1.6 Mathematical Treatment of Measurement Results

• A quality control chemist at a pharmaceutical company is tasked with checking the accuracy and precision of three different machines that are supposed to give 10 ounces of cough syrup into storage bottles.
• She uses each machine to fill five bottles and then uses the actual volume to calculate the result in Table 1.5.

• She will report that the values are close to one another, but not accurate, and that the values are more than 10 mL too low.
• The results for dispenser #2 show improved accuracy but worse precision.
• She was able to report that the dispensers are working well, both accurately and precisely, with all volumes within 0.1 mL of the target volume and differing from each other by no more than 0.2 mL.

• Sometimes a quantity of interest can't be measured directly but must be calculated from other directly measured properties and appropriate mathematical relationships.
• Consider measuring the average speed of an athlete.

• The same relation is used to predict the time required for a person to travel a distance.

• This method can be used to perform computations ranging from simple unit conversions to more complex multi-step calculations.

• The conversion factors are given in Table 1.6.

• 1 m is 1.0936 yd 1 L is 1.0567 qt.

• We convert the quantity to an equivalent value with different units when we use an appropriate unit conversion factor.
• A basketball player's jump of 34 inches can be converted to centimeters by 34 in.

• The number of the product quantity, 86, is calculated using the numbers of the two quantities.

• The ratio of identical units is the same as the number.

• To find out if a unit conversion factor has been set up correctly, we have to check to see if the original unit will cancel and the result will contain the sought unit.

• The mass in kilograms can be determined using an equation similar to the one used for converting length from inches to centimeters.

• The ratio that cancels the units of grams and ounces is the correct unit conversion factor.

• A volume of 9.345 quarts to liters.

• The factor-label method can be used to solve more complex problems.
• The method is referred to as the factor-label method.
• You will find many opportunities to apply this approach as you study chemistry.

• A sample of the substance weighs 9.26 lbs.

• We need to divide the mass in grams by the volume in liters.
• The conversion factors are given in Table 1.6.

• Two steps are needed to convert volume from quarts to liters.

• A car that is being driven from Philadelphia to Atlanta uses 213 L gasoline.

• A Toyota Prius hybrid uses 59.7 L gasoline to drive from San Francisco to Seattle, a distance of 1300 km.

• The word temperature refers to the hotness or coldness of a substance.
• The fact that most substances expand when their temperature increases is one way to measure a change in temperature.
• As the temperature changes, the volume of mercury or alcohol in the glass Thermometer changes.
• The liquid expands when it gets warmer and contracts when it gets cooler because the volume of the liquid changes more than the volume of the glass.

• The freezing and boiling temperatures of water at a specified atmospheric pressure are two of the most commonly used reference values.
• 0 degC is the freezing temperature of water and 100 degC is the boiling temperature of water.
• The space between the two temperatures is divided into 100 equal intervals.
• The space between these two points is divided into equal parts.

• Defining the Celsius and Fahrenheit temperature scales as described in the previous paragraph results in a slightly more complex relationship between temperature values on these two scales than for different units of measure for other properties.
• The measurement units are proportional to one another.
• The relationship between the Celsius and Fahrenheit temperature scales is a linear one because they don't share a common zero point.
• To convert a temperature from one scale to another requires more than just multiplication by a conversion factor, it must also take into account the differences in the scales' zero points.

• The two temperatures used to define each scale are used to derive the linear equation relating Celsius and Fahrenheit temperatures.

• The kelvin is the SI unit of temperature.
• The kelvin scale is an absolute temperature scale in which zero K corresponds to the lowest temperature that can be achieved.
• The early 19th-century discovery of the relationship between a gas's volume and temperature suggested that the volume of a gas would be zero.
• William Thompson, a British physicist, proposed an absolute temperature scale based on this concept in the 19th century.

• The boiling temperature of water on this scale is 373.15 K and the freezing temperature is 273.15 K.

• The 273.15 in these equations is not exact.
• We don't use the degree sign with the temperatures on the kelvin scale.

• The temperature scales are compared.

• Although the kelvin is the official temperature scale, Celsius is the scale of choice for nonscience contexts in almost all areas of the world.
• Only the US and its territories still use Fahrenheit for weather, medicine, and cooking.

• Although it varies depending on time of day and method of measurement, normal body temperature has been accepted as 37.0 degC.

• Baking a pizza requires an oven temperature of 450 degrees.

• 50 degF to degC and K.

• Chemistry deals with the composition, structure, and properties of matter.
• It is a central part of the study and practice of science and technology.

• Chemists use the scientific method to conduct experiments, pose hypotheses, and develop theories, so that they can better understand the behavior of the natural world.
• They operate in the symbolic domain.
• A wide variety of substances that are important to our lives are measured, analyzed, and synthesised by chemists.

• There is something that occupies space and has mass.
• The atom is the smallest unit of an element that can enter into combinations with other elements.
• atoms are combined into Molecules.
• Solids, liquids, and gases are commonly found in three states: fixed shape and volume, variable shape and volume, and variable shape and volume.
• Matter can exist under high temperature conditions.
• There are two or more types of matter that can be present in varying amounts and can be separated by physical means.
• Heterogeneous mixtures have different compositions from point to point.
• A pure substance can be an element, which consists of only one type of atom and cannot be broken down by a chemical change, or a compound, which consists of two or more types of atoms.

• Substances have different physical and chemical properties.

• Hardness and boiling point do not involve a change in the composition of matter.
• Chemical properties, such as flammability and acidity, and chemical changes, such as rusting, involve production of matter that is different from the present.

• There are two categories of measurable properties.
• The mass of gold is dependent on the amount of matter present.
• The density of gold does not affect intensive properties.
• The temperature is an example of an intensive property.

• Quantitative information is important in studying and practicing chemistry.
• There is an amount, a unit for comparison and an uncertainty in each measurement.
• Measurement can be represented in either decimal or scientific notation.
• The SI or metric systems are used by scientists.
• Base SI units such as meters, seconds, and kilograms, as well as derived units, such as liters and g/ cm3 are used.
• We find it convenient to use unit prefixes that yield fractional and multiple units, such as microseconds and megahertz.

• The essential ideas can be measured or exact.
• The number of significant figures in the measurement represent the associated uncertainty of measured quantities.
• The uncertainty of a calculated value depends on the uncertainties in the values used in the calculation and is reflected in how the value is rounded.
• The values can be close to the true value or precise.

• A variety of units are used to make the measurement.
• It is possible to convert a measured quantity from one unit to another.
• The unit conversion factors are derived from simple applications of a mathematical approach called the factor-label method.
• This strategy is used to calculate sought quantities.

• If they are symbols for a feature, indicate it.

• If you're in the symbolic domain, tell us if they're symbols for a macroscopic or a microscopic feature.

• Many of the items you purchase are pure compounds.
• Prepare a list of the ingredients that are pure compounds by selecting three of the commercial products.

• The sulfur atom and sulfur molecule are not the same.

• The astronauts in space are not without mass.

• We don't think about the chemicals we consume as we drive.
• Prepare a list of the chemicals used in an automobile.

• There is a lot of matter around us.
• A list of fifteen different kinds of matter is what you should make.
• You should include at least one example of each of the following: a solid, a liquid, a gas, an element, a compound, a heterogeneous mixture, and a pure substance.

• Red brown iron(III) oxide, also known as rust, is formed when oxygen and iron combine in the air.

• There are few and far between convincing examples of the law ofConservation of matter outside of the laboratory.

• A wonderful smell of freshly baked bread is created when the dough is cooked in an oven at 350 degrees.

• The pale yellow gas florine reacts with most substances.
• The metals burn with a bright flame.
• Nineteen grams of fluorine will react with one gram of hydrogen.

• As the temperature went up, the volume of the sample went down.

• A 2.0 liter volume of hydrogen gas combined with 1.0 liter of oxygen gas to produce 2.0 liters of water vapor.

• The following properties are either extensive or intensive.

• The density of a substance is defined as the ratio of its mass to its volume.

• Explain why density is intensive considering that mass and volume are both extensive properties.

• The name and symbol of the prefixes used with SI units should be given.

• Give the name and quantity of the symbols used with the SI base units.

• A piece of jewelry has a mass of 132.6 g. The total volume increases when the jewelry is submerged.

• Go to the Custom Blocks and then My Block.

• There are Mystery Blocks to visit.

• The quantities were reported on the labels.
• Determine the number of significant figures.

• Each answer should be reported with the correct number of significant figures.

• Take the results of the archery contest into account.

• The following sets of measurements should be classified as accurate, precise, or neither.

• The volume in two units is given on the soft drink bottle label.
• This information can be used to derive a conversion factor between English and metric units.

• The mass of cereals in two units is given on the label.
• This information can be used to find a conversion factor between English and metric units.

• Soccer is played with a ball with a diameter between 27 and 28 in.

• A woman's basketball has a maximum weight of 20 ounces and a circumference between 28.6 and 28.6 inches.

• A barrel of oil is 42 gal.

• A red blood cell has a diameter of 3 x 10-4 in.

• In many countries, gasoline is sold by the liter.

• Milk can be purchased by the liter in many countries.

• A long ton is defined as 2240 lbs.

• The men's world record long jump, 29 ft 4 1/2 in., to meters, is the greatest depth of the ocean in the state of Oregon.

• The length of a soccer field, 120 m, to feet, is indicated in each of the following.
• The Angstrom Run is held by many chemistry conferences.
• A chemist's 50-trillion Angstrom Run.
• According to the owner's manual, the gas tank of the car holds 22.3 gallons.
• The mass in kilograms and pounds of fuel in a full tank is determined by the density of gasoline.

• The instructor needs 225 g of phosphoric acid for the experiment.
• The only container that is readily available is the Erlenmeyer flask.

• A student lab assistant needs 125 g of compound to prepare for a lab period.
• A bottle is available.

• A chemistry student is 159 cm tall.

• The winner of the recent Grand Prix averaged 229.8 km/h.

• The width and length dimensions are 1.50 in.

• The mercury content of a stream was thought to be above the minimum safe amount by weight.
• The concentration was found to be 0.68 parts per billion.

• One of the densest elements is Osmium.

• The temperature of water can be converted to degrees Fahrenheit and kelvin.

• The freezer's temperature can be converted to degrees Celsius and kelvin.

• The label warns against heating the can above 130 degrees.

• The summer of 1995 was warm in Europe.
• The news reported temperatures as high as 45 degrees.

• Early diagnosis of diseases and detection of environmental exposure to harmful substances can be achieved by analyzing exhaled breath.

• It is difficult to predict the outcome of the interaction between your genetic makeup and environmental exposure.
• Detection and treatment of diseases can be done before a condition becomes serious or irreversible.
• Recent studies have shown that exhaled breath can be a good indicator of recent exposure to environmental contaminants or pathological conditions such as asthma or lung cancer.
• Scientists are working to develop a way to diagnose a disease based on the amount and identities of certain molecules in a patient's exhaled breath.
• The identity of a molecule is determined by the numbers and types of atoms it contains and how they are bond together.
• Some of the fundamental chemical principles related to the composition of matter will be described in this chapter.