CHE: 101 - Chapter 2: Chemistry and Measurements
Exact definitions -
- The numbers in any definition between 2 metric units or between 2 U.S. system units are exact. Both numbers in a definition are exact, they are not used to determine significant figures. For example, the equality of 1 g = 1000 mg is a definition, which means that both of the numbers 1 and 1000 are exact.
Conversion Factors from a Percentage, ppm, and ppb -
A percentage (%) is written as a conversion factor by choosing a unit and expressing the numerical relationship of the parts of this unit to 100 parts of the whole. - For example, a person might have 18% body fat by mass. The percentage quantity can be written as 18 mass units of body fat in every 100 mass units of body mass. Different mass units such as grams (g), kilograms (kg), or pounds (lb) can be used, but both units in the factor must be the same. - When scientists want to indicate very small ratios, they use numerical relationships called parts per million (ppm) or parts per billion (ppb). The ration of parts per million is the same as the milligrams of a substance per kilogram (mg/kg). The ratio of parts ber bills equals the micrograms per kilograms (ug/kg, mcg/kg).
Equalities and Conversion Factors Stated Within a Problem -
An equality may also be stated within a problem that applies only to that problem. For example, the speed of a car in kilometers per hour or the price of onions in dollars per pound would be specific relations for that problem only.
Measuring Length -
An ophthalmologist may measure the diameter of the retina of an eye in centimeters (cm), whereas a surgeon may need to know the length of a nerve in millimeters (mm). - If we compare the lengths of a millimeter and a centimeter, we find that 1 mm is 0.1 cm; there are 10 mm in 1 cm. - These comparisons are examples of EQUALITIES, which show the relationship between 2 units that measure the same quantity. Examples of equalities between different metric units of length follow: 1 m = 100 cm 1 m = 1000 mm 1 cm = 10 mm The metric length of 1 m is the same length as 10 dm, 100 cm, or 1000 mm.
Writing Conversion Factors
Any equality can be written as fractions called conversion factors with one of the quantities in the numerator and the other quantity in the denominator. 2 conversion factors are always possible from any equality. Be sure to include the units when you write the conversion factors.
Measured numbers
Are the numbers you obtain when you measure a quantity such as your height, weight, or temperature.
Exact numbers
Are those numbers obtained by counting items or using a definition that compares 2 units in the same measuring system. Exact numbers are not measured, do not have a limited number of significant figures, and do not affect the number of significant figures in a calculated answer.
A zero is not a significant figure if it is -
At the beginning of a decimal number. Used as a placeholder in a large number without a decimal point. If a measurement is written as 500. g, the decimal point after the second zero indicates that both zeros are significant. To show this more clearly, we can write it as 5.00 X 10 to the 2 power.
Problem Solving Using Density -
Density can be used as a conversion factor. For example, if the volume and the density of a sample are known, the mass in grams of the sample can be calculated.
Rounding off
Each time you use a calculator, it is important to look at the original measurements and determine the number of significant figures that can be used for the answer. - If the first digit to be dropped is 4 or less, then it and all following digits are simply dropped from the number. - If the first digit to be dropped is 5 or greater, then the last retained digit of the number is increased by 1.
Conversion Factors from Dosage Problems -
Equalities stated within dosage problems for medications can also be written as conversion factors. Keflex (cephalexin), an antibiotic used for respiratory and ear infections, is available in 250-mg capsules. Vitamin C, an antioxidant, is available in 500-mg tablets. These dosages can be used to write equalities from which 2 conversion factors can be derived.
Significant figures
In a measured number, the significant figures (SFs) are all the digits including the estimated digit. Nonzero numbers are always counted as significant figures. However, a zero may or may not be a significant figure depending on its position in a number.
Addition and Subtraction with Measured Numbers
In addition or subtraction, the final answer is written so that it has the same number of decimal places as the measurement having the fewest decimal places.
Multiplication and division with measured numbers
In multiplication or division, the final answer is written so that it has the same number of significant figures (SFs) as the measurement with the fewest SFs. - Sometimes, a calculator display gives a small whole number. For example, suppose the calculator display is 4, but you used measurements that have 3 SFs. Then 2 significant zeros are added to give 4.00 as the correct answer.
Using 2 or More Conversion Factors -
In problem solving, 2 or more conversion factors are often needed to complete the change of units. In setting up these problems, one factor follows the other. Each factor is arranged to cancel the preceding unit until the needed unit is obtained.
Density in the Metric System -
In the metric system, the densities of solids and liquids are usually expressed as grams per cubic centimeter (g/cm3) or grams per milliliter (g/mL). The densities of gases are usually stated as grams per liter (g/L).
The International System of Units (SI), or Systeme International,
Is the official system of measurement throughout the world except for the United States. In chemistry, we use metric units and SI units for volume, length, mass, temperature, and time. TABLE 2.1 Units of Measurement and Their Abbreviations (METRIC vs. SI)
Chemistry Link to Health: Toxicology and Risk-Benefit Assessment -
Many hazardous chemicals or substances have been identified by these tests. One measure of toxicity is the LD50, or lethal dose, which is the concentration of the substance that causes death in 50% of the test animals. A dosage is typically measured in milligrams per kilogram (mg/kg) of body mass or micrograms per kilogram (mcg/kg) or body mass. Other evaluations need to be made, but it is easy to compare LD50 values. Parathion, a pesticide, with an LD50 of 3 mg/kg, would be highly toxic. This means that 3 mg of parathion per kg of body mass would be fatal to half the test animals. Table salt (sodium chloride) with an LD50 of 3300 mg/kg would have a much lower toxicity. You would need to ingest a huge amount of salt before any toxic effect would be observed. Although the risk to animals can be evaluated in the laboratory, it is more difficult to determine the impact in the environment since there is also a difference between continued exposure and a single, large dose of the substance.
Table 2.5
Metric and SI Prefixes!
A number is a significant figure it it is -
Not a zero. A zero between nonzero digits. A zero at the end of a decimal number. In the coefficient of a number written in scientific notation. The number of significant figures in measured numbers determines the number of significant figures in the calculated answer.
Figure 2.10 -
OBJECTS THAT SINK IN WATER ARE MORE DENSE THAN WATER; OBJECTS THAT FLOAT ARE LESS DENSE PICTURE!
Chemistry Link to Health: Bone Density -
Our bones' density is a measure of their health and strength. Out bones are constantly gaining and losing calcium, magnesium, and phosphate. In childhood, bones form at a faster rate than they break down. As we age, bone breakdown occurs more rapidly than new bone forms. As bone loss increases, bones begin to thin, causing a decrease in mass and density. Thinner bones lack strength, which increases the risk of fracture. Hormonal changes, disease, and certain medications can also contributes to the bone thinning. Eventually, a condition of severe bone thinning known as osteoporosis, may occur. Scanning electron micrographs (SEMs) show (a) normal bone and (b) bone with osteoporosis due to loss of bone minerals. Bone density is often determined by passing low-dose X-rays through the narrow part at the top of the femur (hip) and the spine (c). These locations are where fractures are more likely to occur, especially as we age. Bones with high density will block more of the X-rays compared to bones that are less dense. Recommendations to improve bone strength include calcium and vitamin D supplements. Weight-bearing exercise such as walking and lifting weights can also improve muscle strength, which in turn increases bone strength.
Table 2.8 -
Some LD50 for Substances Tested in Rats!
Table 2.7 -
Some common equalities!
Specific Gravity -
Specific gravity (sp gr) is a relationship between the density of a substance and the density of water. Specific gravity is calculated by dividing the density of a sample by the density of water, which is 1.00 g/mL at 4 C. A substance with a specific gravity of 1.00 has the same density as water (1.00 g/mL). Specific gravity is one of the few unitless values you will encounter in chemistry.
Table 2.9 Densities of Some Common Substances -
Table 2.9 gives the densities of some common substances!
Temperature
Temperature tells us how hot something is, tells us how cold it is outside, or helps us determine if we have a fever. In the metric system, temperature is measured using Celsius temperature. On the Celsius (C) temperature scale, water freezes at 0 C and boils at 100 C, whereas on the Fahrenheit (F) scale, water freezes at 32 F and boils at 212 F. In the SI system, temperature is measured using Kelvin (K) temperature scale on which the lowest possible temperature is 0 K. A unit on the Kelvin scale is called a kelvin (K) and is not written with a degree sign.
Table 2.4 - Daily Values (DV) for Selected Nutrients
The U.S. Food and Drug Administration (FDA) has determined the Daily Values (DV) for nutrients for adults and children age 4 or older. Exampls of these recommended Daily Values, some of which use prefixes, are listed in Table 2.4.
Volume
The amount of space a substance occupies. The metric unit for volume is the liter (L), which is slightly larger than a quart (qt). In a laboratory or a hospital, chemists work with metric units of volume that are smaller and more convenient, such as the milliliter (mL). 1 L = 1000 mL 1 L = 1.06 qt 946 mL = 1 qt
Cubic Centimeter (cm3 or cc)
The cubic centimeter is the volume of a cube whose dimensions are 1 cm on each side. A cubic centimeter has the same volume as a milliliter, and the units are often used interchangeably. 1 cm3 = 1 cc = 1 mL
Density -
The mass and volume of any object can be measured. If we compare the mass of the object to its volume, we obtain a relationship called density - Density = mass of substance/volume of substance Every substance has a unique density, which distinguishes it from other substances. For example, lead has a density of 11.3 g/mL, whereas cork has a density of 0.26 g/mL. From these densities, we can predict if these substances will sink or float in water. - If an object is less dense than a liquid, the object floats when placed in the liquid. If a substance, such as cork, is less dense than water, it will float. However, a lead object sinks because its density is greater than that of water.
Mass
The mass of an object is a measure of the quantity of material it contains. The SI unit of mass, the kilogram (kg), is used for larger masses such as body mass. In the metric system, the unit for mass is the gram (g), which is used for smaller masses. There are 1000g in 1 kg. One pound (lb) is equal to 454 g. Some relationships between units for mass are: 1 kg = 1000g 1 kg = 2.20 lb 454 g = 1 lb Scientists measure mass rather than weight because mass does not depend on gravity. In a chemistry laboratory, an electronic balance is used to measure the mass in grams of a substance.
Length
The metric and SI unit of length is the meter (m). The centimeter (cm), a smaller unit of length, is commonly used in chemistry and is about equal to the width of your little finger. Some relationships between units for length are: 1 m = 100 cm 1 m = 39.4 in. 1m = 1.09 yd 2.54 cm = 1 in.
What is the common measuring system in all but a few countries in the world?
The metric system
Specific Gravity and Urine -
The normal range of specific gravity for urine is 1.003 to 1.030. The specific gravity can decrease with type 2 diabetes and kidney disease. Increased specific gravity may occur with dehydration, kidney infection, and liver disease. In a clinic or hospital, a dipstick containing chemical pads is used to evaluate specific gravity.
Problem Solving Using Unit Conversion -
The process of problem solving in chemistry often requires one or more conversion factors to change a given unit to the needed unit. - For the problem, the unit of the given and the unit of the needed are identified. From there, the problem is set up with 1 or more conversion factors user to convert the given unit to the needed unit as seen in Sample Problem 2.8 - The unit you want is in the final answer is the one that remains after all the other units have canceled out.
Prefix
The special feature of the metric system is that a prefix can be placed in front of any unit to increase or decrease its size by some factor of 10. For example, the prefixes milli and micro are used to make the smaller units, milligrams (mg) and microgram (mcg).
Measuring Volume
Volumes of 1 L or smaller are common in the health sciences. When a liter is divided into 10 equal portions, each portion is a deciliter (dL). There are 10 dL in 1 L. Laboratory results for bloodwork are often reported in mass per deciliter. In a 1-L container of physiological saline, there are 1000 mL of solution. Exampled of equalities between different metric units of volume follow: 1 L = 10 dL 1 L = 1000 mL 1 dL = 100 mL 1 mL = 1000 mcL
Metric Conversion Factors -
We can write 2 metric conversion factors for any of the metric relationships. Both are proper conversion factors for the relationship; one is just the inverse of the other. - The usefulness of conversion factors is enhanced by the fact that we can turn a conversion factor over and use its inverse.
Time
We typically measure time in units such as years (yr), days, hours (h), minutes (min), or seconds (s). Of these, the SI and metric unit of time is the second (s). The standard now used to determine a second is an atomic clock.
Measured definitions -
When an equality consists of a metric unit and a U.S. unit, 1 of the numbers in the equality is obtained by measurement and count towards the significant figures in the answer. For example, the equality of 1 lb = 454 g is obtained by measuring the grams in exactly 1 lb. In this equality, the measured quantity 454 g has 3 significant figures, whereas the 1 is exact. An exception is the relationship of 1 in. = 2.54 cm, which has been defined as exact.
Measuring Mass
When you go to the doctor for a physical examination, your mass is recorded in kilograms, whereas the results of your laboratory tests are reported in grams, milligrams (mg), or micrograms (ug or mcg). Examples of equalities between different metric units of mass follow: 1 kg = 1000 g 1 g = 1000 mg 1 mg = 1000 mcg