Chapter 2 Notes:                                                                        Chem. Hons.

Measurement :

A measurement must always contain a quantity (number) and a unit.

Example:   1 Centimeter

               Quantity    Unit

Scientific Notation:

Chemists often work with numbers that are extremely large or extremely small. For example, there are 10,300,000,000,000,000,000,000 carbon atoms in a 1-carat diamond each of which has a mass of 0.000,000,000,000,000,000,000,020 grams. It is impossible to multiply these numbers with most calculators because they can't accept either number as it is written here. To do a calculation like this, it is necessary to express these numbers in scientific notation, as a number between 1 and 10 multiplied by 10 raised to some exponent. In scientific notation, the numbers are written in the form of Mx10ⁿ, where factor M is a number between 1 and 10 and n is a whole number.

                                                45637= 4.5637 x 10⁴

Exponent Review

Some of the basics of exponential mathematics are given below.

 

 

 

Converting to Scientific Notation

The following rule can be used to convert numbers into scientific notation: The exponent in scientific notation is equal to the number of times the decimal point must be moved to produce a number between 1 and 10. The direction of the move determines whether the power of ten is positive or negative.

           Direction of movement of decimal

                                       +  Exponent ------------------------------------ - Exponent

4312.5 --------------  4.3125 x10³ ( exponent of 10 is positive, because decimal point had to be moved to left to get a number between 1 and 10)

0.000312 -----------  3.12 x 10^-4  (exponent of 10 is negative, because the decimal point had to be moved to right to get a number between 1 and 10)

Do problem number 6 on page 57, Section Review.

a.

b.

c.

Converting Scientific Notation in Usual Long Form Number

To write out a number in the usual long form that is given in Scientific Notation, the above procedure is reversed.

Change the following to the long form:

7x10⁴=

2.31x10^-7=

Mathematics involving Scientific Notation:

1.       Addition and Subtraction: To perform these operations, the exponents have to be the same. If they are not then the adjustments need to be made to make them equal. The coefficients then may be added or substracted.

(Look at he example given on page 51in your text book)

2.       Multiplication: The M factors are multiplied , and the exponents are then added.

3.       Division: The M factors are divided and the exponent of the denominator is subtracted from that of the numerator.

(Look at page 52 in your book.)

Do problem 4 in the section review on page 57.

a.

b.

c.

SI Measurement:

Scientists all over the world have agreed upon this system of measurement .

Two other most widely used systems of measurement are ‘English System’ (used in U.S.A.) and ‘Metric System’ ( which  is the forerunner of the SI system.)

SI Base Units:

Refer to page 34 in textbook.

Derived SI Units:

The units of every measurement in the SI system must be derived from one or more of the seven base units.

Refer to page 36 table 2-3 in your textbook.

Mass Versus Weight

Mass is a measure of the amount of matter in an object, so the mass of an object is constant.

Weight is a measure of the force of attraction of the earth acting on an object. The weight of an object is not constant.

Unlike weight mass does not depend on force of attraction of earth (gravitational pull)

Density:

Density of a material is mass divided by volume or mass per unit volume.

Density= Mass/volume

D=M/V

Units: Kg/m³ or g/cm³

Density of a substance does not depend on its size.

Density of a substance varies with the temperature. Why?

Sample Problem on Density:

What is the density of a block of marble with a mass of 552 g and a volume of 212 cm³?

                Density= Mass/Volume,    Density= 552g/212cm ³    = 2.60 g/cm³

Do problems 5a and 5b on page 42, section review.

5a.

5b.

Problem Solving and Dimensional Analysis( Factor Label Method)

Changing from one unit to another via a conversion factor is called ‘ dimensional analysis’ or ‘ factor label method’.

A conversion factor is the ratio derived from the equality between two different units that can be used to convert one unit into another. Ex. To convert the dollars into quarters the conversion factor could be:

4 Quarters/1 dollar

When a conversion factor is used to change one unit into another, the problem can be set up like this:

Quantity sought= Quantity given x Conversion factor

Steps Used in Dimensional Analysis:

Example:

An Italian Bicycle has its frame size written as 62 cm. What is the frame size in inches?

62 cm x conversion factor= ? in

62 cm         1 in            = 24 in

                   2.54 cm   

Do problem 3 on page 42 in section review.

#3. a.

b.

f.

Accuracy and Precision

Refer to page 44 in the textbook.

Percent Error

Refer to book on page 45.

Uncertainty in Measurement

Refer to page 46 in the book.

Significant Figures

In a measurement all certain numbers plus the first uncertain number are called as ‘Significant Figures’.

Rules for counting Significant Figures:

1.        Nonzero integers. Nonzero integers always count as significant figures. For Example. The number 2345 has four nonzero integers ,all of which count as significant figures.

2.        Zeros: There are three classes of zeros:                                                                                                                           a. Leading zeros are zeros that precede all of the nonzero digits. They never count as significant figures. Ex. 0.0025 has only 2 significant figures.

b. Captive zeros are zeros that fall between nonzero digits. They always count as significant figures. Ex. 1.008 has four significant figures.

c. Trailing zeros are the zeros at the right end of the number. They are significant only if the number has a decimal point. Ex. 100 has one significant figure and 100. has three.

3.        Exact number. Often calculations involve numbers that were not obtained using measuring device but were determined by counting. Such as 3 apples, 8 molecules . Such numbers are called as exact numbers. They can be assumed as having an unlimited number of significant figures.

Practice Problems

Do #1a, 1c , 1f and #2 on page 48.

1a.

1b.

1c

2a.

2b.

2c.

Rules for rounding off numbers

When the answer to a calculation contains too many significant figures, it must be rounded off.

In a series of calculations, carry the extra digits through to the final result and then round off.

For the rules regarding rounding off refer to page 48 in your textbook.

Addition and Subtraction with significant figures:

When measurements are added or subtracted, the answer can contain no more decimal places than the least accurate measurement.

Multiplication and Division with significant figures

When measurements are multiplied or divided, the answer can contain no more significant figures than the least accurate measurement.

Density = Mass/Volume  = 3.05 g/8.47 ml=0.360094451 g/ml

Answer in Sig Fig is 0.360 g/ml

Do practice problems 1,2 and 3 given on page 50 of your book.

#1.

#2.

#3.