Measuring Mass and Volume

Why do scientists wony about units The National Aeronautics and Space Administration (NASA) recently was reminded of just why keeping track of units is so important. In 1999 a 125 million satellite was lost in the atmosphere of Mars because scientists made some improper assumptions about units. NASA s scientists at the Jet Propulsion Lab (JPL) in Pasadena, California, received thrust data from the satellite s manufacturer, Lockheed Martin Aeronautics in Denver, Colorado. Unfortunately, the Denver scientists used American units in their measurements and the JPL scientists assumed the units were metric. This mistake caused the sateUite to fall 100 km lower into the Mars atmosphere than planned. The spacecraft burned up from the friction with the atmosphere. 

Measuring and using units correctly is very important. In fact, it can be critical, as we have just seen. For example, a Canadian jet almost crashed when the tanks were filled with 22,300 pounds (instead of kilograms) of fuel. Calculations for distance were based on kilograms, and the jet almost ran out of fuel before 

Unit Abbreviation Gram equivalent Exponential equivalent 

Note that multiplying a number by 1000 is the same as multiplying the number by 10 and can be done simply by moving the decimal point three places to the right  

To change milligrams to grams, we use the conversion factor 1 g/1000 mg. For example, we convert 155 mg to grams as follows  

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Calculate the density of objects by using their measured mass and volume. 

The density of a substance can be calculated from its measured mass and volume. The examples that follow show how this can be done and demonstrate more of the unit analysis thought process. 

Besides apparatus for measuring mass and volume, there are a number of other items of equipment commonly used in analytical procedures. 

The volume appeared to increase by 2.6 mb when the medallion was added, so 2.6 mb represents the volume of the medallion. Now we can use the measured mass and volume of the medallion to determine its density ... 

Measurements are made using appropriate equipment or instruments. The array of equipment and instrumentation used in analytical chemistry is impressive, ranging from the simple and inexpensive, to the complex and costly. With two exceptions, we will postpone the discussion of equipment and instrumentation to those chapters where they are used. The instrumentation used to measure mass and much of the equipment used to measure volume are important to all analytical techniques and are therefore discussed in this section. 

There are a few basic numerical and experimental tools with which you must be familiar. Fundamental measurements in analytical chemistry, such as mass and volume, use base SI units, such as the kilogram (kg) and the liter (L). Other units, such as power, are defined in terms of these base units. When reporting measurements, we must be careful to include only those digits that are significant and to maintain the uncertainty implied by these significant figures when transforming measurements into results. 

Density can be found in a straightforward way by measuring, independently, the mass and volume of a sample (Example 1.5). 

Mass and volume often can be measured easily, and density is then calculated using Equation. The equation can also be rearranged to find an objects volume or mass, as Example illustrates. 

Measure the mass and volume of several different objects. 

By measuring the mass and volume of blocks of wood, can the identity of the wood be determined ... 

It is common to achieve accuracies of 1 part in 105 in using equation (1.1) with pycnometers as small as 5 cm3 and routine measurements can achieve 1 part in 104. However the main sources of error in assigning density to a particular compound in a particular state arise from factors other than the measurment of mass and volume. See Section 1.4.1... 

The pharmacist often uses measurable quantities such as density and specific gravity when interconverting between weight (mass) and volume. 

The measurement system that you will most likely encounter is the SI (Metric) system. Each quantity (such as mass and volume) has a base unit and a prefix that modifies the base unit. The prefixes are the same for all quantities and are based on a decimal system. Below are some basic SI units we will introduce others in later chapters ... 

The density of a substance may be obtained simply by measuring its mass and volume and making the necessary calculation. The units for mass are typically given in grams, while the units for volume may be milhhters (cubic centimeters) or liters, depending on the physical state of the substance. The volume of solids and liquids is given in cubic centimeters or milliliters. 

Measuring To calculate density, you need to know both the mass and volume of an object. You can find the volume of an irregular solid by displacing water. 

The thickness of wire often is measured using a system called the American Wire Gauge (AWG) standard. The smaller the gauge number, the larger the diameter of the wire. For example, 18-gauge copper wire has a diameter of about 0.102 cm 12-gauge copper wire has a diameter of about 0.205 cm. Such small diameters are difficult to measure accurately with a metric ruler. In this experiment, you will plot measurements of mass and volume to find the density of copper. Then, you will use the density of copper to confirm the gauge of copper wire. 

Results Exposure testing and end-point measurements were interpreted to determine mass and volume changes for the product compounds Viton ETP, EPDM, and neoprene. EPDM proved to be the most suitable material for process water service, while Viton ETP was found to be the most suitable material for product gas service in the GPCR process environment. 

Although it is not explicitly stated in the above quote, it was clear from Craig s interview that what he wanted were numerical examples. Other students made their preferences known in their responses during tutoring sessions. In a discussion of the differences between general chemistry and physical chemistry courses, the interviewer talked about problem-solving questions that involved calculating the density of a sample from measurements of the mass and volume of the sample. He then noted ... 

EXAMPLE 3.3 Excluded Volume of Bovine Serum Albumin from Osmotic Pressure Measurements. A plot of 7r/c versus c for an aqueous solution of the bovine serum albumin molecule at 25°C and pH = 5.37 is shown in Figure 3.6. The molecule is known to be nearly spherical and uncharged at this pH. Evaluate the molecular weight and the excluded volume of this protein from the intercept and slope of this line, 0.268 torr (g kg-1)-1 and 1.37 10 3 torr kg2 g 2, respectively. From the particle mass and volume, estimate the partial specific volume of the solute in solution. The specific volume of the unsolvated protein is about 0.75 cm3 g 1 does the solute appear to be solvated ... 

The density of a ceramic or metal powder is determined with the help of a so-called pycnometer. The density of a piece of ceramic or metal material can be determined by measuring its mass and volume in order to obtain the volume, the object is immersed in a liquid. For plastics a number of liquids with known densities are used and you determine whether a plastic floats, sinks or is suspended in a certain fluid. This will tell you that its density is less than, more than or equal to that of the liquid respectively. 

There is of course more than one chain of comparisons and all the component measurement processes associated with the chemical measurement need to be considered. These include physical measurements, such as mass, volume, etc., and chemical issues, such as identity and amount, which together constitute an amount of substance (see later). The traceability of component measurements needs to be established at a level of uncertainty that is consistent with the required overall uncertainty of the final measurement. Components such as temperature, and even mass and volume measurements, often contribute little to the overall uncertainty and thus can be simply and easily addressed. 

Matter comprising biomolecules has distinct physical and chemical properties, which can be measured or observed. However, it is important to note that physical properties are distinct from chemical properties. Whereas physical properties can be directly observed without the need for a change in the chemical composition, the study of chemical properties actually requires a change in chemical composition, which results from so-called chemical reactions. Chemical reactions encompass processes that involve the rearrangement, removal, replacement or addition of atoms to produce a new substance(s). Properties of matter may be dependent (extensive) or independent (intensive) on the quantity of a substance, for example mass and volume are extensive properties of a substance. 

The concept of atoms and molecules emerged in the earliest days of modern chemistry from meticulous measurements of mass and volume. These were the only probes of matter available to early workers. The reality of atoms and molecules was established both by the explanatory power of the atomic model and by experimental evidence of microscopic entities, with Einstein s famous interpretation of Brownian motion in 1905 providing irrefutable confirmation of the atomic hypothesis. 

Together with information on the sample pellet density (from measurements of its mass and volume) and heat capacity (see below), the thermal conductivity of the sample could be calculated. 

When you use a calculator to find a result, you must pay special attention to significant figures to make sure that your result is meaningful. The calculator in Figure 18 was used to determine the density of isopropyl alcohol, commonly known as rubbing alcohol. The mass of a sample that has a volume of 32.4 mT was measured to be 25.42 g. Remember that the mass and volume of a sample can be used to calulate its density, as shown below. 

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