Experiment 2: Measurements and Conversion Factors |
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Experiment 2 is an extension of Experiment 1. This is how important measurements are in chemistry. Without measurements everything is guesswork. | |
A. Length A conversion factor is made from an equality. In our case the measurements are of the same edge of paper, so 10.875 inches = 27.4 centimeters. Conversion involves canceling one unit. So we can set up this way if we want cancel out centimeters. The fraction bar can be interpreted as divided by, per, for each, or for every. If we wanted to say inches for each centimeter, we can reduce the fraction this way: |
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B. Volume: 3. Calculate the conversion factors between cm3 and mL from your measurements. Let's say the measurements of the box were 8.5cm x 5.3cm x 3.4cm. That multiplies out to be 157.17cm3. Notice the answer has 5 significant digits, but we are only justified in using two because our measurements were had only two significant figures. In this case, when you fill the container with water and then pour the water into a 100mL graduated cylinder, it's going to be more than one full graduated cylinder. Just fill it somewhere between 80 and 100mL and read the exact amount and write it down. Empty the graduated cylinder and pour the rest of the water into it. Add the to volumes together. Let's say the volume added up to 159.4 mL. See data page below for how to record your volume data and make conversion factors. |
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For the last boxes above, write in the cubic centimeters calculated. In my example, it was 157.17cm3 (157.17cc). (your instructor my want this in 3 significant digits, which would be 157cc) The volume measured in graduated cylinder was 159.4mL. The ratio would be written as: 157.17cc 159.4 mL The Calculated Value (cc per 1 mL) is found by dividing both numerator and denominator by 159.4, which gives us 0.986cc per mL (using 3 significant digits). 0.986cc mL The reverse ratio would be the same figures but inverted: 159.4 ml 157.17cc The Calculated Value (mL per 1 cc) is found by dividing both by 157.17, to give 1.01mL per cc (written with 3 significant digits). 1.01mL cc |
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Percent Composition |
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C. Percent Composition You are going to be given some salt water. The lab manual says it has "unknown composition", however, the instructor and lab technician know the composition. It is just unknown to you. Your task is to find the percent composition and see if it matches the known value. The formula above indicates that if you need two quantities: grams of NaCl (salt) and the grams of the solution that holds that salt. So that's just two weights that you need. However, in chemistry you never weigh the grams of a powder (salt) or the grams of a solution directly on the balance. These have to be in some kind of container. So that means you usually have to know the weight of the container. In this lab, the solution is placed in an evaporating dish. So you need the weight of that so you can subtract it from the weight of the dish plus the solution. |
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Like we predicted. They want you to know the weight of the evaporating dish. It needs to be clean and dry because when you heat it, any water on it will evaporate and you want know how much. It says to put in about 3 mL of the salt solution. Because you are going to weigh it, you don't need an exact volume. If the task was to find %w/v (weight per volume), then you would have found the exact volume. But since we are finding weight (grams) of salt per weight (grams) of solution, we don't have to measure volume exactly. The 3 mL is just an amount that gives you enough to weigh without being so much that it takes a long time to evaporate. |
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g) %NaCl found Notice that when we got the denominator to 100 grams, we replaced it with "%" sign. The grams over grams is indicated with "w/w" (weight to weight or with the words, "by weight") |
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Exercises: Show methods clearly, label all units correctly | |
1. An unknown salt solution was made in the stockroom using 150.0 grams of salt and 500.0 grams of water. Do the following based on this solution. Notice that 150 g is not the same as 150.0 g. "150 g" is only accurate to two significant digits (15). If it was written as "150. g" then it would be 3 significant digits. Here it is "150.0 g" so that's 4 significant digits. |
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a) Calculate the %NaCl and %water by weight. |
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b) If you evaporated 88.840 grams of solution, what weight of salt should you get? |
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c) If a student needs to recover 15.605 grams of salt, what weight of solution should the student take and evaporate? This problem is like (b) except it's the reverse situation. Here we are given grams of salt (NaCl) and need to find the grams of the salt solution needed to give us this. We can use the same concentration of salt that we found in (a) and used in (b), except it needs to be inverted in order for us the cancel grams of salt and give us grams of solution. Let's use the last one from (b) but invert it 15.605 g NaCl x 100 g solution = ??? g solution 23.08 g NaCl So we invert it so that the g NaCl cancels. So multiply 15.605 by 100 and divide by 23.08 to get the grams of solution needed. The above grams of solution need to be rounded to 4 significant digits because our NaCl concentration is only to 4 significant digits. There is a hitch with this problem. |
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2. A student measured the width of his text with a cm ruler and with his hand. The student found that it is 21.5 cm or 2.10 "hands" wide. Write the conversion factors below: |
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Problems: A. Factor-Label Problems 1. Convert 552 grams to kg, mg, (lbs). |
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2. Calculate the cost of gasoline for a 420 mile trip if your car averages 20.0 miles/gal of gas, and the gas costs $0.95/gallon (I think this problem was written a long time ago, but the setup is the same). In solving these kind of problems, you look at the units of measurement and use them in a way to cancel out the units that are not in the final answer and to keep the unit(s) that are. Here are final answer is just dollars. So miles in the "420 miles" and the miles in "20.0miles/gal" must cancel. The gallons must cancel and we only need to keep dollars ($). Let's start with the 420 miles and the 20.0miles/gal. We need the miles to cancel, so we write it like this: 420 miles x 1 gal = 20.0 miles What this does is cancel miles and gives us gallons to travel that far. It makes sense because every time 20 miles divides into 420 miles that's another gallon. Notice I wrote "1 gal" instead of "gal". Both are OK, but "20.0miles/gal" means miles per 1 gallon. Now we can use the $0.95/gallon. This conversion factor is good because dollars is on the top and gallons in the denominator, which will cancel the gallons to travel the 420 miles: Here's what we have now: 420 miles x 1 gal x $0.95 = $ 20.0 miles 1 gal Here's the whole conversion. Miles cancel and so do gallons. Plus we end up with dollars. So we multiply all the numerators (420 x 1 x 0.95) and divide by (20.0 x 1). Remember significant digits. "20.0 miles" has 3, but 420 miles has just 2. "1 gal" and $0.95 are exact numbers because they are counted not measured. So the final answer should be rounded to 2 significant digits. |
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3. A small glass fish tank is 30.0 cm long, 15cm high, 20.cm wide. Calculate the volume of water needed to fill it to the top in mL, cc, and L. This one is pretty easy. The volume is 30.0cm x 15cm x 20cm, which is 9,000 cc. Since mL = cc, we also have 9,000 mL. (I'm assuming your instructor doesn't want you to use your conversion from earlier.) To get to liters (L), we need to cancel the "m" in "mL" 9,000 mL x 0.001 = ? L m Since m means milli, which is 0.001, we use that conversion factor. The "m" will cancel leaving us with just liters (L). Some instructors will show it this way: 9,000 mL x 1 L = ? L 1,000mL This works, too because "mL" cancels leaving you with just "L". Here you know that 1 Liter is the same amount as 1,000 mL. As long as the numerator and denominator are the same size, it works. |
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B. Percent Problems: Show your work using the factor-label method |
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1. A TUMS antacid tablet weighs 1.265 g, most of which is filler. Each tablet contains 0.500 g of the active ingredient, calcium carbonate | |
a) What is the percent by weight of the calcium carbonate in each tablet? In other words, what fraction of the tablet is calcium carbonate? More specifically, what fraction of the weight of the tablet is the weight of calcium carbonate (CaCO3)? |
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b) Write the percent value as two conversion factors with units and labels. I'm not sure here, but I think they want this: |
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c) How many grams of calcium carbonate are in 15.2 g of TUMS. Yes, the conversion factors above is handy for this problem. We are given the grams of the tablets, but they want grams of calcium carbonate. It looks like the left conversion factor from b) will cancel the tablet weight and give us the calcium carbonate weight. |
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2. If 6.6% of a class earns A's, how many A's are earned in a class of 92 students? Whenever you see "% of" you should think of multiplying because a fraction of something is calculated with multiplying. For example, if is said two thirds of this 600 dollars is yours. You can find that amount with 2/3 x 600. So in this problem "6.6% of a class" means 6.6% x the class. In this case it is 6.6% x 92. Or 6.6/100 x 92. |
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3. Rust is a compound that is 70.7% iron, and the rest is oxygen. How many grams of iron, and how many grams of oxygen are there in 680.0 grams of rust? The question is a little sloppy here. It says rust is 70.7% iron, but it doesn't say if that means 70.7% of the weight of rust is iron, or 70.7% of the volume in rust is iron, or that 70.7% of the number of atoms in rust is iron. So that's not a clear way to express %. Reading the rest of the problem, we might assume they mean percent by weight. So that should have been written as "rust is 70.7% iron w/w ( or by weight). So here it is 70.7% of the weight of rust (680.0 grams) is iron's weight. Mathematically, that's written |
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