Previously, we learned how to use the analytical balance, one of the chemist's most important measuring devices. This week, we will use the analytical balance and other measuring devices to determine the specific heat of some solid substances. Before we can intelligently measure specific heat, however, we must understand how scientists deal with measured quantities.
Measured Numbers Present a Problem
Suppose we wanted to describe a chemistry textbook, called Introductory Chemistry, to a person who has never seen the book. Among the information might be the following:
The book contains 19 chapters.
We get this information by opening the book and counting the chapters.
But, suppose we wanted to describe the length of the book's spine. To report this information about the book, we must measure the length, using a measuring device (perhaps a meter stick). We might report the following information:
The length of the book's spine is 260.4 millimeters.
We would obtain this information by lining up one end of the meter stick with the edge of the book, then reading the length from the meter stick at the book's other edge.
Now, aside from the obvious difference in the size of the two numbers (19 chapters; 260.4 millimeters), how do these numbers differ? The answer is this: The book has exactly 19 chapters, but the length of the spine may not be exactly 260.4 millimeters. The reason for this is simple: the
19 chapters were counted, but the 260.4 millimeters were measured. As long as we don't miscount, we will always get 19 chapters for our book. But, the measured length depends on the quality of the measuring device used. A better measuring device than our meter stick may indicate that the length is 260.35 millimeters; a poorer measuring device may indicate that the length is 260 millimeters. Of course, the length of the book is not changing as we use different measuring devices: the differences in length are all due to differences in the QUALITY of the measuring devices used.
Scientists realize that any quantity obtained with the help of a measuring device will only be as good as the measuring device used. Therefore, scientists agree to include information about the quality of the measuring device every time they report a measured quantity. Scientists do this through the use of significant figures . Significant figures are those digits in a number that give reasonably reliable information about a measurement. By counting the number of significant figures in measured quantities, we can make comparisons of the quality of measured quantities: the more significant figures a measurement has, the higher its quality.
So, we actually communicate three kinds of information when we report a measured quantity.
For example, our value of 260.4 millimeters conveys the following information:
The numerical value (260.4)

2
The units (millimeters)
The quality, as the number of significant figures (4).
We’ll use the following rules to determine the number of significant figures in a measurement:
1.
All nonzero digits are significant .
2.
All zeros that lie between two nonzero digits are significant .
3.
None of the zeros that lie to the left of the first nonzero digit are significant, regardless of the position of the decimal .
4.
Zeros to the right of the last nonzero digit are significant if they lie to the right of a decimal point .
5.
Zeros to the right of the last nonzero digit but to the left of a decimal point may or may not be significant, depending on the context .
Doing arithmetic with measured quantities also requires that we deal with significant figures.
Basically, the result of arithmetic with measured quantities is only as good as the least precise measurement used in the arithmetic. Apply the following rules to give you the correct number of significant figures for your calculations:
For addition and subtraction :
The answer must contain significant figures that extend to the right only as far as the term that extends the least to the right.
For multiplication and division :
The answer must contain the same number of significant figures as the term that has the fewest significant figures.
These rules require that you round the result of the calculation to the correct number of significant figures: When rounding, increase the least significant figure by one if the digit that follows it is five or larger.
Chemists and other scientists the world over use these rules to communicate the significant figures in any quantity associated with measurement.
Understanding Properties
How is one substance different from another? Well, the two substances may have different masses, or their colors may be different. They may differ in odor, or in their ability to react with oxygen. One may be radioactive, while the other gives off no radiation. We could observe many properties that, by their differences from one sample of matter to the next, help us to distinguish the samples, one from another.

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We can record properties of a substance from three sources:
1. direct observations by our five senses
2. measurement by an instrument
3. combination of two or more measurements in a calculation.
Can you think of one or two examples of properties that we know from each source?
Regardless of the source, properties fall into two categories, intensive and extensive.
An intensive property is one that relates to the essential nature or constitution of the substance.
Extensive properties, by contrast, depend on the amount of substance present, and the essential nature or constitution of the substance. In addition to density and specific heat, we find that color, temperature, malleability (the ability to be beaten into a flat sheet), and ductility (the ability to be drawn into a thin wire), are also examples of intensive properties. Mass, volume, and electrical charge are extensive properties. Since intrinsic properties are independent of the amount of the substance, they can be used to classify or identify the substance.
Your life experiences and the measurement exercise that we did on the first day of lab have provided you with the opportunity to make direct observations and measurements of both extensive and intensive properties. In this lab, you will have an opportunity to use measurement and calculation to obtain the specific heat and the density of several samples. Knowledge of these properties will then be used to identify one of your samples.
Measuring the Specific Heat of a Solid
The specific heat is a physical property that tells us how a substance's temperature will change when heat is added to (or removed from) a sample of the substance. As a mathematical formula, the definition of specific heat is: s
 g

H
 
T term meaning
S Specific heat

H heat added (or removed)
Units
Cal/g o cal
C g mass of the sample

T change in the sample's temp. g o
C
By measuring

H, g, and

T for a sample, we can solve for S. Although we have measuring devices to measure mass and temperature, we have no measuring device for

H , the heat added.
Unless we can figure out a way to get

H, we can't solve for S. (Why?) Fortunately, chemists have found a way to avoid this problem: by using a calorimeter, the transfer of heat can be controlled, allowing us to calculate the amount of heat transferred to (or from) our solid sample.

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A workable calorimeter design is shown at left.
The polystyrene cups insulate the water from the rest of the lab, so heat is not transferred from water to lab, or from lab to water. If we add a heated solid to the water, however, the water will absorb heat from the solid, resulting in a rise in the water's temperature. The equation for this process is given below:

H = Sg

T or

H = (1.00cal/g o
C )g(T f
- T i
) where g = the mass of water in the calorimeter
T f
= the water's final temperature
T i
= the water's initial temperature
But (and here's the key point), the

H absorbed by the water can only come from the hot solid, so -

H is the amount of heat lost by our solid sample. This loss of heat by the solid results in a drop in the metal's temperature.
Note that you should use TWO ringstands in this lab. One supports the thermometer used to measure the temperature in the calorimeter, as pictured above; the other will hold the beaker for the boiling water bath.
We can then use the following equation to get the specific heat for our solid sample: s
 g



H

T
. where

H = the heat transferred, as calculated above
g = the mass of the metal

T = T f
- T i
T f
= the metal's final temp.
T i
= 100.0 o
C, metal's initial temp.
I. Procedure for Determining Specific Heat
1. You may work in teams of two . Obtain a calorimeter and a solid sample from the stockroom.
2. Write the sample's number or letter designation here: ___________
3. Set up a Bunsen burner and ringstand to heat a 400 mL beaker. Fill the 400 mL beaker 2/3 full of tap water, light the burner, and bring the water to a boil.
4. While the water is heating, weigh the solid sample. Use a plastic weighing boat to hold the sample. Record your data on the next page:

5 mass of empty weighing boat g mass of weighing boat + sample g mass of sample g
5. Pour the metal into a large test tube after you have the masses.
6. Place the test tube (with sample) into boiling water for about 10 minutes.
7. While the sample is heating, weigh the calorimeter empty, add 40 mL of water, and then weigh again. Record your data: mass of empty calorimeter mass of calorimeter + water
g
g mass of water g
8.
Set up the calorimeter as shown in the previous drawing.
9.
Record the water's initial temperature to the nearest 0.1 o
C.
10.
Using a paper towel, remove the test tube from the boiling water, wipe it dry, and pour the entire solid sample into the calorimeter. What error would result if you splashed some of the water out of the calorimeter when you added the metal sample? Replace the calorimeter lid and stir with the stir rod as you read the thermometer. Record the highest temperature measured: _ o
C.
11.
Move the solid from the calorimeter to a weighing boat, and pat it dry with a paper towel.
II. Procedure for Density - Another Physical Property
Like specific heat, density is determined by measuring properties, which are then used in a calculation. The equation for density is simple: d = m/v where d is the density, m is the mass, and v is the volume. If we can measure the mass and volume of our sample, we can get the density.
A. Volume of a Soda Can
Before Archimedes made his historic discovery, measuring the object’s dimensions and then using a formula developed by mathematicians could determine the volume of an object. Each shape required a different formula. Consider the following information for a cylinder:
Both r (radius) and h (height) can have units of cm, because they are lengths.
V =
 r
2 h gives the volume in units of cm
3
.
1. Using careful measurements and the information about cylinders given above, determine the

6 density of the soda in a 12 oz. (355 mL) soda can.
2. Determine the density of the soda in the soda can by using a graduated cylinder to measure the water required to fill the can. Repeat the measurements two more times, so that you can obtain an average value.
3. Determine the density of the soda in a can using Archimedes' discovery, and a graduated cylinder large enough to hold the entire can. Be very careful here: the big graduated cylinder costs over
$100!
B. Volume of a Metal Sample
After we calculate the specific heat of our unknown metal sample, we might want to use it to identify our solid as one of the following metal elements: lead (Pb) silver (Ag) zinc (Zn) tin (white; Sn) bismuth (Bi) gold (Au) magnesium (Mg) copper (Cu) calcium (Ca) iron (Fe) lithium (Li) nickel (Ni) aluminum (Al)
The CRC Handbook contains values for the specific heats of these elements. (Newer editions report values in J/gK ; older versions report cal/g o
C . You may have to convert units to complete the data table in your formal report.) Inspection of these values, however, shows that several of them are almost identical. Therefore, the specific heat alone would not allow us to identify our sample.
When chemists are confronted with a situation like this, they often resolve the problem by measuring a second physical property. When two properties are available, the chances of finding a single metal that exhibits both the properties becomes much greater.
1. Carefully measure the mass and volume of your unknown metal sample, for the purpose of determining the density of the sample. Repeat the measurements two more times, so that you can obtain an average value.
2. Dry the sample and return it to the stockroom. If your sample came with special information, be sure to return the information sheet with your sample.
Your lab report is due next Tuesday at 6:30 p.m. Be sure to include all data and show all calculations used to obtain your results.