Method
Introduction
In this lab, I will be proving my ability to take very accurate measurements. I will take the measurements of samples of pure, one-element metals. Once I determine the specific heat of a metal sample, I will compare it with the actual value, and calculate my percent error. My goal is to have 5% error or less. After demonstrating my measurement proficiency, I will find the specific heat of two unknowns, in this case, glass and brass.
I must prove the credibility of my accuracy (how close an experimental value comes to the actual value) and precision (how close a series of measurements are) techniques to show that I am capable of taking credible and accurate measurements of the specific heat capacities of glass and brass. I will also use the correct number of significant figures (the digits in a number that matter) in my measurements, and after calculations, I will have a number with at least three significant figures.
Metric System
The French originally established the metric system in 1790. They called it Le Systéme International d'Unités. However, English-speaking scientists prefer to refer to it as the SI or International System of Units. The metric system is the official scientific measurement system because it is much easier to use than other systems(i.e. the English system) in converting between units. All SI units are based on 10 or multiples of 10. The metric system conveniently has seven base units from which all other units can be derived for anything you can think of. Isn't that neat? The seven base units are:
| What the Unit is Measuring | Name of Unit | Symbol |
| Length | Meter | m |
| Mass | Kilogram | kg |
| Temperature | Kelvin | K |
| Time | Second | s |
| Amount of Substance | Mole | mol |
| Luminous Intensity | Candela | cd |
| Electric Current | Ampere | A |
Smaller or larger measurements are sometimes more conveniently expressed in units with prefixes. For example, 8000 meters is easier to comprehend when rewritten as 8 kilometers. Here are my favorite(and just about all)prefixes used in converting very large or small numbers to a less confusing form:
| Prefix | Symbol | Meaning(multiply by) | Scientific Notation |
| yotta- | Y | 1 000 000 000 000 000 000 000 000 | 1024 |
| zetta- | Z | 1 000 000 000 000 000 000 000 | 1021 |
| exa- | E | 1 000 000 000 000 000 000 | 1018 |
| peta- | P | 1 000 000 000 000 000 | 1015 |
| tera- | T | 1 000 000 000 000 | 1012 |
| giga- | G | 1 000 000 000 | 109 |
| mega- | M | 1 000 000 | 106 |
| hectokilo- | hk | 100 000 | 105 |
| myria-* | my | 10 000 | 104 |
| kilo- | k | 1000 | 103 |
| hecto- | h | 100 | 102 |
| deka- | da | 10 | 101 |
| deci- | d | 0.1 | 10-1 |
| centi- | c | 0.01 | 10-2 |
| milli- | m | 0.001 | 10-3 |
| decimilli- | dm | 0.000 1 | 10-4 |
| centimilli- | cm | 0.000 01 | 10-5 |
| micro- | µ | 0.000 001 | 10-6 |
| nano- | n | 0.000 000 001 | 10-9 |
| pico- | p | 0.000 000 000 001 | 10-12 |
| femto- | f | 0.000 000 000 000 001 | 10-15
|
| atto- | a | 0.000 000 000 000 000 001 | 10-18 |
| zepto- | z | 0.000 000 000 000 000 000 001 | 10-21 |
| yocto- | y | 0.000 000 000 000 000 000 000 001 | 10-24 |
*myria- is now considered obsolete and most scientists don't use it.
In this lab, grams will be used as a standard of measurement for the weight of the metal samples, water, and other materials that need to be weighed. A gram is 1/1000 the weight of a kilogram. I can see this by referring to the table above.
Also, degrees Celsius will be used to measure temperature increase and decrease. The Celsius scale is derived from the Kelvin scale. Zero Kelvins is absolute zero, meaning that nothing can be colder than zero Kelvins(K), because all activity stops at that point. However, the Celsius scale is based on everyone's favorite compound: H2O; or water if you aren't familiar with the formula. The freezing point of water is 0°Celsius(C), while 100°C is the boiling point. While many people don't like to go outside in swimsuits at 0°C, it certainly isn't absolute zero. In fact, it is 273 on the Kelvin scale. So, 273 K = 0°C. Also, 1°C is the same measure of temperature as one Kelvin. To convert from Celsius to Kelvins, use the following formula:
°C = K + 273
Perhaps you would like to convert from Kelvins to Celsius. This formula will help you right along:
K = °C - 273
Joules will be the third metric unit used in this lab. The SI unit of heat and energy, joules will be very important in determining the specific heat of the metal samples. One joule is defined as the amount of heat needed to raise one gram of pure water 0.2390°C.
Significant Figures
Significant figures can be a little confusing when one first looks at them. But to explain, in short, a significant figure is any number that has meaning to a chemist (and many other scientists). In chemistry, a measurement consists of all the known digits plus a last one that is estimated. This estimated digit is sometimes referred to as the "doubtful digit". For example, if you are looking at a graduated cylinder that measures to the milliliter(mL), and have water in it that definitely goes past the 20 mL mark. In fact, it goes past the 23 mL line, and seems to be halfway between the 23mL and 24mL lines. So, the number that you can be sure of in your measurement is 23, and you might guess that the water measures another 0.5 milliliter. Your scientific answer would be 23.5 mL. This number has three significant figures, or numbers that have importance to you. Scientists have made rules so that they can decide whether a digit is significant or not. Here they are:
1. All nonzero digits in a measurement are significant. For example, all the digits in 23.5 mL are significant.
2. All zeros between nonzeros are significant. Example: 80,902 has five significant figures.
3. Leftmost digits appearing in front of nonzero digits are never significant. They act as placeholders, but that is all the information that they give. If the number is written in scientific notation, there is no need for the zeros. Example: 0.0000609 cm can be written as 6.09 x 10-5 cm. There are only three significant figures in this number.
4. Zeros at the end of a number and right of the decimal point are always significant. They represent a greater degree of accuracy in the measurement. Example: 67.00, 2.050 and .9000 all have four significant figures.
5. Zeros at the end of a number but left of the decimal point must usually be considered insignificant as placeholders. If the zeros in your measurement are significant, express the number using scientific notation instead. In this way, you can avoid confusion. Example: 300 has one significant figure. Although the zeros may be significant, we must assume that they are not. 42830 has four significant figures; again we must assume that the last zero is only a placeholder. If the zero is significant, 42830 should be written as 4.2830 x 104.
6. In two situations, the measurement involves an unlimited number of significant figures. The first is in counting objects. The second is with exactly defined quantities. Example: If you count three stones, you can be sure that there are exactly 3.0000… (to infinity and beyond) stones. If you are talking about one meter, you can be sure that there are exactly 100.00000000… centimeters in that meter, because "100 centimeters" is an exact definition of a meter. It is important to recognize when quantities are exact.
Scientists made these rules so that they would be able to raise the degree of accuracy of their calculations. If you are trying to determine the number of pages of the Sunday Oregonian needed to stretch the length of your school's football field, you carefully measure the width of the paper, finding it to be 52.35cm. However, for the length of the field, you decide that it is probably about 200m long, and use this as your measurement. The unpreciseness of the second number would severely limit the accuracy of your answer. These scientists also made rules for the addition, subtraction, multiplication and division of these significant figures.
Addition/Subtraction
The least precise measurement limits the preciseness of your answer.
Example:
However, the last two digits are not significant, because the measurement 7.3 reaches only to the tenths place. So, the answer can only reach to the tenths place. Rounded, this would give us an answer of 48.4.
Multiplication/Division
Your answer can only have the same amount of significant figures as the number with the fewest number of significant figures.
Example:
777.483 is the mathematical answer, but because the measurement 4.1 has only two significant figures, the correct scientific answer is 780 (rounding up because of the 7).
Generalities About Specific Heat Capacities
Heat is energy that transfers from one object to another because of temperature differences between them. It cannot be detected by the senses or instruments. Only the changes that heat causes can be detected and measured. When heat is added, temperature rises. When heat is taken away, temperature drops. Your refrigerator takes away heat and also prevents more heat from flowing in. Pretty nifty gadget, huh? Normally, if you put an ice cube in a hot cup of coffee, the ice cube melts, because the heat from the coffee flows into the ice cube, raising the temperature of the ice cube (which causes it to melt) and also slightly lowers the temperature of the coffee, because that heat was given to the ice cube. Heat is represented by the letter q. Here is an example:
The specific heat capacity, usually referred to as specific heat, is the amount of heat it takes to raise the temperature of one gram of the substance 1°C. Since water is a sort of base substance, the amount of heat it takes to raise one gram of pure water 1°C is defined as a calorie. Nowadays, we use joules instead. A joule is 0.2390 calories, and 4.18 joules are approximately 1 calorie. Usually, to determine the specific heat of any substance, you have to use the equation:
mCΔT = mCΔT
Now, let me explain what all the letters stand for. m stands for the mass of the substance, which can be measured using a balance. C stands for specific heat. ΔT stands for the change in temperature. In this lab, we are using mCΔT = mCΔT by putting the metal (in which the C is supposedly unknown) in water and measuring how the temperature changes. Here is an example:
If a piece of Metal X is heated to 100°C, then quickly placed in a cup of water which has temperature of 20.00°C, the heat of water and metal becomes 25.50°C. This sample of Metal X weighs 19.80g and the water in the cup is 60.00g. If the specific heat of water at 20°C is 4.1819J/g°C, then what is the specific heat of Metal X?
Answer:Metal X's specific heat is 0.932. Here is the work:
| water = metal |
| (60.00g)(4.1819J/g°C)(22.50-20.00) = (19.80)(C)(100-25.5) |
| 1380J = 1480g°C x C |
| C = 0.932 |
In this lab, we will use a procedure very similar to that of the example. Instead of metal X, we will use samples of aluminum, iron, lead, copper, and other metals. The metal will be boiled for a few minutes, which hypothetically makes it 100°C. Next, it will be quickly transferred to a styrafoam-cup calorimeter(look in the Equipment and Materials section to read more about this structure)where the new temperature will be read, and calculations to find the specific heat of the metal will be made. My answer needs to have at least three significant figures. For this reason, it is a good idea to make sure the water changes more than 1°C. One way to accomplish this is with a smaller amount of water if the amount of metal is smaller. To determine the specific heat of the metal in this lab, we have to measure the mass, initial and final temperatures and look up the specific heat of water. We must also find the mass and change in temperature for the metal sample.
Determining the Mass
In our "humble laboratory setup" we are only equipped with electric balances. These balances are capable of measuring very accurately to the hundredths place. We need to determine the mass of the metal and the water using these illustrious balances. First of all, we made sure the balance was functioning correctly by rezeroing it and having it measure a 200 gram weight. If it was exactly 200 grams, we knew that the balance was having a good day. Measuring the mass of the metal was simple. We placed it as close to the very middle as possible so that the balance wouldn't give us the wrong number. We took note of that mass and plopped the metal in the beaker to boil. Next, we took the bottom half of the calorimeter and set it on the balance, rezeroed the balance, then added a desirable amount of water, of which we found the mass, which usually ended up being something such as 87.09g or 97.25g. Previous to our discovery of the magic of the rezero function, we measured the mass of the cup, then the mass of the water and the cup, and finally subtracted the first measurement from the second measurement. This really was the only time that we needed to determine the mass of a substance, but using the electric balances was extremely handy as well as accurate.
Determining the Temperature
Speaking of accuracy, the accuracy capabilities of our thermometers are what most determines the accuracy of our measurements. The thermometers had a line at every tenth of a degree, so because of our doubtful digit capabilities with significant figures, our measurements always had four significant figures, since the water temperature was usually within a range of 16-25°C. Since the sample was in boiling water for a length of time, its initial temperature should hypothetically be 100°C, which has an infinite number of significant figures as it is an exact measurement. The final temperature of the sample and water will be the same, and it should also have four significant figures. To calculate the ΔT (change in temperature), the final temperature must be subtracted from the initial temperature. Unfortunately, this has only ever given us three significant figures for the change in temperature of water. We only need three significant figures in our answer, however, so it works out fine. Here is an example to illustrate this point (you don't know how much fun I have making these):
| | Aluminum | (Run #1) | |
| (Water)Mass | Sp. Heat | Temp.1 | Temp.2 | = | (Al)Mass | C | Temp.1 | Temp.2 |
| 93.88g | 4.1840 | 16.75°C | 19.72
°C | = | 17.98g | C | 100 | 19.72 |
Determining the Calorimeter Constant
Determining the Specific Heat Capacities of Standards and Unknowns
Somehow, I think I already covered this. However, it is a required subsection of this section, so I will explain again if it was not clear earlier! Alrighty then, here again are the steps to discovering the specific heat capacities of standards (I have referred to them as metals) and unknowns. The unknowns, one more time, are glass and brass.
- Determine the mass of both the water and the standard. This is done using the electric balances.
- Write these numbers in your mCΔT=mCΔT equation.
- Place the thermometer in the calorimeter and determine the initial temperature of the water.
- The initial temperature of the standard is always 100°C after it has been boiling in water. Write that down.
- After the transfer of the standard or unknown, record the final temperature and find ΔT
- Calculate mCΔT = mCΔT.
And there you have it! Six simple steps to finding the specific heat capacity of anything your heart desires.
Class Data Set
Error Analysis
Accuracy
To calculate my percentage error, I will follow the simple formula:
¦experimental measurement-accepted measurement¦
accepted measurement
For example, if I found the specific heat of chemical X to be 0.345 but the actual measurement was 0.357, I would use the equation like this:
0.357-0.345
0.357
and come up with a percentage error of 3.4%.
Did you like my method section writeup? Do you see a typo? E-mail me!
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