Measurements and Calculations (BACK)
Scientific Method
Section 2.1
Solving Problems
Trial and error.
Cause and effect.
Scientific method.
Scientific Method
The process that researchers use to carry out their investigations is called the scientific method.
It is a logical approach to solving a problem by observing and collecting data, formulating hypotheses, and formulating theories that are supported by data.
Scientific Method
Identify a problem.
Isolate the problem from its concept.
Analyze the setting in which the problem exists.
Note the conditions present(variables).
Independent variable.
Dependent variable.
Scientific Method
Research the problem to find any descriptions of the observed behaviors(laws).
Formulate a hypothesis.
An untested solution to the problem.
Also called an educated guess.
Attempts to explain behavior.
Must be testable to be scientific.
Scientific Method
Devise a logical procedure to test the hypothesis(experiment).
Purpose
Procedure
Variables
How many repetitions to do(limitations?)
Keep all conditions except one the same for all samples.
On one sample hold all conditions the same(control)
How long to conduct the experiment.
What data to collect.
Quantitative(objective)
Qualitative(subjective)
Scientific Method
Data
Units
Numbers
Calculations
Results
May be graphical.
May be tabular.
May be mathematical.
Scientific Method
Conclusions
Must be specific for this experiment.
Are opinions, judgements, or predictions.
May confirm hypothesis.
May deny hypothesis.
May require modification of hypothesis.
After many experiments a generalization may be made(theory) which explains a large group of related behaviors and may include a model.
Theories
The first great theory of chemistry was the phlogiston theory formulated by Joachim Becker, who believed that everything contained phlogiston or “fire stuff”.
It was later disproved by Lavoisier, who believed that burning substances united with something from the air. This became the modern theory of burning.
Lavoisier is known as the founder of modern chemistry.
Lavoisier is famous for recognizing the role of measurement in chemistry.
Units of Measurement
Section 2.2
Units of Measurement
Why do we measure?
To get reproducible results.
To search for possible modifications to achieve better results.
To make comparison.
To accurately communicate results.
Units of Measurement
There are two kinds of measurement. Both provide important information.
One kind of measurement is quantitative. It gives results in numerical form. It is objective because it requires an instrument.
The other kind of measurement is qualititative. It gives results in a descriptive form. It is subjective because it depends on the bias of the observer.
Units of Measurement
What are standards?
Agreements on sizes of certain quantities.
Measures that eliminate controversies about quantities.
Comparisons of quantities.
Objects or phenomena that are of constant value and easy to preserve and reproduce.
Comparing and contrasting measurement systems
There are 3 systems of measurement in use in the United States today.
The English system
The metric system
The SI system
Comparing and contrasting measurement systems
The English system has no standards of comparison.
The English system has no easy conversion from a small unit to a larger unit measuring the same quantity.
The English system uses oF for temperature.
The English system uses fractions.
The metric and SI systems have standards. The metric system is based on Pt-Ir objects whereas the SI is based on physical phenomena.
The metric/SI conversions are based on powers of 10.
The metric system uses oC for temperature whereas the SI system uses K for temperature.
The metric/SI system uses decimals.
The SI System
There are seven fundamental units: meter, kilogram, second, Ampere, candela, mole, and kelvin.
All other units are derived from these.
The meter is based on the distance light travels in a vacuum in 1/3x108 ths of a second.
The second is based on the number of disintegrations from a cesium-133 atom.
Prefixes are added to the base units to change the size of the unit.
Centigram = 1/100 of a gram
Milligram = 1/1000 of a gram
Dekaliter = 10 liters
Metric Prefixes
SI Base Units
Mass
Measures the quantity of matter.
Has the standard unit of kilogram.
Is measured with a triple beam balance.
Is NOT the same as weight.
Never changes, no matter where you are.
SI Base Units
Length
Has the standard unit of meter.
Is measured with a meter stick.
SI Derived Units
Volume
Has the derived unit of m3.
May be measured by
Using a graduated cylinder(for liquids)
Using displacement(for irregular solids)
Using dimensions and calculating.
Changes for most materials when heated or cooled.
Remember 1 mL = 1 cm3.
Remember liter is the common unit.
SI Derived Units
Density
Is defined as mass per unit of volume.
Changes as temperature changes.
What happens to density as temperature increases?
Has the standard unit kg/m3.
Has units of g/cm3 or g/mL usually.
D = m/V
Does not depend on the size of the sample and is used for identifying a substance.
Sample Problem
A sample of aluminum metal has a mass of 8.4 g. The volume of the sample is 3.1 cm3. Calculate the density of aluminum.
m = 8.4 g
V = 3.1 cm3
D = m/V = 8.4g/3.1 cm3 = 2.7 g/ cm3
Sample Problems
Diamond has a density of 3.26 g/cm3. What is the mass of a diamond that has a volume of 0.350 cm3?
What is the volume of a sample of liquid mercury that has a mass of 76.2g, given that the density of mercury is 13.6g/mL?
Conversion Factors
Conversion factors are used to change from one unit into another.
They come from equivalent quantities, such as 1 m = 100 cm.
Equivalent quantities may be written in one of two ways, 1 m/100 cm or 100 cm/1 m, depending on what unit is desired.
Using Scientific Measurements
Section 2.3
Accuracy
Closeness to a true value
Dependent upon the quality of the measuring device.
Only one measurement.
Can be compared by using percent error.
Precision
Closeness of a set of values
Not related to accurate value
Dependent upon the skill of the person making the measurement.
Significant Figures in Measurements
These are digits which may be read from an instrument plus one digit which is estimated.
Check each instrument before using it to determine how many figures may be read from it. Then estimate one more figure.
The use of these lends reliability and consistency to measurements.
What digits are significant?
All nonzero digits are significant.
All captive zeroes are significant.
All beginning zeroes are NOT significant.
All zeroes to the right of a nonzero digit and a decimal point are significant.
Ending zeroes in numbers without a decimal may or may not be significant. The final significant zero may be noted with a bar over it.
What about calculations?
When adding or subtracting, the answer may have only as many DECIMAL PLACES as the least precise number in the operation.
When multiplying or dividing, the answer may have only as many SIGNIFICANT DIGITS as the least precise number in the operation.
Scientific Notation
To write a number in scientific notation, write the digits expressed as a number from 1-10 and then write the decimal characteristic as a power of 10.
To add or subtract numbers in scientific notation, first put both numbers in the same power of 10 or change both to standard notation. Then do the operation.
To divide numbers in scientific notation, divide the number and then subtract the powers of 10.
To multiply numbers in scientific notation, multiply the numbers and then add the powers of 10.
Using Sample Problems
Analyze the problem. Read the details. Write down the given information.
Plan a solution. Draw a diagram if necessary. Check on conversion factors you might use.
Compute the answer.
Evaluate the reasonableness of the answer. Check units. Check significant figures.
Direct Proportions
Two quantities are directly proportional if dividing one by the other gives a constant value.
Another way to test proportionality is to see if the quantities increase or decrease at the same rate.
y/x = k(which is a proportionality constant) OR y = kx
All directly proportional relationships produce linear graphs which pass through the origin.
Inverse Proportions
Two quantities are inversely proportional if their product is constant.
Another way to test inverse proportionality is to see if one quantity decreases regularly as the other one increases.
xy = k
The graph of such a relationship is a hyperbola.