Experiment 1: Measurement of Length, Volume, and Mass 

The first experiment addresses a critical part of science, which is to communicate clearly. Words like "big, small, heavy, and light" might be good enough for every day conversation but they can easily be misleading because they may mean something different to different people. In science you want to communicate so that everyone gets the right meaning. Measurement is one way to make yourself clear. Of course, that all depends if you can measure items properly. Experiment 1 gets you started with that skill. The building of a ship like the Titanic involves thousands of measurements. They are all crucial to the integrity of the ship. Measurements are also critical to the operation of the ship. The tragedy of the Titanic can be attributed to a lack of attention to measurements. 

Objective 1: Use measuring tools correctly. In this experiment "tools" mean meter stick, graduated cylinder, and analytical balance. These measure length, volume, and mass (weight). These tools let you communicate accurate facts about items such its size, volume, and mass. A lot can be learned from these simple measurements. 

Objective 2: Read and record measurements correctly (significant digits and unit). This means you try to get the most out of the tools mentioned above by being as accurate as possible. The words, "significant digits", mean being clear about its accuracy; neither underestimating or overestimating the accuracy. The words, "and unit", means don't forget to include the unit of measurement (its dimension). In math classes, you normally deal with abstract numbers like "5, 3, and 7.5"; however, chemistry deals with measurements, so "5, 3, and 7.5" are not good enough. You have to say 5 somethings, 3 somethings, and 7.5 of something. Writing "7.5" instead of "7.5 cm" is wrong because "cm" is just as important as "7.5" 

Example of the value of measuring: Lets say you think you found a natural diamond like the one in the picture. To help confirm its identity and value, you need to make accurate measurements of length, width, height, plus volume and mass. Let's say the shortest distance across was 1.6 centimeters. The "1" in this measurement says it is at least 1 cm. The ".6" says it is also has 6 tenths of a centimeter. Both of those numbers reflect its size and are significant. So this measurement has 2 significant digits. Don't round it to 2 cm because then you've not used the ruler to its full accuracy. If you measured it as 16 millimeters (mm), you still have 2 significant digits and the accuracy is the same. But don't report 16mm as 16.0mm because that implies you measured it to the nearest tenth of a millimeter showing 3 significant digits of accuracy. In math 16 and 16.0 are the equivalent, but in chemistry, they are very different because 16.0mm is ten times more accurate than 16mm.  
A pure diamond has a density of 3.52 grams per milliliter. So to find the density of our suspected stone, we need its volume and mass. So let's measure volume. Because the diamond is irregularly shaped, you can't use geometry, but you can measure volume by placing the diamond in a graduated cylinder with an amount of water that you've measured accurately. Let's say it was 3.4 milliliters (mL). Dropping the diamond into the water will raise the level. You measure the level again and it is now 7.5 milliliters (mL). Again, don't round off any of these numbers. The difference in volume is 4.1mL (7.5mL3.4mL) which is the diamond's volume. Notice the answer of 4.1 mL has 2 significant digits. Next you need to weigh it.  
An analytical balance in this lab is capable of measuring to one thousandth of a gram or smaller. Let's say the digital display says "14.300". It would be a mistake to write that down as 14.3 grams because the analytical balance actually measured its mass to the nearest thousandth of a gram giving us 5 significant digits of accuracy. An $80 balance can measure 14.3grams, but it takes a $2,000 balance to measure 14.300grams. Going from 14.3g (3 significant digits) to 14.300g (5 significant figures) is increasing the accuracy 100 fold so don't drop these zeros. To get density we divide our grams by the milliliters. OK, so that is 14.300g / 5.8mL, which the calculator says is 3.4878049. Do we report our density as 3.4878049 grams per mL? No, because that would imply accuracy of 8 significant digits. When dividing or multiplying two measurements, the final accuracy is only as good as the least accurate value. So for "14.300g/5.8mL" the "5.8mL" has only 2 significant digits meaning we are only justified to use 2 significant digits in our answer. So 3.4878049g/mL would get rounded to 3.5g/mL. Hey that's pretty close to the pure diamond density of 3.52g/mL. So we may have a valuable natural diamond. Again, this knowledge comes from making accurate measurements and recognizing how accurate (how many significant digits) each measurement gives us. When we add, subtract, multiply, or divide, we also have recognize how accurate our final answer is (how many significant digits). A tutorial on significant figures is in the lecture at this address: (click browser's back arrow button to return here) 

Objective 3: Associate metric units with the quantity being used. Metrics is one of the lecture tutorials. You can visit it by following this link: 

A. Length and Volume. For a rectangular object, when you multiply by length (L) and width (W), you get the area of the top (or bottom) of the object. For example, here we have a length and width of 5 and 4 centimeters, which gives us the area of 20 square centimeters (cm^{2}). If the height was one centimeter, each of those square centimeters are considered cubic centimeters giving us a volume of 20 cubic centimeters (cm^{3} or cc). If the height were 4 centimeters, then there would be 4 layers of 20 cm^{3} each. So by multiplying by the height, we get the total number of cubic centimeters of 80 cm^{3}. 

This activity is good for three reasons. First, it gives plenty of practice of measuring distance and also shows how there are often two ways to accomplish a measurement. In this case we can find the volume of the box by using geometry or by filling the object with water and then measuring water's volume. The third benefit of this activity is to show that milliliters (shown on the markings on a graduated cylinder) are equivalent to the cubic centimeter volume you get by calculating its volume through diameter and height measurements. Here you prove to yourself that cubic centimeters (cm^{3} or cc) are the same as milliliters (mL). After proving it to yourself, burn it to your memory. You will use this fact a lot.  
There's a tripping point with this section. did you notice that the height is measured in millimeters (mm) and in centimeters (cm)? In order to get cubic centimeters, each measurement has to be in centimeters. In other words cm^{3} is "cm x cm x cm". So be sure to convert mm to cm. The quick way is to move the decimal one place to the left. Let's say the height was 38mm. That would be same as 3.8cm because centimeters are 10 times larger than millimeters. Here is a method you will use for more complicated conversions. 

B. Length: 

Note that volume in the metric system comes from the length of the meter. One tenth of a meter (1 decimeter) made into a cube is called a cubic decimeter which was given the name "liter". A cubic centimeter is a thousand times smaller than a liter, so it is called a milliliter (milli=thousandths). So it's fairly easy to visualize the size of metric volumes. For example, 4 liters could be a box 1 decimeter by 1 decimeter by 4 decimeters. In centimeters that would be 10cm x 10cm x 40cm. English units of volume like pints, gallons, or teaspoons, have no easy way to know their actual dimensions. For example, a gallon is a cube 6.13579 inches on each side. There's no rhyme or reason with English units and no way to remember these conversions. 

a. Number of drops in one mL. Because water molecules have such as strong pull on each other, they form drops easily. Other liquids like alcohol or oil have more difficulty forming drops, so what you discover about the count of drops with water doesn't apply to other liquids. 

When you have your eye at the correct level, the lines on the graduated cylinder will look horizontal rather than curved. Water has a tendency to creep up the inside wall of the graduated cylinder. So the water surface won't be flat. It will be bowed. The bottom of the curve is where you read the water's volume. They call this curved surface the meniscus from the Greek word meniskos meaning "crescent" like the crescent of the moon. Here the meniscus is just above the 2 mL mark. It's close enough to be called 2 mL.  
So you are first going to count the drops to bring an empty 10 milliliter graduated cylinder up to 2 mL of water and record that count as Trial#1. Then you will count the drops needed to bring the water level from 2mL to 4mL. Record that number as Trial#2. To find the average, just add them together and divide by two. Remember that answer is average drops it takes to make 2.0 mL. The next line is the average number of drops in 1.0 mL. That's easy, just divide the average by 2, to get drops in 1.0 mL and you're done. You might be asking, why are we doing this exercise? Well, counting drops is a quick way to measure small amounts of liquid. For example, let's say you come up with 30 drops of water per 1.0 mL. That means if you needed one tenth of a milliliter, you could simply use 3 drops to get that tenth. Or you can spend a couple hundred of dollars to get a micropipette that can measure a tenth of a milliliter. Now you know why counting drops is a good idea. 

A teaspoon is an odd measurement. Originally a teaspoon was used just for stirring tea. Later it became a volume measurement that was 1/3 of a tablespoon. With liquids a teaspoonful is simply filled to the brim. With solids, you can go over the brim. So there are heaping teaspoons and level teaspoons. Since this activity is with a liquid, then it's filled to the brim, which is basically a level teaspoon. You might realize there are at least a couple of ways to approach this. You can fill the spoon with water and then pour it into a graduated cylinder. Or you can start off with a known amount in the graduated cylinder, and use the cylinder to fill up the spoon. The amount the water level went down in the graduated cylinder is how many milliliters a teaspoon holds. You can also look up the number of mL in a teaspoon on the Web, but that takes the fun out of proving it to yourself. As you will learn later in this experiment, you can repeat the measurement to get more accuracy. 

For a few hundred years, the analytical balance looked like the one in the picture. The item of unknown weight would be put on one of the pans, and small cylinders of known mass would be added to the other pan until it balanced. The small case on the bottom left held these small brass cylinders. It could take several minutes to weigh something. After balancing, you would have to add up the mass of all the little brass cylinders you used to balance the mass of the unknown item. Modern digital balances make weighing very easy. There's just one pan to place the item on. You don't need to have a box of known masses to balance out the weight of your unknown. The balancing is done automatically and internally. Plus readout is directly in grams with 3 or 4 decimal places. 

This is a common sense type of warning. Weighing paper not only protects the pan from corrosive chemicals, it also makes it easier to pick up the powder after it is weighed. Weighing paper has a smooth finish so that powder doesn't stick to it. A weighing boat is similar except it has a lip around it to keep powder from spilling. There are two reasons not to put hot objects on the balance pan. First a hot item can damage the pan. Second, the air around the hot item warms up and then gets pushed up by the cooler room air. This causes air currents around the balance pan, which causes the gram readout to fluctuate. 

Average weight of a penny. Warning: The weight of the penny has changed over the years. If you use a penny that has a date before 1982, it is 24% heavier than pennies made after 1982. Significant digits: Let's say one of your pennies weighs 2.527 grams. You have 4 significant digits of accuracy. Let's say you added up 5 pennies and get 12.654 grams. That has 5 significant digits. You have gained some accuracy by repeating the measurements and adding up masses. To find the average, divide by 5. The calculator says 2.5308000. The accuracy of division or multiplication is only as good as the number with the least number of significant digits. 12.654 g has 5 significant digits and "5" looks like only one. However, 5 was not a measurement. It was a count, which is exact. So your final answer will have 5 significant digits, which would be 2.5308 grams (remember the grams). If you had weighed 3 pennies, the total would have been under 10 grams, so the accuracy would be only 4 significant digits because it would have stayed under 10 grams. 

The question "Would you expect each mass to be identical?" requires some interpretation. Technically, no two items that humans manufacturer will ever be identical in mass. The only way to guarantee equal mass is that you have equal numbers of the same kind of atoms. A better question might be, "Would you expect to find a different mass for each penny on the balance you are using?" Some cheaper balances only weigh to the nearest tenth of a gram (Like one on the left). You may not see any mass variation between the pennies. However, with a balance that measures to the thousandth of a gram or smaller, you should see a difference because even a fingerprint can weigh a thousandth of a gram. Pennies straight from the mint are obviously much closer to each other in mass. After they get used, some will gain weight from oxidation (oxygen combining with the metal) or from dirt, oil, or other contaminants. Some pennies may get scraped and loose mass. So generally, the older they get the farther away from the standard weight they become.  
b. Average mass of an aspirin tablet. Like the pennies, you weigh them separately. Add up their weights and divide by three to find average. Weighing them separately gives you more practice at using the analytical balance. When you don't need the practice, I'd say just place them together and weigh them. Divide by three and then you'd have the average mass. Be sure to report the average to the correct number of significant digits. That will depend on the digits in the total mass. Don't forget to show the units of grams, or it's wrong. 

Doing measurements correctly can make people happy or sad. Imagine telling a carpenter the height of your ceiling was 8 feet and you want a floortoceiling bookshelf. He builds it based on your measurement. When installing it, he finds out that your ceiling is lower than you said. You either didn't use enough accuracy or measured it incorrectly. Either way he is cursing. You both would have been happier if you measured it correctly and reported the accuracy of your measurement. So in future labs remember measuring is your second most important task. Safety is first. Of course, sometimes measuring incorrectly can jeopardize safety. So value these measuring skills and put them to work. For additional instruction on measurement, visit the measurement tutorial in the lecture class: 
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