
gold ingots
Practice: A rod of titanium takes up 850 cm3 of space & weighs 3.86 kg . Find the density of Ti(s) in g/cm3
Example
Density problem #2
The density of mercury, the only metal that is a liquid at room
temperature, is 13.6 g/mL. Calculate the mass of 5.50 mL of the liquid.
m
d= V
Practice: The density of mineral oil is 0.8 g/mL. What volume (mL) would 25 grams of the oil have?
Chemistry In Action
On 9/23/99, $125M Mars Climate Orbiter entered Mars’
atmosphere 100 km (62 miles) lower than planned and was
destroyed by heat.
1 lb = 1 N
1 lb = 4.45 N
Failed to convert
English to metric units
“This is going to be the cautionary tale
that will be embedded into introduction
to the metric system in elementary
school, high school, and college
science courses till the end of time.”
TedEd: Why the metric system matters
https://www.youtube.com/watch?v=7bUVjJWA6Vw
Scientific Notation
The number of atoms in 12 g of carbon:
602,200,000,000,000,000,000,000
6.022 x 1023
The mass of a single carbon atom in grams:
0.0000000000000000000000199
1.99 x 10-23
We can factor out powers of 10 to simplify very large or small numbers
N is the base number
between 1 and 10
N x 10n
Exponent (n) is a positive
or
negative integer
Scientific Notation
• Base x 10exponent
• Base number ≥ 1 and < 10
5
320,000
=
3.2
x
10
.
0.000074
.
Decimal moved left so (+)
= 7.4 x 10-5 Decimal moved right so (–)
Scientific Notation Practice
1st Write these in scientific notation
2nd Rewrite using a prefix instead
• 0.00578 g
• 0.0140 mol
• 5,790 L
• 4,650,000 m
• 9,350,000,000 s
• 0.00000920 g
Mathematics in Scientific Notation
Addition or Subtraction: Must have same exponent
1. Write each quantity with the same
exponent n
2. Combine N1 and N2
4.31 x 104 + 3.9 x 103 =
4.31 x 104 + 0.39 x 104 =
3. The exponent, n, remains the same
4.70 x 104
Tip: change smaller number to match larger exponent
1.36 x 10-1 – 4 x 10-3 =
1.36 x 10-1 – 0.04 x 10-1 =
= 1.32 x 10-1
Practice:
1.45 x 10601 + 2.4 x 10600
More practice:
3.07 x 10-25 – 2 x 10-27
Mathematics in Scientific Notation
Multiplication: Add exponents
-5) x (7.0 x 103) =
(4.0
x
10
1. Multiply N1 and N2
-5+3) =
(4.0
x
7.0)
x
(10
2. Add exponents n1 and n2
28 x 10-2 =
Practice: (3 x 10250) (7.2 x 10200 )
2.8 x 10-1
More practice: (2.2 x 10100) (4 x 10-40 )
Division: Subtract exponents
1. Divide N1 and N2
2. Subtract exponents n1 and n2
Practice: (9.5 x 1045) ÷ (3.7 x 1050)
More practice: (8.4 x 10-5) ÷ (4.2 x 10-7)
8.5 x 104 ÷ 5.0 x 109 =
(8.5 ÷ 5.0) x 104-9 =
1.7 x 10-5
Bell Ringer
a) Write in scientific notation
b) Rewrite above numbers using the nearest SI prefix
c) Perform the below mathematics in Sci. Notation
• (9.01 x 103 g) + (3.8 x 102 g)
• (2.61 x 107 m) x (9.87 x 10-2 m)
• (3.98 x 10-2 m) – (8.2 x 10-3 m)
• (8.4 x 109 g) ÷ (2.0 x 104 mL)
Precision indicates to what degree we know
our measurement.
A measurement of 18.0 grams could be made on an average
countertop food scale (balance). (~$20)
A high-precision milligram scale could weigh the same sample
with a much higher precision (18.0235 grams) (~$1,500)
Every measurement is limited by the equipment’s
level of precision. (Never exact)
e.g. mass of single H2O molecule:
0.0000000000000000000000306 grams
Significant Figures: Used to prevent uncertainty/error using
various levels of precision or unit conversions.
2,500,000 liters of water in an Olympic pool (± 1,000 L precision)
place-holding zeros: not actually measured to be zero
2.500 x 106 L = 6,604,301.309 gallons (± 0.001 precision)
= 6,604,000 gallons (appropriate sig figs)
1) Any digit that is not zero is significant
1.234 L 4 significant figures
15,100 lbs 3 significant figures
± 100 lbs
2) Zeros between nonzero digits are significant
606 cm
3 significant figures
50,050 s
4 significant figures
Significant Figures (Zero: Measured or Placeholder?)
3) If greater than 1, all zeros right of the decimal are significant
25.0 mm
200.00 g
3 significant figures
5 significant figures
Measured to the nearest 0.01 g
4) Zeros to the left of the first nonzero digit are not significant
0.08 mL
1 significant figure
place-holding
0.00054 sec
2 significant figures
zeros
5) If less than 1, then only zeros at the end are significant
0.00420 g 3 significant figures
0.1000 g 4 significant figures
Significant Figures (Sci. Notation)
All significant figures are shown in the base number
when using Scientific notation.
____ m 4 significant figures
0.001400
1.400 x
-3
10
__
500 mL
5.0 x
2
10
Not 1.4 x
-3
10
2 significant figures
Not 5 x
2
10
Example
: Significant Figures
Determine the number of significant figures in the following
measurements:
Example
1.4 Solution
(a) 478 cm -- Three, because each digit is a nonzero digit.
(b) 600,001- Six, because zeros between nonzero digits are significant.
(c) 0.825 m -- Three, because zeros to the left of the first nonzero digit do not count as
significant figures.
(d) 0.0430 kg -- Three. The zero after the nonzero is significant because the number is
less than 1.
(e) 1.310 × 1022 atoms -- Four, because the number is greater than one so all the zeros
written to the right of the decimal point count as significant figures.
(f) 7000 mL - This is an ambiguous case. The number of significant figures could be four
(7.000 × 103), three (7.00 × 103), two (7.0 × 103), or one (7 × 103).
This example illustrates why scientific notation should be used to show the proper
number of significant figures. If no decimal is present it is assumed only non-zeros are
significant. If a decimal is present, than all zero’s are significant. 7,000 mL ≠ 7,000. mL
Significant Figures
Addition or Subtraction
The answer cannot have more digits to the right of the
decimal point than any of the original numbers.
Use the least precise number
89.392 L
one significant figure after decimal point
+ 1.1XX
90.492
round off to 90.5
3.70XX
-2.9133
0.7867
± 50 mL
two significant figures after decimal point
round off to 0.79
(2.888 x 104) + (4 x 104) = 6.888 x 104 = 7 x 104
± 1.0 mL
Significant Figures
Multiplication or Division
The number of significant figures in the result is set by the original number that has the
fewest number of significant figures.
4.51 x 3.0006 = 13.532706 = 13.5
round to 3 sig figs
6.8 ÷ 112.04 = 0.0606926 = 0.061
round to 2 sig figs
(2.222 x 104) x (4 x 105) = 8.888 x 109 = 9 x 109
round to 1 sig figs
Example Using Significant Figures
Carry out the mathematics to the correct number of significant figures:
Least # of sig figs or Least precise measurement
(a) 11,254.1 g + 0.1983 g
11,254.2983
11,254.3 g
(b) 66.59 L − 3.113 L
63.477
63.48 L
(c) 8.16 m × 5.1355 kg
41.90568
(d) 0.0154 kg ÷ 88.3 mL
(e)
(2.64 ×
103
cm)
+ (3.27 × 102 cm)
0.000174405436
2.967 x 103
41.9 mkg
1.74 x 10-4 kg/mL
2.97 x 103 cm
Significant Figures
Exact Numbers
Numbers from definitions or numbers of objects are considered to have an
infinite number of significant figures.
• The average of three measured lengths: 2.64, 2.68 and 2.70?
2.64 + 2.68 + 2.70
= 2.67333 = 3 = 2.67
3
Because 3 is an exact number, not a measured number;
It is not used for sigfigs.
• How many feet are in 6.82 yards?
6.82 yards x 3 ft/yard = 20.5 ft = 20 ft
1 yard = exactly 3 ft by definition
Bell Ringer
a) Perform the below mathematics in Sci. Notation. using Significant Figures
in your answer.
1. (9.8 x 105 g) + (6.75 x 104 g)
2. (5.98 x 10-6 m) – (7 x 10-8 m)
b) Rewrite the first 2 solutions
using the nearest SI prefix
3. (2.612 x 1010 m) x (9.87 x 10-3 m)
4. (7 x 102 mg) ÷ (1.875 x 104 mL)
Accuracy – how close a measurement is to the true value
Precision – how close a set of measurements are to each other
accurate
&
precise
precise
but
not accurate
not accurate
&
not precise
TedEd -What's the difference between accuracy and precision? ; https://www.youtube.com/watch?v=hRAFPdDppzs
Percent Error
A way to determine how accurate your measurements are to a known value.
|Obtained value – Actual value| x 100% = percent error
Actual Value
I weigh a 3 kg block on three different scales:
3.2 kg, 3.0 kg, 3.1 kg = 3.1 kg average
3.1 – 3.0 x 100% = 3.3% error
3.0
Dimensional Analysis of Solving Problems
(Train-Tracks)
1. Determine which unit conversion factors are needed
2. Carry units through calculation
3. If all units cancel except for the desired unit(s), then the
problem was solved correctly.
given quantity x conversion factor = desired quantity
given unit x
desired unit
given unit
= desired unit
Train Track Example
How many inches are in 3.0 miles?
Identify beginning information
Draw a train track
3 miles
Write measurement as a fraction
Train Track Example
How many inches are in 3.0 miles?
Find a conversion factor that changes miles into something smaller.
Conversion Factor: 1 mile = 5,280 feet
• Write your conversion factor on the track so that miles
cancels out and you are left with the unit feet.
3 miles
5280 feet
1 mile
Always need same units on
opposite sides to cancel out
Train Track Example
How many inches are in 3.0 miles?
We now need another conversion factor between
Feet and Inches: 1 foot = 12 inches
Again, place conversion factor so that the previous unit
cancels out.
3.0 miles
5280 feet
1 mile
12 inches
1 foot
Train Track Unit Conversions
How many inches are in 3.0 miles?
3.0 miles
5,280 feet
1 mile
12 inches
1 foot
Inches are the only
remaining unit ✔
Multiply all numbers on the top
Divide all numbers on the bottom
3.0 x 5,280 x 12
1x1
= 190,080 inches
= 1.9 x 105 inches
(2 sig figs)
More practice:
Convert 1.40 x 10-2 L to mL
Example
Metric to Metric Conversion Problems
Convert
2.79 x 105 mm to km
Don’t try to convert directly from mm to km. Go to the base unit (m) first
Conversion factors: 1,000 mm = 1 m; 1,000 m = 1 km
2.79 x 105 mm
10-3 m
1 mm
1 km
103 m
Kilometers are the only remaining units ✔
2.79 x 105= 2.79 x 10(5 + -3 - 3)
103 x 103
= 2.79 x 10-1 km
(3 sig figs)
More practice:
Convert 3.4 x 109 cg to Mg
Example
A person’s average daily intake of glucose (a form of sugar) is 0.0833
pound (lb). What is this mass in milligrams (mg)? (1 lb = 453.6 g.)
A metric conversion is needed for grams to milligrams
(1 mg = 1 × 10−3 g)
0.0833 lb
453.6 g
1 lb
1 mg
10-3 g
= 37,784.88 mg
= 37,800 mg
(3 sig figs)
= 3.78 x 104 mg
Example
2-D Conversion Problems (Unit1/Unit2)
Convert 70.0 miles/hour to m/s
Given Conversion factor: 1 mile = 1,609 meters
• Write the unit/unit as a fraction in the train track.
• We convert one unit at a time, followed by the other
• To cancel out hours (on bottom) it must appear again on the top
70.0 miles
1 hour
1609 meter
1 mile
1 hour
60 min
1 min
60 sec
Meter/sec are the only remaining units ✔
70.0 x 1,609 x 1 x 1
1 x 1 x 60 x 60
= 31.286 m/s
= 31.3 m/s
More practice:
Convert 3.4 kg/L to g/mL
2-D Conversion Problems (Unit#)
Example
Convert
2.5 x 10-5 m3 to mm3
Conversion factors: 1 m = 1,000 mm
1 m3 ≠ 1,000 mm3
1 m3 = (1,000)3 mm3 ✔
1. Write the 1-D units first (1m = 103m)
2. Add exponent to entire conversion factor
3
2.5 x 10-5 m3
1000 mm
1m
=
2.5 x 10-5 m3 109 mm3
1 m3
2.5 x 10-5 x 109 = 2.5 x 104 mm3
More practice:
Convert 1.8 x 109 cm2 to km2
Example
Convert
2-D Conversion Problems
#
(Unit )
6.70 x 103 ft2 to inches2
Conversion factors: 1 ft = 12 in
1 ft2 ≠ 12 in2
1. Write the 1-D units first (1ft = 12 in)
1 ft2 = 122 in2✔
6.70 x 103 ft2
12 in.
1 ft
Alternate 2nd Method
2. Write the same conversion factor again
until they cancel
12 in.
1 ft
= 9.65 x 105 in2
More practice:
Convert 34 yd3 to ft3
More Practice
Conversion problems
• Convert 3.0 mL to
ounces (33.8 oz = 1 L)
• 1.67 Mm to mm
• 2.35 x 1012 inches to cm
(1 ft = 0.305 m)
• 3.50 x 104 mL to cL
• 42.0 km/h to ft/ms
• 0.55 Acres to m2 (247
acre = 1 km2)
• 10.6 g/mm3 to kg/m3
Unit Conversion & Significant
Figures: Crash Course Chemistry #2
www.youtube.com/watch?v=hQpQ0hxVNTg
Sample of Topics to Study
• Base and Derived SI units
• Temperature scale conversions
• Phases of Matter
• Metric Units
• Using Prefixes
• Significant Figures (+ math)
• Scientific Notation (+ math)
• Dimensional Analysis
• Accuracy
• Precision
• % Error