Data and How to Study It Help (page 3)
Chemistry is an experimental science. It is divided into two branches, pure chemistry and applied chemistry . Pure chemistry is theoretical and predicts results of experiments or observations. Applied chemistry involves the practical applications of materials and reactions. How is rust formed and how do you remove it? How can clothes get clean from washing them with soap made from ashes and fat? Why does copper turn green and then black when exposed to air? How can computer chips made from sand (silicon) carry information and electricity?
Observation and measurement, as in all science, are the keys to chemistry. In research, as in other parts of life, we are constantly measuring using common units. The baseball cleared the outfield fence by a foot. The soccer ball missed the flowerpot by three inches. The Austrian driver cruised at 160 kilometers per hour. The Kentucky Derby winner won by a length. The Olympic skier pulled into first place by two one-hundredths of a second. The soldier’s letter home weighed 1 ounce.
A chemical experiment is a controlled testing of a sample’s properties through carefully recorded observations and measurements.
Research is all about measuring. However, to repeat an experiment or follow someone else’s method, the same units must be used. It wouldn’t work to have a researcher in New York measuring in cups while another in Germany measured in milliliters. To repeat an experiment and learn from it, scientists around the world needed a common system.
In 1670, a French scientist named Gabriel Mouton suggested a decimal system of measurement. This meant that units would be based on groups of ten. It took a while for people to try it for themselves, but in 1799 the French Academy of Sciences developed a decimal-based system of measurement. They called it the metric system , from the Greek word metron , which means a measure. On January 1, 1840, the French legislature passed a law requiring the metric system be used in all trade.
International System Of Units (si)
In 1960, the General Conference on Weights and Measures adopted the International System of Units (or SI, after the French, Le Systeme International d’Unites). The International Bureau of Weights and Standards in Sievres, France, houses the official platinum standard measures by which all other standards are compared. The SI system has seven base units from which other units are calculated. Table 2.1 gives the SI units used in chemistry.
When Great Britain formally adopted the metric system in 1965, the United States became the only major nation that didn’t require metric, though people had been using it since the mid-1800s.
The advantage of the SI system is that it is a measuring system based on a decimal system. With calculations written in groups of ten, results can be easily recorded as something called scientific notation . There are written prefixes that indicate exponential values as well. Some of these are listed in Table 2.2 which lists terms used in scientific notation.
Exponential or Scientific notation is a way of writing numbers as powers of ten.
Scientific notation is a simple way to write and keep track of large and small numbers without a lot of zeros. It provides a short cut to recording results and doing calculations. The ease of this method is shown below.
100 = (10)(10) = 10 2 = one hundred
1,000 = (10)(10)(10) = 10 3 = one thousand
10,000 = (10)(10)(10)(10) = 10 4 = ten thousand
100,000 = (10)(10)(10)(10)(10) = 10 5 = one hundred thousand
1,000,000 = (10)(10)(10)(10)(10)(10) = 10 6 = one million
1,000,000,000 = (10)(10)(10)(10)(10)(10)(10)(10)(10) = 10 9 = one billion
1/10 = 10 –1 = one tenth
1/100 = 1/(10)(10) = 10 –2 = one hundredth
1/1,000 = 1/(10)(10)(10) = 10 –3 = one thousandth
1/10,000 = 1/(10)(10)(10)(10) = 10 –4 = one ten thousandth
1/1,000,000 = 1/(10)(10)(10)(10)(10)(10) = 10 –6 = one millionth
1/1,000,000,000 = 1/(10)(10)(10)(10)(10)(10)(10)(10)(10) = 10 –9 = one billionth
Since the English System was used in the United States for many years with units of inches, feet, yards, miles, cups, quarts, gallons, etc., many people were not comfortable with the metric system until recently. Most students wonder why they ever preferred the older system, when they discover how easy it is to multiply metric units.
Table 2.3 lists some everyday metric measurements.
Measurements are never exact, but scientists try to record an answer with the least amount of uncertainty. This is why the idea of scientific notation was set up, to standardize measurements with the least uncertainty. The idea of significant figures was used in order to write numbers either in whole units or to the highest level of confidence.
Significant figures are the number of digits written after the decimal point to measure a quantity.
A counted significant figure is something that cannot be divided into sub-parts. These are recorded in whole numbers such as 9 chickens, 2 bicycles, or 7 keys. Defined significant digits are exact numbers, but not always whole numbers, like 2.54 centimeters equals one inch.
How many significant figures are in the following?
(a) 9.107 (4, zero in the middle is significant)
(b) 401 (3, zero in the middle is significant)
(c) 0.006 (1, leading zeros are never significant)
(d) 800 km (3, zeros are significant in measurements unless otherwise indicated)
(e) 3.002 m (4, zeros in the middle of non-zero digits are significant)
When finding the number of significant figures, the easiest shortcut is to look at the zeros acting as placeholders.
Leading zeros at the beginning of the left-hand side of a number are never significant. You start at the left and count to the right of the decimal point. The measurement 0.096 m has two significant figures. The measurement 13.42 cm has four significant figures. The mass 0.0027 g has two significant figures. (Note: remember to leave off the leading zeros.)
Sandwiched (in the middle) zeros are always significant. The number 26,304 has five significant figures. The measurement 0.000001002 m has four significant figures.
Scientific notation gets rid of guessing and helps to keep track of zeros in very large and very small numbers. If the diameter of the Earth is 10,000,000 m, it is more practical to write 1 × 10 7 m. Or, if the length of a virus is 0.00000004 m, it is easier to write 4 × 10 −8 m.
When multiplying or dividing numbers, the significant digits of the number with the least number of significant digits gives the number of significant digits the answer will have.
40 lbs potatoes x $0.45 per lb = $18.00 or $18 since the first number is only measured to two places
0.5 ounce of perfume x $25.00 per ounce = $12.50 for 0.5 ounces of perfume. (Note: the zero is only written because you cannot divide coins further.
6.23 of wood x $2.00 per linear foot = $12.50 per linear foot.
Imagine you are trying to prove a theory based on a specific property, like boiling point. Unless the boiling point temperature was recorded with precision by other chemists, you will have trouble repeating the experiment, let alone proving a new theory. Since theories become laws by repeated experimentation, it is important to record measurements precisely.
Scientific knowledge moves forward by building upon results and experiments done by earlier scientists. If measurements are taken with little care or precision, a researcher doesn’t know if the observed results are new and exciting or just plain wrong.
Precision is the closeness of two sets of measured groups of values.
Precision is directly related to the amount of reproducibility of a measurement. Closely related to the topic of precision is that of accuracy . Some people use the two interchangeably, but there is a difference.
Accuracy is linked to how close a single measurement is to its true value.
In baseball, when Player A throws balls at a target’s center, it represents high precision and accuracy. Player B’s aim, with balls high and low missing the target, represents low precision and low accuracy. Player C’s hits, clumped together at the bottom left side of the target, define high precision (since they all landed in the same place), but low accuracy (since the object is to hit the target’s center). Player C, then, has to work on hitting the target’s center, if he wants to win games and improve accuracy.
Rounding is the way to drop (or leave off) non-significant numbers in a calculation and adjusting the last number up or down. There are three basic rules to remember when rounding numbers:
(1) If a digit is ≥ 5 followed by non-zeros, then add 1 to the last digit. (Note: 3.2151 would be rounded to 3.22.)
(2) If a digit is < 5 then the digits would be dropped. (Note: 7.12132 would be rounded to 7.12.)
(3) If the number is 5 (or 5 and a bunch of zeros), round to the least certain number of digits. (Note: 4.825, 4.82500, and 4.81500 all round to 4.82.)
Rounding reduces accuracy, but increases precision. The numbers get closer, but are not necessarily on target.
Try rounding the numbers below for practice.
(a) 2.2751 to 3 significant digits
(b) 4.114 to 3 significant digits
(c) 3.177 to 2 significant digits
(d) 5.99 to 1 significant digit
(e) 2.213 to 2 significant digits
(f) 0.0639 to 2 significant digits
Did you get (a) 2.28, (b) 4.11, (c) 3.2, (d) 6, (e) 2.2, and (f) 0.064?
When multiplying or dividing measurements, the number of significant digits of the measurement with the least number of significant digits determines the number of significant digits of the answer.
Do you see how significant digits are figured out?
(1) 1.8 pounds of oranges × $3.99 per pound = $7.182 = $7.18 = $7.2 (Note: 1.8 pounds of oranges has two significant digits)
(2) 15.2 ounces of olive oil × $1.35 per ounce = $20.50
(3) 25 linear feet of rope × $3.60 per linear feet = $90.00
Measurements can be calculated to a high precision. Calculators give between 8 and 10 numbers in response to the numbers entered for a calculation, but most measurements require far less accuracy.
Rounding makes numbers easier to work with and remember.
Think of how out-of-town friends would react if you said to drive 3.4793561 miles west on Main Street; turn right and go 14.1379257 miles straight until Union Street; turn left and travel 1.24900023 miles around the curve until the red brick house on the right. They might never arrive! But by rounding to 3.5 miles, 14 miles, 1.2 miles, and watching the car’s odometer (the instrument that measures distance), they would arrive with a lot less trouble and confusion.
Practice problems for these concepts can be found at - Science Experiment Data Practice Test
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