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A report sheet is used as well as a laboratory notebook to provide more structure in data collection.You should be able to look at your lab notebook a year from now and be able to repeat the experiment or calculations.Calculations should be shown in the lab notebook.Dimensional analysis(unit cancellation)must be used to do all the calculations in this course.If a spreadsheet or graph is used to do the calculations,staple a copy to the report sheet and lab notebook pages.
Before you start an experiment,key aspects of the laboratory procedure should be outlined in your lab notebook.Any procedures not in the lab manual including changes to procedures listed in the manual must be noted.Key data must also be recorded in the laboratory notebook,in case the report sheet is lost.Certain rules need to be followed when keeping a lab notebook:
(1)Record all data and observations directly in the lab notebook.This is by far the most important rule in recording data.Do not transcribe data from other pieces of paper,i.e.,do not record data on scraps of paper and then recopy the data into thelab notebook.Write down exactly what you are doing and your observations as you are doing the experiment.Errors in your procedure can be caught this way.Points can be taken off for writing raw data in places other than the lab notebook/report sheet.
(2)Clearly identify all data,graphs,axes,and use correct units.Use unit cancellation.
(3)A ball point pen must be used for all entries in a lab notebook.A pen must be used for all measured data(mainly mass and volume data)and observations.Do not white out,erase any entry;simply cross out mistakes with a single line (the mistake should still be readable)and give a short note to explain the nature of the mistake,e.g.,“misread.”Sometimes you will find later that the entry was not a mistake after all and will want to retrieve the data.So never obliterate or destroy data no matter how bad it looks!
(4)Before an experiment is started,the entire experimental procedure must be read.As you readit,note the objectives and key points of the experimental procedure in your lab notebook.This will prepare you for the pre-lab quiz and experiment before you come to the lab.
(5)Another important facet of scientific experiments involves the propagation of accuracy(or inaccuracy)of measurements through the calculations to the results.Use the correct number of significant figures,as outlined below,during the collection of data and calculations.
It is important to take data and report answers such that both the one doing the experiment and the reader of the reported results know how precise the results are.The simplest way of expressing this precision is by using the concept of significant figures.A significant figure is any digit that contributes to the accuracy of an experimentally measured number or to a number calculated from experimentally measured numbers.Please refer to the chemistry lecture textbook for a discussion pertaining to the use of significant figures.
Usually,mass,volume,time,and temperature are experimentally measured and used to calculate density,concentration,percent by mass,and other values of interest.For example,mass in grams(g)is always measured using a top loading electronic balance with a precision of±0.001 g.Most mass measurements should be recorded to this precision even though the last digit may vary somewhat.For example,if the mass of an object on a balance reads 25.001,25.000,24.999 and moves between these values,25.000 should be recorded.Recording 25,25.0,or 25.00 would be wrong since these would not communicate the true precision of the number.If values on the balance change randomly from 25.000,25.001,to 25.002then 25.001 g should be recorded.For very precise mass measurements an analytical balance is used to±0.000 1 g.
Time in seconds(s)is measured using a timer,stopwatch,or perhaps a clock so the precision of the measurement might vary from ±1 to ±0.01 seconds.Always record the number to the maximum precision.Temperature will be measured using an alcohol thermometer that can be read to a precision of±0.2℃ so estimate to the tenth of a degree(i.e.21.3℃).
Measuring volume in mL is a tradeoff between speed and the precision of the measurement and requires skill in choosing the right glassware for the task.When an approximate volume is needed,a beaker,Erlenmeyer flask,or graduated cylinder can be used,but when an accurate volume is needed,a pipet,pipettor,buret,or volumetric flask will be specified for use.Recognizing when to make an accurate measurement and when to be satisfied with an approximate measurement can save much time.
Frequently,the written directions will give clues to the needed precision by using the words “approximately”or “about”when the precision is not important and“exactly”or“precisely”when the precision is important.Another clue would be the number of significant figures used to write a number.It is also important to note that glassware used for accurate measurements is calibrated at a specific temperature,which is noted on the glassware.The precision of various types of glassware is shown in the following table 1-1.
Table 1-1 Precision ofGlassware for Volume Measurement
When a measurement is made,the question arises:“How many digits or figures should be recorded?”The answer is straightforward:For a measured number records all digits,which are known with certainty,and the last digit,which is estimated.Many of the measurements in this course involve estimation to the nearest one-fifth or one-tenth of a scale marking.For example,a 25 mL graduated cylinder,which has scale markings every 0.5 mL,should be read to the nearest 0.1 mL,estimation to the nearest one-fifth of a division.The graduated cylinder does not need to be used to this accuracy at all times;for example,if the instruction says“add about 25 mL of water”being within 1—2 mL of 25 would be ok.
NOTE:Whenever estimation between markings is being done and the reading is“on the mark,”the last digit should be included to convey the idea of accuracy to the reader.For example,with a burette,which has markings every 0.1 mL,a reading on the mark of 11.3 mL would be recorded as 11.30 mL;otherwise,the reader will not know that the burette was really read to the nearest 0.01 mL.(You must estimate the last digit by looking carefully between the markings).
Sometimes approximate small amounts of liquid are needed.In this case instructions may indicate to measure out drops from a dropper bottle or eye dropper.One drop of water or a dilute solution on average is about 0.05 mL.This can also be a safer method because it does not involve pouring the liquid from one container to another.
Generally speaking,all the glassware in the table on the previous page is for transferring known volumes of liquid from one container to another except for the beaker and flasks.Beakers along with conical beakers are generally used for conducting chemical reactions or other lab manipulations.The volumetric flaskis used for preparing precise solutions or dilutions.
Significant figures are excellent to express the precision of raw data but not as good to express the precision of calculated values.As a general rule in this laboratory course you should always use at least four significant figures for calculated values to avoid rounding errors.In order to interpret the quality of your results,certain terms are useful.You will need to understand the following definitions.
(1)Accuracy:The term “accuracy”describes the nearness of a measurement to its accepted or true value.
(2)Precision:The term “precision”describes the“reproducibility”of results.It can be defined as the agreement between the numerical values of two or more measurements(trials)that have been made in an identical fashion.Good precision does not necessarily mean that a result is accurate.
Figure 1-2 Probability curve about accuracy and precision
(3)Range:The“range”is one of several ways of describing the precision of a series of measurements.The range is simply the difference between the lowest and the highest of the values reported.As the range becomes smaller,the precision becomes better.
Example:Find the range of 10.06,10.38,10.08,and 10.12.
Range＝10.38-10.06＝0.32
(4)Mean:The“mean”or“average”is the numerical value obtained by dividing the sum of a set of repeated measurements by the number of individual results in the set.
Example:Find the mean of 10.06,10.38,10.08,10.12,
(Note that the value 10.38,which is far greater than the other values,has a large influence on the mean,whichis larger than three out of the 4 individual values.)
(5)Median:The “median”of a set is that value about which all others are equally distributed,half being numerically greater and half being numerically smaller.If the data set has an odd number of measurements,selection of the median may be made directly.
Example:the median of 7.9,8.6,7.7,8.0 and 7.8 is 7.9,the“middle”of the five.
For an even number of data,the average of the central pair is taken as the median.
Example:the median of 10.06,10.38,10.08,and 10.12 is 10.10 which is the average of the middle pair of 10.08 and 10.12.
Notice in the example that the median is not influenced much by the value 10.38,which differs greatly from the other three values as in the example for the mean above.For this reason,the median is usually better to use in reporting results thanthe mean for small data sets.
(6)Error:The absolute error of an experimental value is the difference between it and the true value.For example if the experimental value is 30.9 and the known true value is 26.5,the error would be 30.9—26.5 or 4.4.
Systematic errors occur when there is an error in the experimental procedure.Measuring the volume of water from the top of the meniscus rather than the bottom,or overshooting the volume of a liquid delivered in a titration will lead to readings which are too high.Heat losses in an exothermic reaction will lead to smaller observed temperatures changes.
Random errors are caused by the readability of the measuring instrument,or the effects of changes in the surroundings,such as temperature variations and air currents,or insufficient data,or the observer misinterpreting the reading.Random errors make a measurement less precise,but not in any particular direction.
Random uncertainties can be reduced by repeating readings;systematic errors cannot be reduced by repeating measurements.
Relative percent error would be the error divided by the true value times 100％:(4.4/26.5)×100％＝16.6％or 17％.
(7)Standard deviation(SD,also represented by the Greek letter sigmaσor the Latin letter s)is a measure that is used to quantify the amount of variation or dispersion of a set of data values.In the case where x takes random values from a finite data set x 1 , x 2 ,…, x n ,with each value having the same probability,the standard deviation is
Where, μ is mean of the data set x 1 , x 2 ,…, x n .
Relative standard deviation(RSD),is a standardized measure of dispersion of a probability distribution or frequency distribution.It is often expressed as a percentage,andis defined as the ratio of the standard deviation σ to the mean μ (or its absolute value,｜ μ ｜)
Graphical techniques are an effective means of communicating the effect of an independent variable on a dependent variable,and can lead to determination of physical quantities.The independent variable is the cause and is plotted on the horizontal axis.The dependent variable is the effect and is plotted on the vertical axis.
Sketched graphs have labelled but unscaled axes,and are used to show qualitative trends,such as variables that are proportional or inversely proportional.Drawn graphs have labelled and scaled axes,and are used in quantitative measurements.
When drawing graphs:
(1)Give the graph a title and label the axis with both quantities and units.
(2)Use the available space as effectively as possible and use sensible scales-there should be no uneven jumps.
(3)Plot all the points correctly.
①Identify any points which do not agree with the general trend.
② Think carefully about the inclusion of the origin.The point(0,0)can be the most accurate data point or it can be irrelevant.
A best-fit straight line does not have to go through all the points but should show the overall trend.
The equation for a straight line is:
y ＝ sx ＋ c
Where: x is the independent variable, y is the dependent variable, s ＝Δ y /Δ x ,is the gradient and has units, c is the intercept on the vertical axis.
A systematic error produces a displaced line.Random uncertainties lead to points on both sides of the perfect line.
Figure 1-3 A best-fit of data points
Figure 1-4 Systematic error and random error