11
Honors Chemistry Summer Assignment
Due September 9th
Name ______
CHEMISTRY INTRODUCTORY UNIT
GENERAL REMARKS:
· Chemistry is the science, which addresses the interaction between matter and the changes produced by chemical interactions. The language of chemistry is mathematics. A chemist attempts to explain and analyze chemical phenomena by incorporating quantitative information into mathematical relationships called equations. For you to prosper in this course you must develop your quantitative skills to the fullest extent of your abilities.
· Chemistry involves measuring and calculating. It is a quantitative science. When you describe a property without measurements you are characterizing the object qualitatively, for example, you might say the weather is hot and humid
MEASUREMENT:
· Measurement is the process by which people express quantitatively to each other aspects of the observable universe. In order to engage in the process of measurement a common standard of measure must be used. Ancient measurement systems used objects or parts of the human body for standards.
· The metric system is used by the scientific community for the measurement of physical quantity.
· The metric system uses seven fundamental units (see the chart) to measure all aspects of the physical world.
· All of the fundamental units are conceptual units (units based on repeatable physical phenomena such as the wavelength of light etc.) except mass. Mass is still based on a standard kilogram mass kept in the International Bureau of Weights and Measures in France.
FUNDAMENTAL UNITS IN THE METRIC SYSTEM
PHYSICAL QUANTITY / SYMBOL USED IN EQUATIONS / UNIT OF MEASURE / UNIT SYMBOLlength / L / meter / M
mass / M / kilogram / Kg
Time / T / second / S
electric charge / Q / coulomb / Coul
temperature / T / degree Kelvin / K
amount of substance / (none) / mole / Mol
luminous intensity / I / candela / Cd
· Fundamental units can be combined to form derived units. For example: Distance divided by time equals speed which is measured in meters/sec. Also if we multiply length by length, we get area. Area multiplied by length produces volume. The SI unit for volume is the cubic meter(m3) However this quantity is too large to be practical for the laboratory. Chemists often use cubic decimeters (dm3) as the unit of volume. One cubic decimeter is given another name, the liter (L).The liter is a unit of volume. The units used to express speed, area, volume are all derived units.
· Units in the metric system are modified by prefixes which indicate the order of magnitude of the base unit. An example is centi which stands for 1/100 of the base unit. One centimeter represents 1/100 of a meter. Your instructor will provide you with further information regarding prefixes
The Commonly Used Prefixes in the Metric System
Prefix Symbol Meaning Power of 10
Tera T 1,000,000,000,000 1012
Giga G 1,000,000,000 109
mega M 1,000,000 106
kilo k 1000 103
deci d 0.1 10-1
centi c 0.01 10-2
milli m 0.001 10-3
micro m 0.000001 10-6
nano n 0.000000001 10-9
Pico p 0.000000000001 10-12
Femto F 0.000000000000001 10-15
SIGNIFICANT DIGITS:
· Significant digits in an experimental measurement are all the numbers that can be read directly from the instrument scale (known with certainty) plus one estimated (doubtful) number.
READING THE NUMBER OF SIGNIFICANT DIGITS IN A MEASUREMENT:
RULE / EXAMPLEAll non-zero digits are significant. / 1.345 Kg has 4 significant digits
All zeros between non-zero digits are significant / 220005 Km has 6 significant digits
Zeros to the right of a non-zero digit but to the left of an understood decimal are not significant. / 230000 g has 2 significant digits
Zeros to the right of the decimal but to the left of a non-zero digit are not significant / .0000345 m has 3 significant digits
Zeros to the right of the decimal following a non-zero digit are significant. / .10070 cm has 5 significant digits
MULTIPLICATION AND DIVISION USING SIGNIFICANT DIGITS:
· In the multiplication or division of two or more numerical measurements, the number of significant digits in the answer can be no greater than the least significant digits in any number in the set.
1. Determine the number of significant digits in each of the numbers in the problem.
2. Perform the multiplication or division.
3. Round the answer to the least number of significant digits determined by step one.
ADDITION AND SUBTRACTION USING SIGNIFICANT DIGITS:
· In addition and subtraction, adding or subtraction begins with the first column from the left that contains an uncertain or doubtful figure.
1. Underline the first doubtful digit in each of the numbers in the set (this is the rightmost significant digit).
2. Add or subtract the numbers.
3. Round the sum or difference to the leftmost underlined place (doubtful figure).
ACCURACY:
· The closeness of a result to its accepted value is the accuracy of the result. That which detrimentally affects accuracy is called error. There are three sources of experimental error.
· Human error sometimes called personal error arises from personal bias or carelessness in reading an instrument, in recording data, or in calculations.
· Systematic error is associated with equipment problems such as an improperly “zeroed” instrument or an incorrectly calibrated device.
· Random error results from unknown and unpredicted variations in experimental conditions. Random errors are often beyond the control of the experimenter. Voltage spikes, vibrations, and temperature fluctuations are all examples of the causes of random error.
REPRESENTATION OF THE ACCURACY OF A RESULT:
· Absolute error (Ea) is the numerical difference between the accepted value for a result and the actual experimental value. Equation: Ea = Experimental value - Accepted value.
· Relative error (Er) is a more meaningful representation of error in an experimental setting. The relative error represents the fractional error. You may have called this fractional error percent error.
· Percent error = (Ea/Accepted)(100%).
· PRECISION:
· Precision is a measure of the reliability of a result. It is measured by how close the measurement agrees with other measurements taken in the same way. Poor precision scatters results and makes for an unreliable set of data.
REPRESENTATION OF THE PRECISION OF DATA:
· Mean or average can be computed for a set of data by using this equation: Xmea n= X1+X2+X3...... XN/N. X1 , X2 , etc. are the data points. N is the number of data points in the data set.
· Percent difference is a simple way to show agreement among data.
1. Find the mean of the data.
2. Find the difference between the two data points. If there is a set of data find the difference between the biggest and smallest values (the extremes).
3. Divide the difference by the mean and multiply by 100%.
· Equation: (X1 - X2 /mean)(100%) or (Xmax - Xmin /mean)(100%).
· Absolute deviation represents the absolute value of the difference between a data point and the mean of the data. Equation: Da = çX-meanç.
· Mean absolute deviation represents the mean or average of the absolute deviations of a set of data. When reporting the result of an experiment, the result may be expressed as: Mean of the data ± mean absolute deviation. Example: 123 ± 2 cm.
· Relative deviation represents the fractional deviation for a set of data. To find the relative deviation use the following equation: (mean absolute deviation/mean of the data)(100%). When reporting the result of an experiment, the result may be expressed as: Mean of the data ± relative deviation. Example: 123cm ± .5%.
· Standard deviation(Sx) can be used to measure the precision of a set of data
1. Find the average of the data
2. Find the deviation by finding the difference between a data point and the average of the data
3. Then find the square of the deviation and plug in that value in the given equation to find the standard deviation
Standard deviation (Sx) = √sum (dev)2
n-1
where n = number of measurements
GRAPHICAL REPRESENTATION OF DATA:
· It is often convenient to represent experimental data in graphical form for the purposes of reporting and obtaining information (such as slopes).
· Quantities are commonly plotted on Cartesian graph grids in which the horizontal (X) is called the abscissa and the vertical (Y) is called the ordinate.
GRAPHING PROCEDURE:
1. Determine the range of data and choose scales that are easy to read and plot. Scales which are too small will "bunch up" the data and make the graph unreadable. Choose scales so that the major portion of the graph paper will be used.
2. Label each axis with the name of the quantity plotted (mass, time, velocity, etc.).
3. Indicate the units for the quantity in parenthesis (Kg), (s), (m/s), etc.
4. When plotting the individual data points, locate them as exactly as possible within the parameters of the scale.
5. When all of the data points are plotted, draw a smooth line connecting the points. "Smooth" suggests that the line does not have to pass exactly through each point but connects the general areas of significance of the data points.
6. Title the graph. The title is commonly listed as the Y quantity versus the X quantity. Example: Distance vs. Time.
7. Put your name, date and group number on the paper.
· When two quantities are directly related the graph yields a straight line. These quantities are considered to have a linear relationship. The general equation is (Y = mX + b).
· The slope of the line is useful in many chemistry applications. The slope is found by dividing the "Rise" (DY) by the "Run" (DX). The unit used for the slope is determined by the X and Y units. Example: X represents time (s) and Y represents distance (m), this would yield a slope which has the unit m/s.
· If one quantity increases proportionally as the other decreases, an inverse relationship is present. The graph of an inverses relationship is a hyperbola. The general equation is (X)(Y) = k.
· If one quantity increases as the square of the other then a quadratic relationship is present. The resulting graph is a parabola. The general equation is Y = kX2.
Graphing with a Graphing calculator
Follow the directions given on the Last sheet to graph the given data on the graphing calculator. Directions provided work best with a Ti-82, Ti-83 and Ti-84 type of graphing calculators.
PROBLEMS IN METRIC CONVERSIONS, SIGNIFICANT DIGITS DATA ANALYSIS
AND GRAPHING
1. Convert the following metric measurements
a) 5.78 m = ______Km g) 8.03 Giga m =______mega m
b) 5.78 cg = ______mg h) 9.8 m2 = ______cm2
c) 5.78 mL = ______KL i) 18.9 Km3 = ______mm3
d) 5.78mm = ______m j) 52 dm3 = ______Liters
e) 5.78 Kg/KL = ______g/m3 k) 5.78 cg = .0000578 ?
f) 5.78 inch /min =______feet/hr l) 450 ? = .00045 mm
2. Write the following numbers in scientific notation
a) 156.90
b) 12000
c) 0.0345
d) 0.000000981
e) 50600000000000
f) 0.0000000005632
3. Expand the following numbers
a) 1.23 X 107
b) 2.5 X 10-5
c) 1.54 X 10-1
d) 2.58 X 1012
4. Solve the following and put your answer in scientific notation with correct # of significant digits
a) (2.67x10-3 m) * (9.5x 10-4 m)
b) (2.5x10-6 mm) * ( 3.00 x107mm)
c) (1.56x1052kg ) ÷ (1.269x 1022kg)
d) (6.3x 10-34mL) ÷ ( 2.x10-67 mL)
5. Give the number of significant digits in the following measurements
a) 2.9910m
b) 5600Km
c) .00670Kg
d) 809g
e) 800.00m
f) 801.0cm
6. Find the absolute and relative error in a experiment which yields a result of 90.78 Units and has an accepted value of 88.00 Units.
7. An experiment is performed to find the density of a substance which has an accepted value of 1.23 g/cm3. The mass of the test object is 239 g. and the volume is measured as 190 cm3. Compute the experimental density and the percent error of the result.
8. What is the difference between accuracy and precision?
9 .Density of a substance is expressed as a ratio of its mass and volume, D = M/V .If the density of
nitrogen gas is 1.25g/dm3. Find the mass of 1.00 m3 of nitrogen gas.
10. Iron has a density of 9.80 g/dm3.What volume would 26.3g of iron occupy?
11 An experiment is conducted twice yielding 23.44 Units and 24.05 Units. Compute the mean and
the percent difference for this set of data.
12 An experiment is performed eight times yielding results of 34.40, 34.80, 33.99, 34.00, 34.68,
34.05, 33.98, and 34.55 Units respectively. Compute the mean and the percent difference and the
standard deviation for this set of data.
See the chart:
TRIAL / DATA (UNITS) / Da (UNITS)1 / 32.56
2 / 32.55
3 / 31.98
4 / 32.01
5 / 32.48
6 / 33.00
7 / 32.85
8 / 32.56
mean
For the above data compute the mean, absolute deviation for each trial and the relative deviation for the experiment. Complete the chart and report the experimental results using the mean absolute deviation and the relative deviation.
GRAPH THE FOLLOWING SETS OF DATA ON THE GRAPH PAPER PROVIDED and on your Graphing Calculator.
MASS (Kg) / WEIGHT (N)2.2 / 21.5
2.5 / 24.5
2.8 / 27.6
3.0 / 29.4
3.1 / 30.4
3.2 / 31.3
3.4 / 33.3
3.6 / 35.2
3.8 / 37.2
4.0 / 39.2
· Describe, in words, the relationship shown between mass and weight as shown on the graph.
· Compute the slope of the line in this graph.
· Write the regression equation of the above data and the value of r
11
VOL. (cm3) / MASS (g)10.0 / 7.9
20.0 / 15.8
30.0 / 23.7
40.0 / 31.6
50.0 / 39.6
· Describe the resulting curve.
· Write an equation relating volume to mass.
· Compute the slope of the graph. What is the name given to this quantity?
· Write the regression equation of the above data and the value of r
MASS (Kg) / ACCEL. (m/s2)1.0 / 12.0
2.0 / 5.9
3.0 / 4.1
4.0 / 3.0
5.0 / 2.5
6.0 / 2.0
· Describe the resulting curve.