Measurements in Chemistry Fundamentals of General, Organic & Biological Chemistry 4th Edition Chapter Two Measurements in Chemistry Mohammed Hashmat Ali Southeast Missouri State University 2003 Prentice Hall, Inc.

2.1 Physical Quantities Physical properties such as height, volume, and temperature that can be measured are called Physical quantity. A number and a unit of defined size is required to describe physical quantity. Prentice Hall © 2003 Chapter Two

The number alone doesn’t say much The number alone doesn’t say much. If you say an average textbook weigh 1. The question would then be asked 1 what? 1 pound? 1 kilogram? 1 ounce? You have to mention the unit of mass along with the number for your statement to be more meaningful. Prentice Hall © 2003 Chapter Two

Physical quantities can be measured in many different units Physical quantities can be measured in many different units. For example, mass of an object can be measured in pounds, kilograms, ounce, and many other units. To avoid confusion, scientists around the world have agreed to use a standard units, known as International System of Unit abbreviated as SI units, for some common physical quantities. Prentice Hall © 2003 Chapter Two

In SI Unit, mass is measured in kilogram (kg), length is measured in meters (m), volume is measured in cubic meters (m3), and time is measured in second (s). Many other widely used units are derived from these SI units. For instance, unit of speed is meters per second (m/s), unit of density is grams per cubic centimeters (g/cm3). Prentice Hall © 2003 Chapter Two

2.2 Measuring Mass Mass is a measure of amount of matter in an object. Weight is a measure of gravitational pull on an object. At the same location, two objects with identical masses have identical weights; that is gravity pull them equally. Thus mass of an object can be determined by comparing the weight of the object to the weight of a known reference standard. Prentice Hall © 2003 Chapter Two

Two types of balances used for measuring mass in the laboratory are shown below. Prentice Hall © 2003 Chapter Two

2.3 Measuring Length and Volume Meter (m) is the standard measure of length or distance in both SI and metric system. One meter is 39.37 inches. Centimeter (Cm; 1/100m) and millimeter (mm; 1/1000m) are commonly used for most measurements in chemistry and medicine. Prentice Hall © 2003 Chapter Two

Volume is the amount of space occupied by an object. - The SI unit for volume is the cubic meter (m3). Liter (L) is commonly used in chemistry as a unit of volume. 1L =0.001m3 = 1 dm3. One liter has the volume a cube 10 cm (1dm) on edge. One liter is further divided into 1000 milliliters (mL). 1 mL has the volume of a cube with 1 cm on edge. 1 milliliter is often called 1 cubic centimeter (1 mL = 1 cm3). Prentice Hall © 2003 Chapter Two

The relationship between metric units are shown in Fig 2.2 below. Prentice Hall © 2003 Chapter Two

2.4 Measurement and Significant Figures Every experimental measurement, no matter how precise, has a degree of uncertainty to it because there is a limit to the number of digits that can be determined. Prentice Hall © 2003 Chapter Two

To indicate the precision of the measurement, the value recorded should use all the digits known with certainty, plus one additional estimated digit that usually considered uncertain by plus or minus 1 or + 1. The total number of digits used to express such a measurement is called the number of significant figures. The quantity 65.07 g has four significant figures. Prentice Hall © 2003 Chapter Two

Prentice Hall © 2003 Chapter Two

25.00 m has four significant figures 2, 5, 0, and 0. Rules for determining significant figures 1. Zeroes in the middle of a number are significant. 69.08 g has four significant figures, 6, 9, 0, and 8. 2. Zeroes at the beginning of a number are not significant. 0.0089 g has two significant figure, 8 and 9. 3. Zeroes at the end of a number and after the decimal points are significant. 2.50 g has three significant figures 2, 5, and 0. 25.00 m has four significant figures 2, 5, 0, and 0. Prentice Hall © 2003 Chapter Two

4. Zeroes at the end of a number and before an implied decimal points may or may not be significant. 1500 kg may have two, three, or four significant figures. Zeroes here may be part of the measurements or for simply to locate the unwritten decimal point. Prentice Hall © 2003 Chapter Two

2.5 Scientific Notation Scientific Notation is a convenient way to write a very small or a very large number. Written as a product of a number between 1 and 10, times the number 10 raised to power. Prentice Hall © 2003 Chapter Two

Two examples of converting standard numbers to scientific notations are shown below. Prentice Hall © 2003 Chapter Two

Examples of converting scientific notations back to the standard numbers. Prentice Hall © 2003 Chapter Two

2.6 Rounding off Numbers Often calculator produces large number as a result of a calculation although the number of significant figures is good only to a fewer number than the calculator has produced – in this case the large number may be rounded off to a smaller number keeping only significant figures. Prentice Hall © 2003 Chapter Two

Rules for Rounding off Numbers: Rule 1 (For multiplication and divisions): The answer can’t have more significant figures than either of the original numbers. Prentice Hall © 2003 Chapter Two

Rule 2 (For addition and subtraction): The number can’t have more digits after the decimal point than either of the original numbers. Prentice Hall © 2003 Chapter Two

2.7 Problem Solving: Converting a Quantity from One Unit to Another Factor-Label-Method: A quantity in one unit is converted to an equivalent quantity in a different unit by using a conversion factor that expresses the relationship between units. Prentice Hall © 2003 Chapter Two

Prentice Hall © 2003 Chapter Two

When solving a problem, set up an equation so that all unwanted units cancel, leaving only the desired unit. For example, we want to find out how many kilometers are there in 26.22 mile distance. We will get the correct answer if we multiply 26.22 mi by the conversion factor km/mi. Prentice Hall © 2003 Chapter Two

2.9 Measuring Temperature Temperature, the measure of how hot or cold an object is, is commonly reported either in Fahrenheit (oF) or Celsius (oC). The SI unit of temperature is, however, is the Kelvin (K). Temperature in oK = Temperature in oC + 273.15 Temperature in oC = Temperature in oK - 273.15 Prentice Hall © 2003 Chapter Two

Freezing point of H2O Boiling point of H2O 32oF 212oF 0oC 100oC 212 – 32 = 180oF covers the same range of temperature as 100oC covers. Therefore, Celsius degree is exactly 180/100 = 1.8 times as large as Fahrenheit degree. Fig 2.4 gives a comparison of all three scales. Prentice Hall © 2003 Chapter Two

Fig 2.4 Comparison of the Fahrenheit, Celsius, and Kelvin temperature scales Prentice Hall © 2003 Chapter Two

Converting between Fahrenheit and Celsius scales is similar to converting between different units of length or volume, but is a little more complex. The following formulas can be used for the conversion: oF = (9oF/5oC x oC) + 32oF oC = 5oC/9oF x (oF – 32oF) Prentice Hall © 2003 Chapter Two

2.10 Energy and Heat Energy: Capacity to do work or supply energy. Classification of Energy: 1. Potential Energy: stored energy. Example: a coiled spring have potential energy waiting to be released. 2. Kinetic Energy: energy of motion. Example, when the spring uncoil potential energy is converted to the kinetic energy. Prentice Hall © 2003 Chapter Two

In chemical reactions, the potential energy is often converted into heat. Reaction products have less potential energy than the reactants – the products are more stable than the reactants. Stable products have very little potential energy remaining as a result have very little tendency to undergo further reaction. SI unit of energy is Joules (J) and the metric unit of energy is calorie (cal). Prentice Hall © 2003 Chapter Two

1000 cal = 1 kcal (kilocalorie) 1000 J = 1 kJ One Calorie is the amount of heat necessary to raise the temperature of 1 g of water by 1oC. 1000 cal = 1 kcal (kilocalorie) 1000 J = 1 kJ 1 cal = 4.184 J 1 kcal = 4.184 kJ Not all substances have their temperature raised to the same extent when equal amounts of heat energy is applied. Prentice Hall © 2003 Chapter Two

Unit of specific heat is cal/g .oC The amount of heat needed to raise the temperature of 1 g of a substance by 1oC is called the Specific Heat of the substance. Unit of specific heat is cal/g .oC It is possible to calculate how much heat must be added or removed to accomplish a given temperature change of a given mass of a substance. Specific Heat = Calorie Grams X o C Prentice Hall © 2003 Chapter Two

2.11 Density Density relates the mass of an object with its volume. Density is usually expressed in units as - Gram per cubic centimeter (g/cm3) for solids, and Gram per milliliter (g/mL) for liquids. Mass (g) Density = Volume (mL or cm3) Prentice Hall © 2003 Chapter Two

2. 12 Specific Gravity Specific Gravity (sp gr): density of a substance divided by the density of water at the same temperature. Specific Gravity is unitless. At normal temperature, the density of water is close to 1 g/mL. Thus, specific gravity of a substance at normal temperature is equal to the density. Density of substance (g/ml) Specific gravity = Density of water at the same temperature (g/ml) Prentice Hall © 2003 Chapter Two

The specific gravity of a liquid can be measured using an instrument called a hydrometer, which consists of a weighted bulb on the end of a calibrated glass tube, as shown in the following Fig 2.6. The depth to which the hydrometer sinks when placed in a fluid indicates the fluid’s specific gravity. Prentice Hall © 2003 Chapter Two

Chapter Summary Physical quantity, a measurable properties, is described by both a number and a unit. Mass, an amount of matter an object contains, is measured in kilograms (kg) or grams (g). Volume is measured in cubic meters (m3) or in liter (L) or milliliters (mL). Temperature is measured in Kelvin (K) in SI system and in degrees Celsius (oC) in the metric system. Prentice Hall © 2003 Chapter Two

Chapter Summary Contd. Measurement of small or large numbers are usually written in scientific notation, a product of a number between 1 and 10 and a power of 10. A measurement in one unit can be converted to another unit by multiplying by a conversion factor. Energy: the capacity to supply heat or to do work. Potential energy – stored energy. kinetic energy – energy of moving particles. Prentice Hall © 2003 Chapter Two

Chapter Summary Contd. Heat: kinetic energy of moving particles in a chemical reaction. Temperature: is a measure of how hot or cold an object is. Specific heat: amount of heat necessary to raise the temperature of 1 g of the substance by 1oC. Density: grams per milliliters for a liquid or gram per cubic centimeter for a solid. Specific gravity: density of a liquid divided by the density of water. Prentice Hall © 2003 Chapter Two

End of Chapter 2 Prentice Hall © 2003 Chapter Two