Transcript Chapter 1
CHEM 205 Tutorial 0
chapter 1
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Units of measurement
Measurement
You are making a measurement when you
Check you weight
Read your watch Take your temperature
Weigh an apple What kinds of measurements did you make today?
Some Tools for Measurement
How do you measure….
Temperature?
Time?
Volume?
Weight?
Measurement in Science
In Science we
do experiments
measure quantities
use numbers to report measurements
Units in the Metric System (S.I.)
length volume mass temperature meter liter L m gram g Celsius °C
Stating a Measurement
In every measurement there is a NUMBER
followed by a
UNIT from measuring device The patient’s temperature is 102 °F .
The sack holds 5 lbs of potatoes.
It is 8 miles from your house to school. The bottle holds 2 L of orange soda
Significant Figures
Reading a measure
First digit (known) Second digit (known) = 2 = 0 .7 2 .?? cm 2.7
?
cm Third digit (estimated) between 0.05- 0.07
Length reported = 2.74 cm or or 2.75 cm 2.73 cm
Known, significant, estimated digits
2.74 cm Known
(100% certain)
Estimated
(uncertain)
Significant!
What is the length of the line?
l 5 . . . . I . . . . I 6 . . . .I . . . . I 7 . . cm 1) 6.0 cm 2) 6.06 cm 3) 6.60 cm
Exact Numbers
Obtained when you count objects 2 soccer balls 1 watch 3 pizzas
Obtained from a defined relationship 1 foot = 12 inches 1 meters = 100 cm
Not obtained with measuring tools
Classify each of the following as an exact (E) or a measured (M) number.
A._
M _Gold melts at 1064 °C B._
E _1 yard = 3 feet C._
M _A red blood cell with diameter 6 x 10 -4 cm D._
E _There were 6 hats on the shelf E._
M _A can of soda contains 355 mL of soda
Significant Figures in Calculations
Counting Significant Figures
Number of Significant Figures 38.15 cm 0.008 ft 25000 in 0.48600 gal 4 1 2 5
Significant Numbers in Calculations
A calculated answer cannot be more precise than the measuring tool.
Significant figures are needed for final answers from 1) adding or subtracting 2) multiplying or dividing
Adding and Subtracting
The answer has the same number of decimal places as the measurement with the fewest decimal places.
25.
2
ONE decimal place
+ 1 .34
TWO decimal places
26.54
answer 26.5
ONE decimal place
In each calculation, round the answer to the correct number of significant figures.
A. 235.05 + 19.6 + 2.1 = 1) 256.75
2) 256.8
B. 58.925 - 18.2
1) 40.725
= 2) 40.73
3) 257 3) 40.7
Multiplying and Dividing
Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures .
In each calculation, round the answer to the correct number of significant figures.
A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198
B . 4.311 ÷ 0.07 = 1) 61.58
C. 2.54 X 0.0028
0.0105 X 0.060 1) 11.3
2) 62 = 2) 11 3) 0.041
3) 60
Prefixes and Equalities
Metric Prefixes
Increase or decrease basic unit by 10
Form new units larger or smaller than the basic units
0.00356 = 3.56 x 10 -3 123 000 000 000 000 = 123 x 10 12
Prefix Symbol
giga G mega kilo M k
Value
1,000,000,000 1,000,000 1,000 hecto deca h da 100 10 no prefix means: 1 deci d 0.1 centi milli micro nano c m m n 0.01 0.001 0.000001 0.000000001
Exponential
10 9 10 6 10 3 10 2 10 1 10 0 10 -1 10 2 10 -3 10 -6 10 -9
Give the value of the following units: A. 1 kg = ____ g 1) 10 g 2) 100 g 3) 1000 g B. 1 mm = ____ m 1) 0.001 m 2) 0.01 m 3) 0.1 m
Equalities
State the same measurement in two different units length 10.0 in.
25.4 cm
Conversion Factors
Express an equality between two different units Example: 1 in = 2.54 cm Factors: 1 in 2.54 cm and 2.54 cm 1 in 3 in → ? cm 3 in x 2.54cm
1in
Blood has a density of 0.05 g/mL. If a person lost 0.30 pints of blood at 18 °C, how many ounces of blood would that be?
Initial unit = pints Final unit = oz 1 US pint = 16 US fluid ounces 0.30
pints
16 1 oz pint
4.8
oz
How many seconds are in 14 days?
14 day x 1 day x 60 min x 60 s 24 h 1 h 1 min 14 day x 24 h x 60 min x 60 s 1 day 1 h 1 min = 1.2 x 10 5 s
Steps to solve a problem
READ problem IDENTIFY data Write down a unit plan from the INITIAL UNIT to the DESIRED UNIT Select CONVERSION factors Change initial unit to desired unit CANCEL units and check Do math on CALCULATOR (is the result logical?) Give an answer using SIGNIFICANT FIGURES
Measuring Temperature
Kelvin Scale
0 K is the lowest temperature 0 K = - 273 °C K = °C + 273 K °C °C = K - 273 37 K °C to K?
= °C + 273 = = 37 °C + 273 = = 310 K 298K to °C ?
°C = K - 273 = = 298 - 273 = = 25 °C
Density
Density
Density compares the mass of an object to its volume d
mass volume
g mL
g cm 3 Note: 1 mL = 1 cm 3
What is the density (g/cm 3 ) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL?
1) 0.2 g/ cm 3 2) 6 g/cm 3 3) 252 g/cm 3 25 mL 33 mL
What is the density (g/cm 3 ) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL?
Volume (mL) of water displaced = 33 mL - 25 mL = 8 mL Volume of metal (cm 3 ) = 8 mL x 1 cm 3 = 8 cm 3 1 mL Density of metal = mass = 48 g = 6 g/cm 3 volume 8 cm 3 Solution: 6 g/cm 3 (#2)
V W
K
1 Which diagram represents the liquid layers in the cylinder?
(K) Karo syrup (1.4 g/mL) (V) vegetable oil (0.91 g/mL) (W) water (1.0 g/mL) W
K
V 2
K
V W 3
Density as Conversion Factor
A substance has a density of 3.8 g/mL. Density = 3.8 g/mL Equality 3.8 g = 1 mL = 1 cm 3 Conversion factors: 3.8
g or 1 mL 1 mL 3.8
g
The density of octane, a component of gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane?
1) 0.614 kg 2) 614 kg 3) 1.25 kg
The density of octane, a component of gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane?
Unit plan : mL
g
kg Equalities : 1 mL = 0.702 g and 1 kg = 1000 g Calculation: 875 mL x 0.702 g x 1 kg = 0.614 kg 1 mL 1000 g Solution: 0.614 kg (#1)