Chemistry Lab measurement lab report, ASAP

Lab Measurements

Student Learning Objectives (SLOs)

Your lab report score will be a reflection of how well you meet the following SLOs:

· Understand the difference between accuracy and precision

· Apply knowledge of accuracy and precision, and your experimental results, to choosing the appropriate laboratory glassware for a particular task.

· Record measurements that reflect the full capability of the measuring device.

Pre-Lab

Before you perform this or any other experiment in this course, you’re going to take a small quiz to test your knowledge of them. The questions you receive will come from both the experiments’ backgrounds (to test your understanding of their rationale and theory) as well as their procedures (to see if you know what you’ll do in the lab room). The questions will focus on concepts and ideas, not trivial facts. For instance, we may ask how you take a reading from a measuring tool, but we would never ask how much solution you will dispense from that tool.

Here are some of the things you’ll need to know about for this experiment’s quiz:

1. Know what “accuracy” and “precision” are, and the difference between them.

2. Why variance occurs in measurements

3. The kinds of data you will collect, and how you will collect these data

4. How to properly use the equipment in this experiment. These things are described in the experiment’s appendix. Especially pay attention to the section on interpolation.

Background

Many of the experiments you’ll perform in this course will require to you measure the masses and volumes of the stuff you’re working with. For mass measurements, your choice of tools is simple: you’ll use a balance. For volumes, however, you will have a wider variety of options at hand.

The thing you select for volume measurements will generally be a piece of glassware of some kind, but as you’ll discover, lab glassware comes in many different shapes and sizes. Many of these have markings on them that suggest they could be used to measure a volume, but which piece is the best choice for what you’re doing? Before you can answer this question, there are two things you’ll want to know about your glassware: (1) can the piece you select measure things out with the accuracy you need and (2), can that piece measure things out with the precision you want? And before we can answer these questions, we need to know a little more about what it means for something to be “accurate” and “precise.”

Accuracy

Of these two concepts, accuracy is perhaps the easier to understand. It basically refers to how close to the “true” value a measurement is. To illustrate this, let’s say you put a weight you know is 500 kg on two different scales. One of these scales gives you a reading of 501 kg (not perfect, but pretty good), and the other 373 kg. The 501 kg reading is much closer to the actual mass of 500 kg, so the first scale is clearly the more accurate of the two.

Since the scale or whatever else you’re using to take measurements may be inaccurate (the scale that read 373 kg, for example), it is important to always perform your experiments/measurements on things you already know the properties of: a positive control. In our example, this would be the known 500 kg weight. Only after we’ve checked the equipment with a control would we use it to measure an unknown object/system/etcetera.

Precision

Precision is more-or-less synonymous with “consistent” and describes how close together multiple measurements/data points are. Going back to our scales, let’s say instead of two individual scales, you test out two groups of them. One of these groups is from Precision Scales, Inc. (we’ll call them PSI) and the other from Camp’s Roadside Analytical Products (CRAP). As for the first two scales, you put a weight you know has a mass of 500 kg on each. This is what you find:

The difference between the highest and lowest reading is 3 kg for the PSI scales and 26 kg for the Camp’s ones. Clearly, those from PSI are more consistent than those from the other company; that is, the PSI scales are more precise.

Accuracy vs Precision

Something that is accurate is not necessarily precise and vice-versa. In fact, it is possible for any instrument to be any of the following:

1. Accurate and precise

2. Accurate but not precise

3. Precise but not accurate

4. Neither accurate nor precise

We can visualize these better with the dart-board analogy. Xs are places where darts hit the dart boards.

Collecting Data: The Need for Multiple Samples

Besides the build quality of different brands of equipment, there are many different things that can cause data to vary. For example:

· The reading on a thermometer fluctuates slightly when a temperature is taken

· A single plant in a botanical study receives slightly more light than others in that same study

· A few drops of liquid cling to the inside of a piece of glassware instead of being dispensed

Because of things like these, it is considered poor practice to draw conclusions from a single observation of an unknown system or sample; a single data point might not reflect its “true” mass, height, etc. This is why proper science experiments always involve multiple measurements, trials, and/or tests. However, having multiple data points leads to an interesting question: if you take multiple mass or height measurements of an unknown and the measurements differ and you don’t know how much it “should” weigh or how tall it “should” be, how do you know which measurement is the true, accurate one? The answer is quite simple: you can’t. What, then, do we say about the thing we’re studying when we write our report on it?

Averages

Since there’s no way of knowing which data point is true and accurate, reports are generally written with two numbers. The first number is the average of several data points. If we needed to know how tall a plant grows when it’s given a new kind of fertilizer, we would grow several individual plants, measure their heights, and average them. If we had four plants that grew to 46.09 cm, 53.39 cm, 47.91 cm, and 50.09 cm in length, their average would be 49.62 cm.

Averages are nice and convenient, but they don’t tell us anything about the precision (that is, the variability) in the numbers used to calculate them. However, it is important to account for variability because it tells you how reliable your average is. This brings us to the second number we’ll include in our report. This second number will tell us if the data are tightly clustered around their average, or if they are widely spaced around it. To get it, we turn to statistics.

Statistics

Statistics is a branch of mathematics that is concerned with the analysis and interpretation of numerical data. Like chemistry, it is a broad topic that encompasses a variety of sub-topics and techniques. Although many of its concepts are beyond the scope of this course, there is one that you will become familiar with: the standard deviation.

Calculation of the Standard Deviation

The standard deviation of a set of numbers is, roughly speaking, a measurement of how much those numbers vary from their average. Thus, data that vary widely from their average would have a higher standard deviation than data that cluster tightly around their average. To calculate the standard deviation of a group of numbers, follow these steps:

1. First, calculate the mean (i.e., the average) of the numbers you are analyzing. In the case of the plant measurements mentioned above, their average is 49.62 cm.

2. Next, take one of the numbers used to calculate the mean, subtract the mean from it, and square the resultant number:

([value] – [mean])2

If we do this with the first plant measurement, we get 12.46 cm2. Do the same calculation on all remaining numbers.

3. Add together (or sum) all of the numbers that were calculated in the previous step. For the plants, this gives us 27.40 cm2.

4. Take the number of figures you have minus one and divide your answer to the previous step by this number. There are 4 figures in our plant example, so we would divide 27.40 cm2 by 3.

5. Take the square root of the previous step. In our example, this would return 3.02 cm

The equation that summarizes what you just did is:

where x with a line over it is the average of all the numbers used, xi is the value of any given number, Σ is a mathematical symbol that means “add them all together,” and n is the number of values you are analyzing.

If we expanded this equation and put all our example data values into it, it would look like this:

This final number calculated in the last step, 3.139 cm, is the standard deviation of the four plant length measurements.

This number we’ve just learned to calculate, the standard deviation, is the second number we mentioned earlier that we report along with the average. The reason we calculate it is to give the person who reads the report an idea of how reliable it is. If the numbers cluster tightly around their average with little variability, that average is more likely to be close to the “true” value than if the numbers are widely scattered around it.

As you’ll see later, in this experiment you will use the standard deviation to report how precise your glassware readings are. There’s more on what exactly you’ll calculate the standard deviation of in the Calculations section below.

If you have taken a statistics course, you have likely seen a similar version of the deviation equation in which the product of the third step is divided by the total number of figures, rather than this number minus 1. This alternate form of the equation is used to calculate the standard deviation of an entire population of data, as opposed to a sample of it. However, small sets of data such as the ones you will collect are more properly treated as samples rather than whole populations.

Comparing Numbers with the Standard Deviation

The range of plus and minus one standard deviation about a number (e.g., 49.62 cm ±3.02) will be used in this course to compare two numbers; that is, to say whether the two numbers are the same, or if they are significantly different from each other. Basically, if one number falls inside the standard deviation range of another, then the two numbers are not significantly different. For example, let’s say you calculate the density of a liquid to be 0.790 g/mL with a standard deviation of 0.020 g/mL, which gives you a range between 0.770 g/mL and 0.810 g/mL. Since the density of water, 0.998 g/mL, falls outside this range, you can conclude that the substance is not water.

Comparing two numbers that both have standard deviation ranges is somewhat similar. For the purposes of this course, if the standard deviation ranges around two numbers overlap, you may conclude there is no significant difference between them. The following example will illustrate this and also demonstrate how to use a control to evaluate results in a science experiment.

Earlier we said the group of plants with an average height of 49.37 cm was grown to test a new kind of fertilizer. Suppose now we also grew a second group of plants with a standard fertilizer we already know works. Since the standard fertilizer has known properties, the plants grown with it can serve as our control in this experiment. When grown under otherwise identical conditions, the plants in this group end up having an average height of 45.25 cm and a standard deviation of 7.47 cm (45.25 cm ±7.47).

Going just off the averages, it looks like the new fertilizer works better than the standard one; the average plant given new fertilizer was a little taller than the average plant given the standard. However, being proper scientists doing this experiment the proper way, we know that we have to consider the precision of our data as well as the average before we make any conclusions. Since the range of the second group’s standard deviation around the average (37.78 cm – 52.72 cm) overlaps with the range of the other group (46.23 cm – 52.51 cm), we cannot say the heights of the two groups of plants is significantly different.

If you’ve made it this far and still don’t get the importance of considering both the average and variability of a data set, consider the following tale. A statistician needed to cross a river, but he didn’t have a boat, there was no bridge, and he didn’t know how to swim. “No problem,” he exclaimed, “this river has an average depth of only 2 feet. I can just wade across it.” Sometime after he got about 1/3 of the way across, he drowned.

A Caveat

We should probably tell you that, in professional work, there are more advanced statistical techniques that are often used to account for the variability in data sets. When you take a statistics course, you will learn some of these techniques and how to apply them. However, in this course it will be sufficient to use the standard deviation in the manner described.

Precision as Significant Figures

As if the concept of “precision” was not yet complicated enough already, there’s one more aspect to it we need to tell you about. Besides the variability in numbers, it can also refer to the number of digits you use to record it. These digits are referred to as the significant figures (or “sig figs”) of that number. Significant figures include all digits except: (1) all zeros to the left of the first non-zero digit and (2) all zeros to the right of the last non-zero digit in numbers that do not have a decimal point. For example, consider the numbers 74900 and 0.0130. Although both of these numbers consist of a total of five digits, only three of the five are considered significant:

Since the “normal” way of writing a number can make it unclear how many significant figures it has, it is often preferable to report numbers in scientific notation instead. In this system, numbers are written as a coefficient between 1 and 10 multiplied by a power of ten. The number 74900 in the above example would be written as 7.49·104 in scientific notation; 0.0130 would be written as 1.30·10-2. In this system, all of the digits in the coefficient are significant figures.

These two aspects of “precision” are related to each other, for how precise a group of numbers are in one way affects how precise they are in the other. This can be seen if we go back to the height data for the first group of plants. As you know, all their heights were taken to the hundredths place, or the nearest 0.01 cm. Let’s say that instead of taking the measurements this precisely (with this number of significant figures), we only took them to the nearest tens of a centimeter; that is, to the nearest 10 cm. If we did that, their heights would be all be the same: 50 cm (because all four measurements round to 50).

With a standard deviation of zero, it may seem that four 50s have a very high degree of precision in the “variance” sense. However, this is not the case. Because the number “50 cm” is only recorded to the tens place, it effectively tells us the plants’ heights could be anything between 45 cm and 54 cm (because these round to 50). Therefore, the measurements taken to the tens places are actually “sloppier” than those taken to the hundredths despite their smaller standard deviation.

Experimental Overview

Now that you know all about accuracy, precision, multiple data points, and controls, we can finally get to the experiment you’ll do. You are going to evaluate the accuracy and precision of four pieces of glassware: an Erlenmeyer flask, a graduated cylinder, a burette, and a pipette. This will be done by:

1. Using each piece to measure out a quantity of water. The markings on the glassware will tell you how much water should be inside the container, or its “indicated” volume.

2. Using the mass of the water inside the glassware to determine how much water actually is inside it; its actual volume. This will require you to use the density of water to calculate its volume from its mass

Since the balances you will use to take the mass measurements are calibrated down to one milligram, we will assume the volume derived from the mass data is the more accurate.

Mass to Volume via Density

The density of an object is its mass per unit volume (or how much something weighs for its size). If you know the mass of a substance, you can use its density to calculate its volume. For example, suppose you are given a sample of metal you know has a density of 5.47 g/mL and a mass of 78.1 g and you need to know its volume. This can be done as follows.

So our 78.1 g piece of metal has a volume of 14.3 mL. Finding the volume of a sample of water is similar, but you’ll use the density of water, 0.998 g/mL at room temperature, for this calculation instead.

Your Approach

Here is a diagram of the general procedure you will follow to evaluate the Erlenmeyer flask and graduated cylinder:

This being a “proper” science experiment, it will be necessary for you to collect three sets of data for each piece you evaluate. Each set will consist of:

1. The mass of the empty vessel (since this requires the vessel to be completely dry, you'll only measure this once and this one reading will be used in all three sets)

2. A water volume read off the vessel’s markings (indicated volume). Some of these readings will require you to interpolate to collect them correctly. We describe what “interpolation” is in the appendix at the end of this document.

3. The mass of the vessel + water

Neither the burette nor the pipette won't fit on the balances in your lab room, so you’ll have to employ a variation on this:

Procedure and Data

Before you go forth to collect the data you'll need, there are a few things we want to tell you about organizing your data, and things to remember to make sure you get everything you need.

· Your procedure is divided up into four parts, one for each piece of glassware you're going to evaluate. When you record your data, give each part a heading so it's obvious what you're collecting data for.

· Every time you encounter a number in this lab, you have to record it. This includes the size of the glassware you use. It’s up to you to remember this; you won’t be prompted to do it.

· Reading the markings on the grad cylinder will require you to interpolate. Interpolation is described in the Techniques section.

· The balances you use in this lab are capable of measuring masses to the thousandths place (0.00X). Your data must be recorded to this many digits.

· Make sure you use the same balance for all mass measurements. Slight differences between the balances can affect the quality of your data.

Part A: Evaluation of an Erlenmeyer Flask

Before You Do Anything

Before you start experimenting, write your name on the name card attached to the front of your lab drawer, in the row that corresponds to the day and time you have your lab. This will be your drawer for the rest of the semester. It’s your responsibility to keep it clean and tidy.

Check your clothing. With the exception of your forearms and hands, does your clothing cover everything from the neck down? If not, you’ll need to get pants, or shoes or whatever you need that does. Your TA can direct you to people who can help you with this.

OK, Now The Experimenting

Follow the general procedure given above to collect the data you'll need to evaluate the accuracy of the markings on a 125 mL Erlenmeyer flask. You'll need three sets of data. Fill it about one-third full of water when you take your measurements. The level of water inside does not have to be exactly the same each time you collect a data set.

Record all your data with a pen. Real notebooks and logbooks are always kept in pen.

You may find your data a little easier to manage if you put it into a table. Here's an example table. You'll have to make your own for the next few parts:

	Empty Vessel Mass	Water Reading	Mass Vessel + Water
Trial 1
Trial 2	[same as trial 1]
Trial 3	[same as trial 1]

Part B: Evaluation of a Graduated Cylinder

Follow the general procedure given above to collect the data you'll need to evaluate the accuracy of the markings on a 10 mL Graduated Cylinder. As for the flask, you'll need three sets of data. Fill it about half-full of water for your measurements.

Part C: Evaluation of a Burette

Collect the data you’ll need to evaluate the accuracy of a burette. Use it to dispense between 10 and 15 mL of water for each data set. Again, you'll need three sets of data. If you’ve never used a burette before, see the Appendix at the end of this document; there’s more to using one than you might think.

Part D: Evaluation of a Pipette

Collect the data you’ll need to evaluate the accuracy of a pipette. As for the graduated cylinder, you'll need three sets of data.

We should probably tell you that part of your grade for this assignment will be based on how closely the results you get from the pipette match what they “should” be. It’s therefore in your best interests to review its use in the Appendix at the end of this document. We’ve singled the pipette out for this treatment because, of all the pieces you’re working with today, it tends to be misused more than the rest.

Two More Things

Before you leave, every piece of equipment in your drawer must be clean and organized like the picture below. Your TA may tell you to leave some things out to dry, but everything else has to be lined up where it belongs. If you're missing something, get a replacement piece from the stockroom. Part of your grade will depend on how well you do this.

Your Data Pages

Make sure you turn in your signed data page to your TA before you leave the lab. No credit will be given for data pages that have been either unsigned, or have been signed and left the lab before being turned in to your TA

Calculations

Glassware: Markings vs. Reality

Now that you have your data, your next task is to compare the “read” or “indicated” water volumes to the actual volumes, the latter being calculated from the water’s mass and density. We are assuming the calculated volume is the more accurate of the two, so it will be the actual volume.

This comparison begins with taking the water mass data and using it to calculate the volume of water dispensed. You’ll have to perform the following calculation on each data set you collect.

When you're done with these calculations, you'll have three "indicated" and three "actual" water volumes for each glassware piece. The next step is to take the difference between the readings for each piece, average the differences, and calculate their standard deviation. If we did this for the following data set, the calculations would look like this:

EXAMPLE

Trial	Indicated Volume (mL)	Actual Volume (mL)
1	53.4	56.1
2	52.1	48.8
3	55.4	57.3

STEP 1. Take the difference between the two volumes for each trial. Subtract the smaller number from the larger in each case:

STEP 2. Average the numbers you just calculated.

The bigger this average is, the more the glassware’s indicated reading tends to deviate from actual, which means the less accurate it is. In the calculations section of this experiment, when they direct you to “Calculate how much, on average, the _____’s indicated readings differed from the actual amount of liquid inside it (or dispensed from it)”, this is what they want you to do.

STEP 3. Calculate the standard deviation of the differences (in this case, the 2.7 mL, 3.3 mL, and 1.9 mL)

The bigger this number is, the more inconsistent the glassware’s readings are, which means the less precise it is. In the calculations section of this experiment, when they direct you to “perform the calculations needed to determine how precise the ____’s readings are”, this is what they want you to do.

Excel to the rescue!

Since these calculations can become tedious, unless you’re told to show your work you can use Excel to do them for you. See the "Math Operations in Excel" page of this Lab Book if you don’t know how. Averages are calculated from the =AVERAGE([cells]) function and standard deviations from the =STDEV.S([cells]) function. Of course, if you have another spreadsheet program you would rather use, you can use it instead.

Glassware: Piece vs. Piece

The final question you will address in this experiment is how the cylinder and pipette compare to each other with respect to their accuracies and precisions. All you have to do for this is look and see how their average and standard deviation compare to each other (are they bigger or smaller?)

Appendix

Interpolating

One of the fundamental skills we hope you’ll get out of this course is how to interpolate. This skill will let you take readings to a higher degree of precision than the actual, physical markings on a gauge, ruler, glassware, whatever can give you. The trick to this is to mentally divide the area between the physical markings and see where the reading lies on these. For example, consider the diagram of a bar and ruler.

The bar’s end falls somewhere between the 1.5 cm and 1.6 cm mark, and closer to the former. If we divide this area into ten segments in our mind’s eye with nine more imaginary marks, we can see the bar is about 1.52 cm long. Maybe it’s not exactly on the imaginary 1.52 cm line, but that’s OK; it’s the best we can do.

As a general rule, the digit you measure by interpolation will be 1/10 the value of the markings on the measuring tool. In this case, the markings were in 0.1 cm increments, so we interpolate to the nearest 0.01 cm.

Interpolation is, to an extent, subject to interpretation; therefore, it will not provide an absolutely “right” value. It is important, though, that you are consistent in how you take your readings.

For your viewing pleasure, interpolation is also described in the video at the following link: (starting about 2:00 minutes in).

https://www.youtube.com/watch?v=Kinj8wk2t9Q

Reading a Meniscus

Whenever you pour water or a solution made from water into a container, the water’s surface makes what we call a meniscus, a half-bubble shaped affair that curves upwards. The trick to reading one is to line up the meniscus’ bottom with the graduation marks on the glassware.

Take a look at the diagram of a graduated cylinder on the right. Though its markings are only to the tenths place (0.1 mL), by properly interpolating between them it is possible to read the fluid level to the hundredths place (nearest 0.01 mL). Since the meniscus is halfway, or perhaps a little more than halfway, between 6.5 mL and 6.6 mL, we might read it as either 6.55 or maybe 6.56 mL.

As you will discover in lab, reading these can be difficult at first and takes some practice. Don’t worry if you don’t get it exactly right your first few tries.

Significant Zeros

Whenever you record a number, always do it to the correct number of significant figures. This includes writing down a zero if the last digit in your reading is zero. For example, if the meniscus in a graduated cylinder falls exactly on the 5.1 mL index mark, you would record 5.10 mL, not 5.1 mL. The reason for this is that it lets the person who checks or otherwise has to work with your data know to what precision the measurement was made to; 5.10 mL means the measurement was taken to the hundredths place and is therefore more precise than 5.1 mL.

The Burette

Here’s how to use a burette to dispense a certain volume of fluid.

1. First rinse your burette with whatever solution you’re going to work with.

1. Fill the burette to a point above the 0.00 mL mark, then open the stopcock and let it drain past the 0.00 mL mark. You’re doing this to ensure the tip is filled with fluid and all the air has been purged from it; check to make sure it has. Draining it down to exactly the 0.00 mL mark is an unnecessary waste of time and is considered improper. Wipe the tip to remove any drops hanging from it.

1. Take an initial meniscus reading. Our burettes have markings in increments of 0.1 mL and are read to the hundredths place (0.0X) by interpolation. In this example, we’ve drained the burette down to 0.37 mL.

1. Figure out what you need to drain the burette to to get the amount of fluid you want out of it. If, for example, you’re told to dispense something between 1.0 mL and 1.4 mL, take the middle—1.2 mL in this case—and add it to the initial reading. 0.37 mL plus 1.2 mL is 1.57 mL, so we’ll drain it down to about 1.57 mL (give or take.)

1. Subtract the final reading from the initial to calculate the actual amount you added. As the initial reading cannot be 0.00 mL, the final cannot be 25.00 (or whatever the burette’s maximum volume is). During use, the last drop will often hang from the tip; dispense it by touching it to the side of the receiving vessel.

Using the burette in a tiration experiment is similar, except you will use some reaction indicator to tell you when you've dispensed enough liquid from it. The rules about taking an initial and final reading, and not making the initial 0.00 mL, still apply.

We’ll be looking for three main things in your data when we give you credit for any experiment where you use a burette:

1. All your burette readings must consist of both an initial and final value.

1. Your readings must be taken to the hundredths place (0.0X).

1. Your readings won’t all come out to the nearest whole mL. If you're using the burette correctly, this is unlikely in the extreme.

The Volumetric Pipette

Volumetric pipettes are glass tubes designed to dispense a certain quantity of fluid. They are available in different sizes that each deliver one specific volume, which is marked on it. In this course, if you are instructed to use one of these to dispense a volume of liquid, the amount you dispense will be equal to that of your pipette.

How to use a pipette

(This stuff is also summarized in a picture on the next page)

1. Attach a pipette filler or bulb on the top of the tube just firmly enough to get suction. Do not force it; the bulb or pipette filler should be easily removable (you will remove it in a subsequent step).

1. Rinse the pipette by drawing up the solution you will use it to dispense and let this solution drain into a waste container. Do this three times.

1. Without letting the tip touch the bottom of the container, pull the liquid up until it is above the index mark. Be careful when the bulb portion of the pipette is nearly full; once it is and the portion above it begins to fill, the level will rise very rapidly. This makes it easy for fluid to shoot all the way up into the vacuum pump or bulb.

1. Remove the bulb or pipette filler and cover the top of the pipette with your finger. You’ll have to manage this before the liquid drains below the index mark. Carefully let the liquid drain until the meniscus is at the index mark.

1. Hold the pipette over the container the liquid is being transferred to and let it gravity drain. The pipettes you will use in this course are of the “to deliver” type. This means that they are calibrated to deliver the indicated amount of liquid when they are allowed to gravity drain. A small portion of fluid will remain in the tip, but this is accounted for in the pipette’s calibration. For this reason, you must not “blow out” this last remaining portion of liquid. Forcing it out will compromise the pipette’s accuracy.

1. Touch the last drop hanging from the tip to the inside surface of the container.