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SI UNITS, DENSITY, AND GRAPHICAL ANALYSIS

THE SI UNITS AND SIGNIFICANT DIGITS
Chemical laboratories have evolved significantly over time. However, some things have not changed since time memorial and the experimental protocol includes measurements of mass, volume, temperature, and other physical properties. These measurements are reported in either Base or Derived SI units. Some SI units we will be using in this experiment are:

QUANTITY Length Area Volume Mass Density
NAME/DEFINITION Meter Meter Squared Meter Cubed Kilogram Mass per Unit Volume
SYMBOL OF UNIT m m2 m3 kg kg/m3

Length and mass are base SI units; area, volume and density are derived SI units,
Volume = Length X Length X Length = Length3
density = Mass / Volume

In order for the SI units to follow a certain pattern, the kilogram and the cubic meter are the SI units of mass and volume respectively. However, these quantities are impractical for use in chemistry. Instead, the gram and the liter are most widely used. One gram is equal to 1 X 10-3 kg and one liter is equal to 1 X 10-3 cubic meters. At this point, the reader should know that 1 X 10-3 means 1/1000.
Depending on the task at hand, the values to be reported might be larger or smaller than the base SI units. Such quantities are written with prefixes that represent multiples of ten. Commonly used prefixes in the chemistry laboratory are:

PREFIX kilo centi mili micro nano
SYMBOL k c m μ n
POWER OF 10 103 10-2 10-3 10-6 10-9

Appropiate SI units (depending on their use) can be obtained by combining the base unit with a prefix. To change any of the resulting units of length into their equivalent values in meters use the appropiate operation and conversion factor.

Due to the nature of the research and materials, small units are used in biotechnology. Some procedure indicates that you are to obtain 0.0500 mL of cultured cells suspended in buffer. Then add 75.0 μL of Lysozyme sulution (concentration 100 μg/mL) and 50.0 μL RNase A (concentration 500 μg/mL).
Compute (a) the total volume of the solution in liters, (b) the number of grams of Lysozyme and RNase A added (c) the mass of the entire solution in grams if its density is 1050 kg/m3.

volume of cells + buffer = 0.0500 mL X [1 L/103 mL] = 0.0500 X 10-3 L
volume of Lysozyme solution = 75.0 μL X [1 L/106 μL] = 75.0 X 10-6 L
volume of RNase A solution = 50.0 μL X [1 L/106 μL] = 50.0 X 10-6 L
Total volume = [0.0500 X 10-3 + 75.0 X 10 10-6 + 50.0 X 10-6] L = 1.75 X 10-4 L
For the mass of Lysozyme, the units of density should match the units of volume.
mL --> L = # of mL X 10-3
μg --> g = # of μg X 10-6
100 μg/mL --> 100 [g X 10-6]/[L X 10-3] = 0.100 g/L
mass of Lysozyme = 75.0 X 10-6 L X [.100 g/L] = 7.50 X 10-6 g
mass of RNase A = 50.0 X 10-6 L X [.500 g/L] = 25.0 X 10-6 g
For the mass of solution the units density should match the units of volume. Density is often reported in g/mL for liquids and g/cm3 for solids. The two expressions are equivalent,
1.0 mL = 1.0 cm3

Some conversion factors to use at the present time are:
m3 --> L = # of m3 X 103
L --> mL = # of L X 103
m3 --> mL or cm3 = # of m3 X 106
kg --> g = # of kg X 103
To convert 1050 kg/m3 to its g/cm3 equivalent,
1050 kg = 1050 X 103 g
1.0 m3 = 1.0 X 106 cm3
1050 kg/m3 --> 1050 [g X 103]/[cm3 X 106] = 1.050 g/cm3
Volume of solution = 1.75 X 10-4 L X [103mL/ L] = 0.175 mL or cm3
mass of solution = Volume X density = 0.175 cm3 X 1.050 g/cm3 = 0.18375 ~ 0.184 g

Note that the number has been rounded off to three significant digits. In order to understand significant digits, the measurements must be recorded properly. The typical biotechnology lab includes pipets that are accurate to the nearest μL and even smaller volumes. Some instruments are very easy to use because the measuring process is automated. A digital balance for example will make measurements at the actual uncertainty of the instrument and display the correct number of significant digits. Reading the volume on a graduated cylinder takes a lot more practice. For example, there are various types of graduated cylinder of 10 mL capacity. The volume readings to be reported depend on the number of graduations per unit volume. Some cylinders have graduations at 0.1 mL intervals so they have a 0.1 mL tolerance. Volumes should be reported to the nearest tenth of mL plus one more digit. This means that the number of mL is accurately known to the nearest tenth of mL because the liquid level is either above or below one of the graduations and the next digit is an estimate. If the graduations on the cylinder are more disperse, then the cylinder has a larger tolerance value and the readings will not be as accurate.

GRAPHICAL ANALYSIS
Suppose, we know the general shape of a mathematical function, which seeks to analyze some relationship between two quantities by performing a series of measurements. For each measurement, we set some quantity X to a chosen value and measure the corresponding value of the quantity Y and represent these two points by a coordinate pair (X, Y) on a two dimensional grid. But need to figure out where each datapoint is to be placed specifically, and how to divide the axes. The following are some standard steps of the graphing procedure,

-Include a complete, descriptive title for your graphs.
-Sort the datapoints (smallest to largest) in a table of the ordinate (Y) and abscissa (X).
-Scaled the graph axes so that the coordinate points (X,Y) are well distributed across the graph, covering as much of the paper as possible. The graph axes do not have to start at zero. This is what happens when if you don't start the axes at the correct value,

Correcting this small problem we obtain,

-Note that if the axes of this graph had started at zero, only ~25% of the graph area would have been used.
-Also note the error bars, here drawn as a '+'
-Here, the axes have been labeled with the quantity plotted divided by the unit used: instead of writing 150000 grams, we write 150 and label the axis as [grams X 103].
-Only a few labels need to be included: we label 150 then 175 instead of [150, 151, 152, 153, 154...], that would make the axes look messy.
-The few labels that you include should be equally spaced.
-If drawing the graph by hand, make the smallest subdivision of the paper into whole numbers or simple fractional values of the unit being plotted. For example, if you make 20 subdivisions of the paper equal to 1 gram, then 5 subdivisions will be equal to 1/4 of a gram and one subdivision will be equal to 1/20 of a gram.
-Error bars can also be drawn as circles around the datapoint. Remember when drawing graphs by hand that you are not connecting the dots, you are trying to draw the best straight line through the dots for linear functions and a smooth line for nonlinear functions...

-When plotting two lines on the same graph, make one of them look different from the other. Here, one is solid and the other is a broken line. Note that a key has been included on one corner to help the reader distinguish between the two sets of data.
-Some graphs span both, negative and positive ranges of a dataset. That is why it is important to sort the data and decide as to the appropriate range that an axis is to span.

-The slope of a straight-line graph is determined by choosing two points on the line of best fit, not just from any two points from the original data.

THE GRAPHICAL ANALYSIS PROGRAM
The program displays three main screen areas: TEXTBOX, DATA, and GRAPH. Only one of these areas is active at any time, to activate the area click on it once. To work in either the data table, the graph, or the text box, the area has to be active. How important is this? if you try to use the ANALYZE menu with while the GRAPH area is grey, you will not be able to draw your straight line.
To access the program
GO TO START --> PROGRAMS --> CHEMISTRY --> GRAPHICAL ANALYSIS VERSION #2
To plot graphs of data
First you MUST label the data. To do that:
-Click on the top box in the X column (LABEL).
-Enter the name of the measured quantity (volume, time, concentration...)
-RETURN, or down arrow, or click on, to get to the box below (UNIT)
-Enter the unit of measurement for this parameter (Liter, sec, mol/L...)
-Do the same with the Y column.
To enter the data
-Click on the first space in the X column and start entering the data. Pressing return will move the cursor over to the Y data, then to the next X, ...
-Click on the column headings to enter the name and unit for the column.
-You will see the graph change automatically as you enter data.
-You need to enter the data in the order you want. If one point seems too low and the next seems too high, the data points are probably out of place.
-To add a column to the table choose New Column from the DATA menu.
-To alter data in the table, such as raising a data column to a power, or multiplying it by a constant, click on the top of the column to highlight all of the data. Then choose Column Formula from the DATA menu. Make your choice from the list provided.
To alter the graph
-The graphing changes can be made from the GRAPH menu. Click on it to see what is available.
-To change scale, click on the last number on the axis and type in the new number, or use the scaling option in the GRAPH menu.
-To change what is graphed on the Axes, click on the axis label and choose a different column from the data table. This is the best way to see different combinations from the data table.
-Under the GRAPH menu: these items are on by default.
*point protectors --> Turn on so you can see the data points.
*Connecting lines --> can help you see the trends in the data.
*Regression line/statistics --> makes a straight line if the data is linear.
To create an equation of the data:
This is an equation which relates the two variables being graphed: Y = mX + b in this class.
-Choose Automatic curve fit from the ANALYZE menu. Make your selection from the list provided.
-The program will put the best line (maybe) for that type of relationship on the graph with the coefficients listed at the bottom.
-If the curve is not the correct type, click on NEW FIT in the lower right corner.
-You can change the coefficients by clicking on them and entering the new number. This is useful if the curve is slightly off.
Finishing your work
-In the TEXT BOX enter your name and your coworker's.
-The saving and print options are listed under the FILE menu.
-You can print the data alone, the graph alone, or both together. In this class we will need to PRINT WHOLE SCREEN, that way we will get the data, the graph, and the text box.
-Do not print until you are authorized to do so. Your work might not be ready to print and if too many print jobs are sent to the printer at one time, it might get jammed and nobody will be able to print.

EXPERIMENTAL PROCEDURE
This method is a way to find the volume of an irregularly shaped solid if it does not float in the liquid. Since the materials we will use have densities far greater than that of water, (the density of water is 1.00 g/cm3) all samples will sink completely.
First, the mass of the metal sample will be determined by weighing the sample on a toploader balance. To find volume, fill a graduated cylinder with enough water to cover the sample, place the sample against the graduated cylinder to see how much water is required. Read the volume and record the value as Vol1. Tilt the cylinder and slide the sample down the side. Read the volume and record the value as Vol2.
Substract [Vol1 - Vol2], this is the volume of the sample.
Then compute the density:

ρ = Mass / Volume


DATA PROCESSING
-The above procedure is to be carried out with a number samples of Metal I Metal II. Report the average density for each metal. Suppose you did this for five samples, the average density would be,
1 + ρ2 + ρ3 + ρ4 + ρ5]
------------------------
5
-Plot the data from Metal I and metal II in each of the sheets of graph paper provided. Mass goes in the ordinate, Volume goes in the abscissa. The density formula looks like a linear equation with y-intercept equal to zero:

Mass --> Y --> ordinate
Volume --> X --> abscissa
Density --> m --> slope

So the slope of the line should be very close to the average density.


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