Math Concepts in Chemistry
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Transcript of Math Concepts in Chemistry
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SY15102 Friday, November 27, 2015
Chemistry 1 Laboratory 1
The study of chemistry involves taking several
observations.
When gathering information, you may ask questions
like:
“what color?” “what shape?”
“how long” “how much?”
• These observations may either qualitative or
quantitative .
•
Quantitative observations are taken throughmeasurements.
• Measurement is the process of finding out how
many measuring units there are in something.
• Metric system is the most widely used system of
measurements.
SI Units
• The most recent version of metric system is the
International System of Units or SI (created by French
scientist in the 1970s).
• There are two types of units:
– fundamental (or base) units; and
– derived units.
• There are 7 base units in the SI system.
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Chemistry 1 Laboratory 2
Powers of ten are used for convenience with smaller
or larger units in the SI system.
Scientific Notation
Scientific Notation is a method used in writing very large orvery small numbers in a simpler way:
A X 10n
where A stands for coefficient number (1 ≤ A
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Chemistry 1 Laboratory 3
Evaluate the following expressions:
1) (6.0 x 104) / (3.0 x 102)
2) (1.0 x 103) - (2.5 x 102)
3) (3.47 x 102) + (7.32 x 104)
4) (1.4 x 10-3) x (5.3 x 10-3)
Fundamental Units
Length and Mass
Note the SI unit for length is the meter (m) whereas
the SI unit for mass is the kilogram (kg).
1 kg weighs 2.2046 lbs.
1) A cube of gold metal measures 0.01 cm on a
side. What is this length expressed in
millimeters?
2) A student told the class that she takes 200
mg of vitamin B every day. What is this mass
expressed in grams?
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Chemistry 1 Laboratory 4
Temperature
There are three temperature scales:
Kelvin Scale
Used in science.
Same temperature increment as Celsius scale.
Lowest temperature possible (absolute zero) is
zero Kelvin.
Absolute zero: 0 K = −273.15 oC.
Celsius Scale
Also used in science.
Water freezes at 0
o
C and boils at 100
o
C.
Fahrenheit Scale
Not generally used in science.
Water freezes at 32 oF and boils at 212 oF.
To convert:
Which of the following shows the relative
temperatures correctly?
A. 12°C > 310K
B. 15°C > 150K
C. 43°C < 300K
D. 158°C > 450K
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Chemistry 1 Laboratory 5
Derived Units
Derived units are obtained from the 7 base SI units.
Example:
Volume
The units for volume are
given by (units of length)3.
SI unit for volume is 1 m3.
We usually use 1 mL = 1 cm3.
Other volume units:
1 L = 1 dm3 = 1000 cm3 =
1000 mL.
Volume Density
• Used to characterize substances.
• Defined as mass divided by volume:
• Units: g/cm3.
• Originally based on mass (the density was defined
as the mass of 1.00 g of pure water).
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Chemistry 1 Laboratory 6
What is the mass in grams of a cube of gold if
the length of the cube is 0.500 cm? The densityof gold is 19.32 g/cm3.
A. 2.42 g
B. 1.55 x 102 g
C. 3.86 x 101 g
D. 4.14 x 10-1 g
Uncertainty in Measurement
• All scientific measures are subject to error.
• These errors are reflected in the number of
figures reported for the measurement.
• These errors are also reflected in the observation
that two successive measures of the same
quantity are different.
Precision and Accuracy
• Measurements that are close to the “correct”value are accurate.
• Measurements that are close to each other are
precise.
Precision and Accuracy
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Chemistry 1 Laboratory 7
Percentage Error
Percentage Error is a way for scientists to express
how far off a laboratory value is from the commonly
accepted value.
The table above shows the data obtained by four
groups of students during a lab investigation
designed to determine the boiling point of
methanol. The accepted value for the boiling point
of methanol is 78.5oC.
a) Whose data was the most accurate?
b) Whose data was the most precise?
Significant Figures
• The number of digits reported in a measurement
reflect the accuracy of the measurement and theprecision of the measuring device.
• All the figures known with certainty plus one extra
figure are called significant figures.
• In any calculation, the results are reported to the
fewest significant figures (for multiplication and
division) or fewest decimal places (addition and
subtraction).
Rules in Significant Figures
• Non-zero numbers are always significant.
• Zeros between non-zero numbers are alwayssignificant.
• Zeros before the first non-zero digit are not significant.
(Example: 0.0003 has one significant figure.)
• Zeros at the end of the number after a decimal place
are significant.
• Zeros at the end of a number before a decimal place
are ambiguous (e.g. 10,300 g).
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Chemistry 1 Laboratory 8
Which statement regarding significant figures is
false?A. Zeros can be significant.
B. The number 50,004 has five significant
figures.
C. When dividing, the answer is determined by
the number of decimal places.
D. When multiplying, the answer is determined
by the number of significant figures.
What is the product of 2.32 centimeters and 1.1
centimeters expressed to the correct number of significant digits?
A. 3 cm2
B. 2.6 cm2
C. 2.55 cm2
D. 2.552cm2
Expressed to the correct number of significant
digits, the sum of two masses is 445 grams.
Which two masses produce this answer?
A. 210.10 g + 235.100 gB. 210.100 g + 235 g
C. 210.1 g + 235.1 g
D. 210.10 g + 235.10 g
In chemistry lab, a student was instructed to findthe density of a rectangular piece of metal. Aftercareful measurement, he recorded a mass of 25.45g and a volume of 5.7 cm3. Using the formuladensity = mass ÷ volume and a calculator, hisanswer was 4.464912 g/cm3. Which of these is thecorrect answer to report for the density of themetal?
A. 4 g/cm3
B. 4.5 g/cm3
C. 4.47 g/cm3
D. 4.465 g/cm3
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Chemistry 1 Laboratory 9
Dimensional Analysis or Factor-Label Method
• Method of calculation utilizing a knowledge of units.
• Given units can be multiplied or divided to give the
desired units.
• Conversion factors are used to manipulate units:
Desired unit = given unit × (conversion factor)
• The conversion factors are simple ratios:
Using Two or More Conversion Factors
• Example to convert length in meters to length in inches:
cm2.54
in1
m
cm100mof numberinof Number
incmconversion
cmmconversionmof numberinof Number
Using Two or More Conversion Factors
In dimensional analysis always ask three questions:
• What data are we given?• What quantity do we need?
• What conversion factors are available to take us
from what we are given to what we need?
1) If a raindrop weighs 0.10 mg on average and2.0 x 105 raindrops fall on a lawn everyminute, what mass (in kg) of rain falls on thelawn in 1.0 hr?
2) The recommended adult dose of Elixophyllin®, a drug used to treat asthma, is6.00 mg/kg of body mass. What is the dose inmilligrams for a 121-lb person?
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Chemistry 1 Laboratory 10
The End
SCIENTIFIC NOTATION
Express the following quantities in scientific
notation:
a. 158000 km
b. 0.000009782 L
c. 837100000 cm3
d. 6500000000 mm2
e. 0.00593 g
SCIENTIFIC NOTATION SCIENTIFIC NOTATION
Express the following quantities in scientific
notation:
a. 158000 kmb. 0.000009782 L
c. 837100000 cm3
d. 6500000000 mm2
e. 0.00593 g
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Chemistry 1 Laboratory 11
SIGNIFICANT FIGURES
Determine the number of significant figures inthe following measurements:
a. 0.0120 m f. 1000 kg
b. 100.5 mL g. 180. mm
c. 101 g h. 0.4936 L
d. 350 cm2 i. 0.020700 s
e. 0.97 km
SIGNIFICANT FIGURES
Round the following quantities to the specified
number of significant figures:
a. 5,487,129 m to three significant figures
b. 0.013479265 mL to six significant figures
c. 31,947.972 cm2 to four significant figures
d. 192.6739 m2 to five significant figures
e. 786.9164 cm to two significant figures
SIGNIFICANT FIGURES
Perform the following calculations, and express
the answer in the correct units and number of
significant figures.
a. (651 cm)(75 cm)
b. 7.945 J + 82.3 J - 0.02 J
c. 7.835 kg / 2.5 L
d. 7.382 g + 1.21 g + 4.7923 g
UNIT CONVERSION
1. How many milliliters of water will it take to fill
a 2 L bottle that already contains 1.87 L of
water?
2. A piece of copper wire is 150 cm long. How
long is the wire in millimeters? How many 50
mm segments of wire can be cut from the
length?
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Chemistry 1 Laboratory 12
UNIT CONVERSION
3. The ladle at an iron foundry can hold 8500 kg
of molten iron. 646 metric tons of iron are
needed to make rails. How many ladlefuls of
iron will it take to make 646 metric tons of iron?
(1 metric ton = 1000 kg)
UNIT CONVERSION
4. How many palisade cells from plant leaves
would fit in a volume of 1.0 cm3 of cells if the
average volume of a palisade cell is 0.0147
mm3?
UNIT CONVERSION
5. A person drinks eight glasses of water each
day, and each glass contains 300 mL. How many
liters of water will that person consume in ayear? What is the mass of this volume of water
in kilograms? (Assume one year has 365 days
and the density of water is 1.00 kg/L.)
Four Steps for Solving
Quantitative Problems
A. If a liquid has a density of 1.17 g/cm3, how
many liters of the liquid have a mass of 3.75 kg?
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Chemistry 1 Laboratory 13
Four Steps for Solving
Quantitative Problems
B. The radioactive decay of 2.8 g of
plutonium-238 generates 1.0 joule of energy as
heat every second. Plutonium has a density of
19.86 g/cm3. How many calories (1 cal = 4.184 J)
of energy as heat will a rectangular piece of
plutonium that is 4.5 cm x 3.05 cm x 15 cm
generate per hour?