Chapter One Part II Measurements in

Chemistry

Chem101: General & Consumer Chemistry

Natural Sciences Department College of Science & Information Technology

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.

The number alone doesn’t say much. If you say an average textbook weighs 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.

u  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.

u  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.

u  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).

u  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).

2.2 Measuring Mass u  Mass is a measure of amount of matter in

an object. u  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 pulls 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.

Two types of balances used for measuring mass in the laboratory are shown below.

2.3 Measuring Length and Volume

u  Meter (m) is the standard measure of length or distance in both SI and metric system. One meter is 39.37 inches.

u  Centimeter (cm; 1/100m) and millimeter (mm; 1/1000m) are commonly used for most measurements in chemistry and medicine.

u  Volume is the amount of space occupied by an object. - The SI unit for volume is the cubic meter (m3).

u  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.

u  1 milliliter is often called 1 cubic centimeter (1 mL = 1 cm3).

The relationship between metric units are shown in Fig 2.2 below.

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.

u  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.

u  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.

Rules for determining significant figures 1.  All non-zero digits are significant.

789 g has 3 significant figures. 2.  Zeroes in the middle of a number are

significant. 69.08 g has four significant figures, 6, 9, 0, and 8.

3.  Zeroes at the beginning of a number are not significant.

0.0089 g has two significant figure, 8 and 9.

4.  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.

5.  Zeroes at the end of a number and before an implied decimal point 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.

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.

M x 10n

Two examples of converting standard numbers to scientific notations are shown below.

Examples of converting scientific notations back to the standard numbers.

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.

Rules for Rounding off Numbers: Rule 1 (For multiplication and division): The answer can’t have more significant figures than either of the original numbers.

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

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.

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.

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 K = Temperature in oC + 273.15 Temperature in oC = Temperature in K - 273.15

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.

Fig 2.4 Comparison of the Fahrenheit, Celsius, and Kelvin temperature scales

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)

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.

u  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.

u  Stable products have very little potential energy remaining as a result have very little tendency to undergo further reaction.

u  SI unit of energy is Joules (J) and the metric unit of energy is calorie (cal).

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.

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

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.

Density = Mass (g)

Volume (mL or cm3)

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)

Density of water at the same temperature (g/ml) Specific gravity =

The specific gravity of a liquid can be measured using an i n s t r u m e n t c a l l e d 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.

Chapter Summary u  Physical quantity, a measurable properties, is

described by both a number and a unit. u  Mass, an amount of matter an object contains, is

measured in kilograms (kg) or grams (g). u  Volume is measured in cubic meters (m3) or in

liter (L) or milliliters (mL). u  Temperature is measured in Kelvin (K) in SI

system and in degrees Celsius (oC) in the metric system.

Chapter Summary Contd. u  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.

u  A measurement in one unit can be converted to another unit by multiplying by a conversion factor.

u  Energy: the capacity to supply heat or to do work.

Potential energy – stored energy. kinetic energy – energy of moving particles.

Chapter Summary Contd. u  Heat: kinetic energy of moving particles in a

chemical reaction. u  Temperature: is a measure of how hot or cold an

object is. u  Specific heat: amount of heat necessary to raise

the temperature of 1 g of the substance by 1oC. u  Density: grams per milliliters for a liquid or

gram per cubic centimeter for a solid. u  Specific gravity: density of a liquid divided by

the density of water.

End of Chapter 2